CA1219329A - Method of seismic processing involving converted p- or s-wave data - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE

METHOD OF SEISMIC PROCESSING
INVOLVING CONVERTED P- OR S-WAVE DATA

This invention relates to a method of increasing resolution of high-intensity amplitude events in seismic records provided by common midpoint collection methods (CMP) wherein nonsymmetrical travel paths of incident and reflected rays of the generated conventional waves are taken into account prior to trace stacking irrespective of dip or depth of the target reflector. In accordance with the invention, the converted phases of the conventional seismic wave, are processed as to define a series of common reflection point (CRP) coordinates each associated with a gather of converted traces as if a source associated with a given corrected trace was placed at each CRP
and activated followed immediately by the relocation of a detec-tor at the CRP and the reception of converted phases of the generated wave comprising the trace.
Aspects of the invention interrelate properties of simultaneously collected conventional to converted traces (via a series of multicomponent detectors positioned along the line of survey) to improve the processing of the latter traces.

Description

~_2~g3~9 METHOD OF SEISMIC PROCESSING
INVOLVING CONVERTED P- OR S-WAVE DATA

SCOPE OF THE INVENTION
-The present invention relates to geophysical exploration and more particularly to the simultaneous collection of conventional and converted P- or S-wave.
data, followed by processing oE resultant traces wherein non-symmetrical path lengths of the incident primary waves and the reflected converted waves are accounted for prior to trace stacking to transform a resulting finite offset section to a true zero offset section irrespective of reflector depth or dip. Use of multicomponent receivers for collection purposes, is contemplated.
~ACKGROUND OF T~E INVENTI~N

Traditional collection and processing of seismic reflection data begins with the separate generation of conventional pressure waves (P-waves) or shear waves (S-waves) followed by their separate recording on single co~ponent receivers, i.e. receivers that have active ele-ments that respond to motions of the reflected waves in only one direction. Assuming a vertically oriented seis-mic source, conventional P-waves travel down into the earth and are reflected from one (or more) geologic layers as P-waves. A spread of receivers whose active elements respond to vertically oriented elastic wave motion only, record the P-waves. Similarly, for shear wave explora-tion, S-waves produced by a horizontally oriented seismic source, are reflected from similar reflectors as S-waves, and ars recorded by the spread of receivers in similar fashion except that the active elements of the receivers would respond to horizontally oriented wave motion exclu-Sively Processing of either P-wave and/or S-wave data is further co~plicated by the fact that collection is usually carried out using common midpoint (CMP) "roll-along" methods. Such methods utilize overlapping spreads of receivers in combination with "forward rolled" sources ~2~3~29 along a line of survey to generate substantial numbers of"redundant" seismic traces. That is, the latter are 05 redundant in that a certain number of traces can be asso-ciated with the same common center point lying midway between a plurality of respective source-receiver pairs that generated the traces in the first place. After application of time shifts to such traces (called static and dynamic corrections), a common midpoint (CMP) gather is created. Thereafter, the associated traces of that gather are stacked, to provide improved signal-to-noise characteristics.
(In regard to the importance of undarstanding the relationship between collection coordinates wherein traces are identified by either source-positions (s) and receiver-locations ~g) coordinates along the line of sur-vey, or by coordinates associated with source-to-rece ver stations offset distance (f), and midpoint location (y) between respective source and receiver pairs, see, in detail, John F. Claerbout's book "FUND~MENTALS ~F
GEOPHYSICAL DA~A PROCESSING", McGraw-Hill, 1976 at pages 228 et seq.) Even though the stacked gather of traces are 2S enhanced (because of stacking), interpretations can still made difficult due to the fact that at boundaries between different rock types, partial conversion occurs between one wave type and another, assuming the angle of the inci-dent wave is greater than zero. For example, a P-incident wave can be partially converted to an ~v-refle~ted wave.
or an Sv-incident wave can be partially converted to a P-wave reflected signal.
While the Zoeppritz equa~ions determine the amplitudes of the reflected and converted waves, they have been seldom used by interpreters of geophysical data in spite of the fact that modern seismic reflection collec-tion methods such as CMP methods, use long offsets and involve significant angle of incidence. Reason-: for deeper reflectors, the angles of incident are relatively low and the velocity and density contrasts between layers 121~3Z9 ( 01 ~3~
are assumed tO be small. See for example, page 21 et seq of Kenneth H. Waters' book "A TOOL FOR ENERGY ~ESOURCE
05 EXPLORATION", John Wiley and Sons, 1978 for further edification.
In addition, the complexity involved in applying such equations to the many different energy levels asso-ciated with the various reflected waves for all angles of incidence and various material contrasts that exit in the field, can generate so much data as to simply overwhelm the interpreter. ~e may find it too difficult to apply the Zoeppritz equations on a systematic basis especially where the field data is collected by modern CMP methods.
In this regard, even though center points/reflection points may not be vertically aligned, the interpreter usually ignores that fact, viz., ignores the differences in converted P-wave to Sv-wave path lengths about vertical projections through centér points midway between respec-tive source-receiver pairs.
That is to say, with conventional incident and reflected waves, reflection points of flat, horizontal reflectors are located directly below the vertical projec-tions of the midpoints of respective source-receiver pairs associated with the traces of interest. Thus, traces associated with common reflection points (or depth points on flat reflectors, although from different source-receiver pairs can be summed ~stacked), after appropriate corrections to align the traces. But with con~erted waves under the same circumstances, the reflection points are not located below projections from the midpoin.s of respective source-receiver pairs but instead are displaced a certain distance from those projections.
The closest prior art that I am aware of that describes the ~roblem of non-symmetrical path lengths ls found in "DIGITAL ~ROCESSING OF T~ANSFORI~ED REFLECTED
WAVES", SOVIET GEOLOGY AND GEOPHYSICS, V. 21, NO. 4, pp. 51-59.

~Z1~33~9 T. T. Nefedkina et al there describe use of P-wave to Sv-converted waves in permafrost regions of ~S Siberia and like regions. A stacking procedure for such converted waves teaches the advantage of varying the stackin~ point of the gathers in accordance with a series of normalizing values associated with a special Soviet digital processing code called "Kondakova's alpha-lan-guage". But since the procedure uses exotic processingterminology, inferior data sets, and simplistic models, conventional use of their work in the context of modern exploration methods especially where dipping reflectors are contemplated, has not been possible.
UMMARY OF TEIE INVENTION
In accordance with the present invention, non-symmetrical path lengths of primary incident waves and reflected converted waves, irrespective of whether or not the incident wave is a P-wave or an Sv-wave, is accounted for, so that converted Sv- or P-wave traces can be correctly collected into gathers where the traces associ-ated with each gather sample essentially the same reflec-tion point on a common target reflector. That is, the converted Sv- or P-wave traces can be identified in terms of common reflection points (CRP) coordinates tha~ have been correctly transformed from source-point (SP) and detects station (~) coordinates so as to account for the non-symmetrical path lengths of the incident and converted waves.
The pre~ent invention is based in part on the fact that the non-symmetrical path lengths are a function of source type, the ratio of P-wave to S-wave velocities, i.e., Vp/Vs ratio of the overburden above the target reflector, as well as the dip angle and the depth of that reflector. In order to relate the aforementioned vari-ables, the present invention contemplates simultaneous collection of conventional and converted P- or S-wave data in the field utilizing conventional common midpoint (~MP) coliection methods. Such techniques involve sequential activation of a conventional seismic source located at a ~X~33~:9 01 ~5~
series of sourcepoint locations (SP) along a line of survey and redundantly collecting reflections of both the 05 conventional waves and converted phases thereof via a series of multicomponent ~etectcrs. Such detectors are positioned alo~g the line of survey at a plur~lity of detector stations (~). As a result, each conventional and converted trace can be associated with a sourcepoint-detector station pair of known (S~ vs. D) coord-nate loca-tion. Next, the conventional traces undergo coordinate transformation and enhancement so as to account (a) for different travel paths of the conventional wave in the overburden above the target reflector, and (b) for depth and dip of each target reflector. After the depth and dip of the target reflector have thus been deter~ined, the invention adjusts the slope of imaginary straight gather lines on an (SP vs. D) coordinate stacking chart that identifies common converted traces. Such adjustmant takes into account the differences in path length and incident and reflection angles for the incident and reflected waves, as well as dip and depth of the target reflectors.
Stacking of the reordered traces then occurs to form a true zero offset section of converted traces.
For flat reflectors, the common reflection point (CRP) coordinates for a gather of conventional traces pro-jected to a horizontal datum plane, relate to the source-point (SP) and detector station (D) coordinates in accordance with CRP = (D+SP)/2.
The above transformation can be thought of as a process for determining the coordinates of a reflection point on the target that have been projected to the datum plane via multiplying a constant (k) that also takes into account the velocity ratio (of the incident and reflected ~aves in the overburden) times the (SP) and (D) coordi-nates of respective common source-receiver pairs making up the trace gather, in accordance with an equation of trans-formation of the form:
CRP = k3 + (l-k)SP, where k is equal to .5.

lZ~329 In accordance with the present invention, thecommon reflection point (CRP) coordinates for a gather of oS converted traces can be similarly related to the source-point (SP) and detector station (D) coordinates, say, in accordance with similar equations of transformation of the form:
Conversion P-Sv : CRP = kD + (l-k)SP
Conversion Sv-P : CRP - (l-k)D + kSP
where SP and D are source and detector coordinates, respectively; and k is a constant that takes into account the velocity ratio of the overburden (Vp/Vs), the dip angle a and depth (h) of the target reflector and the source-receiver offset distance X. Vp and Vs are the P-wave and Sv wave velocities, respectively, of the over-burden.
An approximate formula for k which include aIl these effects, i5:

k = (Vp/Vs) ~Vp/V5) + {1 + (X/h)sin ~}(l+f) 1/2 where f = P S ]+(x/h~2 cos2 Vp, Vs relate to the velocity ratio of the over-burden; the dp angle (a) and tne depth (h) as well as the source-to-receiver offset X are as defined above. This formula has been found to be accurata for dips up to a = 30, and offsets as large as since the reflector depth, viz., 2h, and is also applicable to conventional P-P waves if (Vp/Vs) is unity.
For many offset applications (where offset X is ~uch less than depth h and the dip a is ~ero), k is approximated by the simpler expression:

1;21~3329 k _ ~ p/Vs) (Vp/Vs) ~ 1 For this case with flat target reflectors below an over-burden of Vp/Vs = 2.4, k evaluation via the above equa-tions reduces to P-Sv : CRP = .73 D + .27 SP
Sv-P : CRP = .27 D + . 73 SP
DEFINITIO~S
In the present inver.tion, certain key terms related to collecting and processing multipoint seis~ic data will be used as defined below.
~ ssume that each CMP collected trace is described by the function W (SP,D) and that the source position coordinate (SP) and receiver location coordinate (D) are the independent variables.
In reality, the source position (SP) and receiver location (D) are not distributed in a continuum along the line (or axis) of survey defined by x-coordi-nates but are usually close enough together that it is merely a matter of interpolation to find W for any (SP) and (D) coordinates. Also, along the x-axis are the source-to-receiver distance offset coordinates ~f) and common midpoint location coordinates (CMP's) that are orthogonal to each other but intersect the (SP,D) plane at a given angle depending on field collection parameters.
If the incremental "roll" distance i.s ~SP=~D, then the angle of intersection is 45 degrees and the offset and midpoint coordinates relate to the source and receiver coordinates in accordance with f = D - SP
CMP = (D + SP)/2.

' ~

3~
-7a-Various aspects of this invention are as follows:
In a method of improving resolution of seismic data collected by conventional common midpoint collection (CMP) methods including sequentially activating a conven-tional seismic source at a series of sourcepoint location.s (SP) along a line of survey and redundantly collecting reflections of both the conventional waves and the con-verted phases thereof via a series of multicomponent detectors at a plurality of detector stations (D) along said line of survey, wherein each resulting convention and converted traces is associated with a sourcepoint-detector station pair of known (SP,D) coordinates, the i~provement thereof related to processing both conventional and con-verted traces in a systematic manner whereby resulting conventional and converted gathers of such traces each samples a reflection point of a target reflector in the subsurface common to each gather irrespective of dip and depth of said target reflector, comprising the steps of (i) generating seismic field records including at least separate conventional and converted seismic records, by positioning and employing an array of source and multi-component detector~ such that individual sourcepoint-detector station coordinates can be redundantly associated with a selected number of conventional and converted traces of said records, said converted and conventional traces beinq the simultaneous output of said detectors, (ii) establishing for said conventional and con-verted traces a series of separate common reflection points (CRP's), each CRP being for gathering traces com~on thereto as if a source associated with a given trace of a common gather was placed at said each CRP and activated followed immediately by the relocation of a detector at said each CRP and the reception of conventional or con-verted wa~es comprising said conventional or converted~race;

-7b-(iii) each CRP associated with said common gather of conventional traces being made to account for different travel paths of the wave due to depth and dip of each target reflector;
~iv) each CRP associated with said common gather of converted traces undergoing dynamic sourcepoint-detector station coordinate transformation to account Eor nonsy~-metrical travel paths of incident and reflected ray, dip as well as depth of said target reflectors, wherein the equation of coordinate transfor~ation is selected fro~ the group comprising:

CRP = kD + (l-k)SP : for conversions of P-waves to Sv-waves at said target;
CRP = tl-k)D ~ kSP : for conversions of Sv-waves to P-waves at said target;

( Vp/V5 ) k =
[(Vp/Vs) + {l + (X/h)sin ~}(l+f) l/2];

where [(Vp/Vs) - 1] 2 [ ( Vp/VS ) ~ 1 ]

Vp and Vs are the P-wave and Sv-wave velocities, respectively, of the overburden;
X is the source-receiver offset distance;
h is the depth of the target reflector;
is the dip angle of the target reflector; and SP and D are source and detector coordinates, respec-tively, along the line of survey.

~. -~2~332g -7c-~ method of improving resolution of seismic data collected by conventional common midpoint collection (CMP) methods including sequentially activating a conventional seismic source at a series of sourcepoint locations (SP) along a line of survey and redundantly collecting reflec-tions of both the conventional waves and the converted phases thereof via a series of multicomponent detectors at a plurality of detector stations (D) along said line of survey, whereby resulting conventional and converted gathers of such traces each systematically samples a reflection point of a target reflector in the subsurface common to each gather irrespective of dip and depth of said target reflector, comprising the steps of (i) generating seismic field records including at least separate conventional and converted seismic records, by positioning and employing an array of source and multi-component detectors such that individual sourcepoint-detector station (SP,D) coordinates can be redundantly associated with a selected number conventional and con-verted traces of said records, said converted and conven-tional traces being the simultaneous output of said detectors, (ii) separately establishing for said conventional and converted traces a series of common reflection point (CRP) coordinates each associated with a gather of traces as if a source associated with a given trace was placed at said each CRP and activated followed immediately by the relocation of a detector at said each CRP and the recep-tion of conventional or converted waves comprising said conventional or converted trace, (iii) each CRP associated with conventional traces being made to account for different travel paths of the wave, due to depth and dip of each target reflector;
(iv) each CRP associated with converted traces undergoing at least dynamic sourcepoint-detector station coordinate transformation to account for nonsymmetrical -7d-travel paths of incident and reflected ray, dip as well as depth of said target reflectors, using an equation of coordlnate transformation selected from the group comprlsing:

5 CRP = kD ~ k)SP : for conversions of P-waves to Sv-waves at the target CRP = (l-k)D + kSP : for conversions of Sv-waves to P-waves at the target;
( Vp/Vs ) k =
[(Vp/Vs) + {l ~ (X/h)sin ~}(I+f)-l/2];

where [(Vp/Vs) l1 ~X/h)2 cos2 ~;
[(Vp/VS) + I]

Vp and Vs are the P-wave and Sv-wave velocities, respectively, of the overburden;
X is the source-receiver offset distance;
h is the depth of the target reflector;
is the dip angle of the target reflector; and SP and D are source and detector coordinates, respec-tively, along the line of survey.
In a method of increasing resolution of ampli-tude events in seismic records provided by CMP collection methods involving generating conventional waves by a con-ventional seismic source at a series of sourcepoint loca-tions (s), and redundantly.collecting converted phases ofsaid conventional waves as converted traces at a series of detectors positioned at known detector locations (d) along a line of survey, the improvement thereof related to pro-cessing said converted traces in an efficient manner whereby nonsymmetrical travel paths of incident and reflected rays of said generated conventional waves are ~2~'133Z5~
-7e-taken into account prior to trace stacking, comprising (i) sequentially activating said conventional source at said series of sourcepoint locations;
(ii) reducdantly collecting at least converted phases of said conventional waves at said known detector stations (d) via said series of detectors so as to provide a series of converted traces each associated with a source-detector pair of known sourcepoint-detector station coordinate locations (s,d);
10(iii) processing said converted traces as to define a series of common reflection point (CRP's) coordinates each associated with a gather of converted traces as if a source associated with a siven trace was placed at said each CRP and activated followed immediately by the reloca-tion of a detector at said each CRP and the reception of converted phases of said generated wave comprising said trace, said each CRP undergoing at least dynamic source-point-detector station coordinate transformation to account for nonsymmetrical travel paths of incident and reflected rays, dip as well as depth of the target reflec-tor wherein the equation of coordinate transformation is selected from the group comprising:

CRP = kd + (l-k)s : for conversions of P-waves to Sv-waves at said target;
25 CRP = (l-k) + ks : for conversions of Sv-waves to P-waves at said target;

where k =(Vp/Vs) 30 k = [(Vp/Vs) + {1 + (X/h)sin }(l+f)] 1/2;

( Vp/Vs ) + 1 2 f =+ (X/h) cos2~;
( Vp/Vs ) `:

~LX~L~33~9 -7f-Vp and Vs are the P-wave and Sv-wave velocities, respectively, of the overburden;
X is the source-receiver offset distance;
h is the depth of the target reflector;
~ is the dip angle of the target reflector; and s and d are source and detector coordinates, respec-tively, along the line of survey.
A method of increasing resolution of amplitude events in .seismic records provided by CMP collection methods involving generating conventional waves by a con-ventional seismic source at a series of sourcepoint loca-tions (s), and redundantly collecting converted phases of said conventional waves as converted traces at a series of detectors positioned at known detector locations ~d) along a line of survey, whereby nonsymmetrical travel paths of incident and reflected rays of said genera~ed conventional waves are taken into account prior to trace stacking, comprising:
(i) sequentially activating said conventional source at said series of sourcepoint locations;
~ ii) redundantly collecting at least converted phases of said conventional waves at said known detector stations (d) via said series of detectors so as to provide a series of converted traces each associated with a source-detector pair of known sourcepoint-detector .station coordinate (s,d) locations;
(iii) e~tablishing for each of said converted traces common reflection point (CRP's) coordinates whereby a gather of converted traces can be likewise associated there~ith, as if a source indexed to a given converted trace was placed at said CRP and activated followed imme-diately by the relocation of a detector at said CRP and the reception of converted phases of said generated wave comprising said trace, said each CR~ undergoing at least dynamic sourcepoint-detector station coordinate trans-~Z~329 -7g-~ormation to account for nonsymmetrical travel paths of incident and reflected rays, dip as well as depth of the target reflector wherein the equation of coordinate trans-formation is selected from the group comprising:

CRP = kd ~ k)s : for conversions of P-waves to Sv-waves at said target;
CRP = (l-k) + ks : for conversions of Sv-waves to P-waves at said target;

where 1 o (Vp/Vs) k = ~(Vp/Vs) ~ {1 + (X/h)sin ~}(llf)] 1/2;

(Vp/Vs) + I + (X/h)2cos2a;
( vpivS ) Vp and Vs are the P-wave and Sv-wave velocities, respectively, of the overburden;
X is the source-receiver offset distance;
h is the depth of the target reflector;
a is the dip ansle of the target reflector; and s and d are source and detector coordinates, respec-tively, along the line of survey.

B~IEF DESCRIPTION_OF THE DRAWINGS
FIG. 1 is a plan view of a common midpoint (CMP) collection system illustrating how CMP data is conven-tionally collected in the field using, say, a line of detectors Dl..O.Dm in association with sources at source-points SPl...SPn wherein source activation at SPl permits data to be recorded at detectors Dl.. Dm and wherein source activation at SP2 allows data to be recorded at 05 positions D2...0m+1;
FIGS. 2A-2D are vertical sections of an earth formation that has undergone surveying via the CMP collec-tion system of FIG. 1 and illustrates in detail how con-ventional reflections are recorded for a source as well as illustrates the fact that without mode conversion at t~e reflector of interest, the path lengths of the incident and reflected wave are sy~metrical a~out associated reflection points on a flat reflector so that traces asso-ciated with common midpoint centerpoints between respec-tive source position-receiver locations are coincident, irrespective of whether or not the generated source wave is (i) a P-wave ~FIG. 2A), (ii) an Sh-wave (FIG. 2B), or (iii) an Sv-wave (FIG. 2C), provided the associated receiver has a corresponding component response capability (FIG. 2D);
FIGS. 3 and 4 are vertical sections of an earth formation that has undergone surveying via the CMP collec-tion system of FIG. 1 and illustrates in detail the change in reflection point location as a function of the initial elastic wave propagation mode (viz., whether it is a P-wave or Sv-wave) where target dip equals 0, and depth, detector station coordinates Dl... ~n, and sourcepoint location coordinates SP1, remain constant;
~IGS. 5 and 6 are sections of an earth formation illustrating in detail that traces associated with a common midpoint sather are coincident (or non-coincident) with an associated common depth point on a flat reflector, depending upon the fact whether or not wave conversion has (or has not) occurred;
FIG. 7 is a stacking chart wherein source-receiver coordinates associated with traces produced by CMP collection steps, are superimposed upon a common mid-point v. offset coordinate system to better illustrated processes associated with the method of the present invention;

121~3Z9 01 ` --9--FIGS. 8-11 are sections of an earth formation illustrating in detail ray trace modeling techniques used 05 in accordance with the present invention to determine the degree of change of reflection points along flat reflec-tions (FIG. 8) and along dipping reflectors (FIGS. 9-11) as a function of offset, as elastic wave conversion occurs;
FIG. 12 illustrates a process for carrying the method of the present invention using a properly pro-grammed digital computer wherein converted traces can he gathered along proper gather lines to account for nonsy~-metrical travel paths of incident and reflected rays using a selected equation of coordinate transfor~ation;
FIG. 13 is an enlarged detail of the stacking chart of FIG. 7 wherein common reflection point (CRP) lines along which converted traces can be gathered are established by a selected equation of coordinate transfor-mation;
FIGS. 14 and 15 are flow diagrams of processingsimultaneously collected conventional and converted traces for carrying out the method of the present invention;
FIGS. 16-1~ are seismic sections and portions of sections illustrating the diagnostic capability of the method of the present invention in resolving complex structures in actual field examples;
FIGS. 19 and 20 are plots of stacking Vp, Vs velocities, as well as their geometric means as a function of shot point location, of separate events in the seismic sections of FIGS. 16-18.
PREFERRED EM~DIMENTS OF THE INVENTION
Before discussion of emhodiments of the present invention, a brief description of concepts behind it may prove beneficial and are presented below.
For conventional ganerated ar.d received seismic waves, such as P-wave source generating P--~aves recorded on vertically oriented receiversl the common reflection points (CRP's) for flat reflectors are ver~ical projec-tions of the common midpoints between respective 12~3329 source-receiver pairs associated with the recorded traces.
Such assumption are valid in exploration areas of limited 05 structure or dip and allows the explorationist to gather seismic data conveniently and efficiently. For converted waves, however, the angles of incidence and reflection at subsurface reflectors are unequal. Result: the reflec-tion point is not vertical projections of the midpoints between the source-receiver pair.
FIG. 1 is a plan view of a seismic collection system illustrating how terms of interest in thls applica-tion are derived.
For example, the terms "centerpoint" and "mid-point" are a geographical location midway between a sourcecoordinate, say, source position SPI of a series of source positions SPl...SP4 of a collection field sy~tem 10 and a series of receiver positions, say Dl of a series of receiver positions Dl...Dm at a datum horizon near the earth's surface coincident with line of survey 11. The centerpoints are designated Cl...C4, and each centerpoint is seen to be addressably associated with a selected source-detector pair that produced a given trace.
In common midpoint (CMP) collection, different sets of detector spreads are "rolle~" forward in the direction of arrow 12 in associated with the like, incre-mental forward positioning of a source at new positions along the line of survey 13. Energization at the series of positions then occurs in sequence. That is the source is excited in sequence at the source positions Sp2...Sp4.
Results: traces recorded at the different receiver loca-tions can be related to selected midpoints within the surveyed subsurface. For example, if the reflec~ing interface is a flat horizon, the reflection point where reflection occurs will define vertical lines which pass through the centerpoints Cl...C4 of interest.
Applying static and dynamic corrections to a field trace is equivalent ~under the above facts) to plac-ing the source at the centerpoint, activating that source, followed by replacement with a detector at the same 121~33Z9 location and recording the trace. If all traces associated with a common midpoint are reformatted on a 05 side-by-side basis, the resulting set of traces is termed a CMP gather. If the traces are summed, the resulting trace is a stacked CMP gather. Thus, there are at least two features of conventional CMP processing needed for seismic interpretation:
(i) by summing traces associated with a common sub-surface point, the signal-to-noise ratio (SNR) of the reflections on the resulting stacked gather is improved;
(ii) projections of subsurface reflection points intersect the midpoints o~ (SP,D) source-detector pairs of known coordinate locations; hence, location of structural reflections are known if the incident and reflected path lengths are substantially equal;
FIGS. 2a-2c illustrate reflection phenomena of a three-layer model typical of young, shallow geologic sec-tion 20 consisting o~ a sandstone 21 between layers 22 and 23 as found in the Gulf Coast, illustrating that even if separate P-wave, Sh-wave or Sv-wave energy sources 28, 29 or 30 are located at source positions SPI, SP2, SP3 in FIGS. 2a, 2b and 2c respectively, and then excited, the incident and reflected path lengths of the energy associa-ted with each source-receiver pair will be substantially equal. This assumes that the receivers 31, 32, 33 at receiver positions D1, D2, D3 are set up to receive only the dominant energy of the generated wave. Vertical pro-jections 34, 35, 36 of the common conventional reflection points CMPl, CMP2 or C~P3 intersect ~he centerpoints (mid-points) C1, C2, C3 of the respective source position-receiver position pair coordinates, as shown.
In this regard, the term "conventional" is used to describe received energy at the receivers 31, 32, 33 in which the dominant particle motion matches that of the generated wave, whether the source generates P-wave, Sh-wave or ~v-wave energy in its principle mode of activation.

In FIG. 2a note that the source 2~ at source location point Spl produces an incident wave that travels 05 outwardly from that source location as a series of wave fronts. Each wave front defines a common spherical sur-face that joins points in the subsurface where motion is about to start. If the propagating madium has properties independent of position and direction of travel, the wave fronts form a set of concentric spheres centered at the source location. It is convenient .o "track" such fronts using ray-tracing methods conventional in the art in which the energy of the fronts is conceived at traveling down into the earth along a large number of pyramids of infinitesimal cross-section; and the center line of any one such pyramid in a selected direction being regarded as a ray that traces paths 37, 38, 39. These paths pass through strata 21, 22 of the geologic section 20.
Note that at reflector 23, the angle of inci-dence of the incident wave is equal to the angle ofreflection of the reflecting wave. Hence, incremental path length of the incident and reflecting wave in the overburden, i.e., in the strata 21, 22, are equal.
P-wave source 28 of FIG. 2a is typically a

2~ buried dynamite charge or a vibrator mounted on trucks which vibrate vertically on the ground surface. ~ost com~on shear sources (S-wave of FIGS. 2b, 2c) are a vibrator which shakes the ground sideways instead of up and down. In FIG. 2b, the Sh vibrator 29 shakes horizon-tally at right angles to the direction of the CMP collec-tion arrow 12. If the vibrator is rotated horizontally 90 so that the motion is along the direction of arrow 12, as in FIG. 2c, the source 30 is called Sv-type shear motion. There is another difference between Sh- and Sv-wave energy.
In FIGS. 2a, 2b, and 2c, note also in strata 21, that the direction of particle motion of the incident and reflected energy, as shown via pairs of arrows 40a, 40b;
41a, 41b; and 42a, 42b, may (or may not) change as reflec-tion from reflecting strata 23, occurs. In FIG. 2a, for - 12~329 example, the arrow 40a associated with the incident waveis directed downward along the path 37; while the oS reflected wave associated with arrow 40b is directly upwardly. Similarly, in FI~,. 2c, the arrow 42a associated with the incident wave is directed upward and away from the path 39 (at right angles thereto); while the reflected wave is directed in downwardly relative to the ray path;
On the other hand, in FIG. 2b, the arrow 41a of the inci-dent wave defines particle motions that is perpendicular to the plane of the FIG. Since the particle motion is parallel to the reflecting surface, Sh-waves suffer no mode conversion on reflection or refraction from the target reflector. That is to say, Sh source 29 would generate rays of energy which upon reflection off flat beds, would produce only Sh waves, which, when recorded by receiver 32, would require only that the receiver 32 be oriented at right angles to the collection survey arrow 12.
On the other hand, P-waves and Sv-waves incident on a reflector produce not only like-type, conventional waves, but also generate converted waves. When both wave types arrive at the surface, Sv reflections are recorded on the radial horizontal motion segment o~ the receivers -31, 33 whereas the P-waves are recorded mainly on the vertical response segment of the detectors.
FIG. 2d illustrates how the dominant response directions o~ the receivers 31, 32 and 33, can be ~atched to respond to the particle motion of the upcomins P- or S-wave energy.
As shown, if the response direction of the receivers 31, 32, 33 is vertical with respect to the earth's gravitational field, say along arrow 43, then any upcoming P-wave energy would be detected; if the receiver response is horizontal in the direction of arrow 44, then any upcoming Sh energy would be detected; similarly, i~
the response direction is horizontal in the direc~ion of arrow 45, any Sv upcoming energy will be likewise detected.

~Z~329 ~1 -14-FIGS. 3 and 4 illustrate that the reflectionpoint of a flat reflector tfor conventional waves), is not 05 a vertical projection of the midpoint between respective source-receiver pairs.
In FIG. 3, source 49 at sourcepoint SPl produces an Sv-wave whose wave fronts that trace out incident ray paths 50, 51 and reflective paths 52, 53, respectively, in overburden 51. Reflections from reflector 55 are at points CRPl, CRP2...CRP'n. Due to the production of con-verted P-wave reflections at reflector 55, the reflection angle (r) of the converted P-wave is seen to be greater than that for the incident angle (i). ~ote also that at large incident angles, not only is the amplitude of the converted P-wave increased, but also the reflection point CRP'n at the reflector 55 is not aligned with a vertical projection through the midpoint formed between the respec-tive source-receiver pair, i.e., midway between source-point Spl and receiver position Dn.
FIG. 4 illustrates the same principle but in areciprocal manner.
As shown, P-wave source 60 located at source-point SPl is seen to produce P-waves whose wave fronts trace out incident ray paths 61, 62 and reflection paths 63, 64 in overburden 65. However, the slopes of these paths are seen to be reversed from those depicted in FIG. 3. Due to the production of converted Sv-waves at reflection points CRP'l, CRP'2 and CRP'n, the reflection angles (r) are less than the incident angles (i). ~ut also note that the degree of inequality (between the inci-dent and reflection angles) becomes greater with of~set.
Amplitude of the converted wave similarly increases.
Returning to FIG. 1, it should now be recalled that the detectors at stations Dl, ~2...Dm and sources at sourcepoints SPl, SP2... SP4 are used in redundant fashion so that the similar source and receiver coordinates relate a number of generated traces. Starting with activation of the source at sourcepoint SPl, energy is detected at receiver positions Dl...Dm wherein ground ~otion is 01 ` -15-recorded for a specific time period, often 6 seconds.
Such a time period allows enough time for energy to travel 05 down and be reflected upward from reflectors to the detec-tors at stations Dl...Dm. Next, the source is "rolled"
forward to sourcepoint SP2 and activated. While at the same time the detectors are positioned at stations D2, D3...Dm+l to record reflections. As the above-described sequence is repeated in the direction of arrow 12 along the line of survey 13, the result is a series of overlap-ping trace records that can be identified with redundant source and receiver coordinates and similarly sampled reflection points, as previously discussed.
FIG. 5 illustrates how conventional, non-con-verted traces associated with different sets of source-receiver pairs, sample the same reflection point on a target reflector.
As shown, note that common reflection point 68 is located on flat reflector 69 in -~ertical alignment with imaginary projection 7~ that passes through the center-point Co between all possible source-detector pairs. The common reflection point 68 for the illustrated group of source-detector pairs, is, of course, derived by tracins the wave ray from its sourcepoint SPl, SPl-1, SPl-2...
down to the reflector 69 and then upward to its particular detector 3tation Dj, Dj+1, ~j+2... Thus, coordinates of the common midpoint equals all possible coordinates of pairs of source and detector positions with the same average value. Or CMPi j = CMPi_l,j+l = CMPi-2,j+2 ' (I) for as many pairs as sample the same reflection point 68. Further observations can be ascertained in conjunc-tion with FIG. 5.
E. g., note that even though the path lengths of the rays associated with different source-receiver pairs are substantially different, the path lengths of the inci-dent and reflection waves of any one pair are identical.
And, for that one pair, the angle of incidence equal the angle of reflection at reflector 69. When the traces lZ~L9329 associated with these source-detector pairs are trans-formed into common midpoint gathers, the resulting stacked 05 traces are said to sample the same reflection point on any flat target reflector wherein, the coordinates of the reflection relate to the sourcepoint (SP) and detector station (D) coordinates in accordance with an equation of coordinate transformation of the form:
CMPi j = [~SP)i + ~D)j]/2 (II) FIG. 6 illustrates the fact that converted waves recorded at s~ations Dj, Dj+1... do not provide reflection points that are vertically aligned with midpoint coordi-nates of the respective source-detector pairs from which the traces are derived.
As shown, the reflection points 72, 73, 74, 75, 76 and 77 on flat reflector 78 are shown not to be align-able with the vertical projection 79 that passes through centerpoint Co of all the source-detector pairs at the earth's surface. Reasons for this occurrence are set forth briefly below.
For converted P- to Sv-waves, the angle of reflection r for the converted SV ray does not equal the incident angle i for the P-ray. ~ue to application of Snell's Law which holds for rays in optics, acoustics as well as elastic wave propagation in the earth. Snell~s Law states that angles (i) and (r) are related by the velocity of propagation of the incident and reflected waves. In this case the relation is Sin(r)/sin(i) = Vs/Vp (III) where Vp and Vs are the velocities of compressional and shear velocities, resp~ectively, in the overburden above the reflection point.
In solid materials, like sedi~entary rocks, the P-wave velocity, Vp, is always greater than the shear wave velocity, Vs, often by a factor of about 2. This causes the angle (r) to always be less than the incident angle (i). ~s a result, actual reflection points 73-77 are not vertically alignable with the midpoint coordinate between the source-receiver pairs.

12~3329 Ol -l7-That is to say, the actual reflection points ofconverted P- to Sv-wave are biased away from common mid-05 point location CMPl, on reflector 7~ by selected amountsin the direction of the detector locations. If the con-verted wave data recorded by these pairs of sources and detectors is conventionally is time shifted to bring about alignment about projection 79. Then there is a loss of resolution laterally because of smearing of these points over the target reflector.
In accordance with the present invention, the asymmetry of the incident and reflected ray paths are compensated for so the common reflection points (CRP's) of target reflectors truly correspond to known sourcepoint (SP) - detector station (D) coordinates of CMP collection system along the line of survey.
Briefly, the method of the present invention involves two basic steps:
The first is a ray tracing calculation for con-ventional (unconverted) waves through a layered structure to provide a conventional ~ero offset section. By numeri-cal iteration a series of target reflectors is positioned as to dips depth, and as events along the time axis of each trace. The reflection points for the conventional waves are calculated using midpoint coordinate transforma-tion steps augmented to account for reflector depth and dip. By a geometric trick, the starting ray path of the iteration is guessed using the rms velocity of the hyber-bolic moveout formula.
The second step involves using the reflector dipand depth information of step one, supra, followed by choosing the right combination of source and detectcr coordinates so that trace gathers sample the same reflec-tion point in the subsurface for converted waves. This,fortunately, turns out to be a tilted straight gather line on the (SP vs. D) stacking chart of FIG. 13 rotated with respect to the conventional phase stacking lines. To implement this gathering of data requires a relatively straightforward coordinate transformation, re-addressing ~2~3~9 program which sorts data by common reflection points (CRP's) rather than by common midpoint coordinates.
05 Before the method of the present invention is described in detail, a brief discussion of two different sets of field coordinate systems used in connection with the present invention, is beneficial to understanding certain aspects o~ the invention and is presented below in connection with FIG. 7~.
As shown across the to of the FIG. 7 is a plan view of a CMP collection system similar to that depicted in FIG. l except that the source point locations SPl, SP2 precede the advance of the spread of detectors ~L, D2...Dm, instead of trailing the spread as previously shown. Direction of advancement is in the direction of arrow 90 along line of survey 9l. As a result of similar incremental advances between spread and source positions, say, each is advanced one incremental position per collec-2Q tion cycle, so that ~SP = ~D, traces can be associated notonly with respective source (SP) and receiver (D) loca-tions via orthogonal axes 92 and 93, respectively, on stacking chart 94 but also they can be identified with common midpoint (CMP) and offset (f) coordinates that lie along orthogonal axes 96, 97 in accordance with the equa-tions of coordinate transformation previously set forth, viz ., CMP = ~D + SP)/2, f = D-SP.
Since transformation of coordinates for con-verted waves varies substantially from these formulas, a brief discussion of the theoretical basis for carrying out coordinate transformation of converted traces in accord-ance with present invention will now be discussed.
Briefly, in this regard, transformation equa-tions involving flat reflectors will be initially developed followed by a detailed discussion of the deriva-tion of transforma~ion equations related to dipping reflectors.

- 12193Zg RAY TRACING OF CONVERTED WA~ES FOR FL~T REFLECTORS
For conventional phases such as P-wave generated 05 and then recorded on vertically responding receivers, the common reflection points (CRP's) are assumed to be the common midpoints (CMP's) between associated source and receiver pairs. For a ~iven offset coordinate, say, at a given offset along axis 97 of FIG. 7, traces associated with a given midpoint and is coordinate 96, _an be con-currently gathered. That is to sa~, in areas of no struc-ture or dip CMP data can be conveniently gathered in accordance with the midpoint coordinates of each source-receiver pair and then processed through NMO correction, statics and stacking to provide accurate final seismic sections.
For converted waves, however, since the angles of incidence and reflection are unequal, the reflection points associated on each target are not alignable with the above-mentioned midpoint locations. But can be accurately determined -- and then eliminated -- in accordance with the steps of the present invention.
FIG. 8 illustrates conversion ray tracing aspects of the present invention to bring about alignment.
~s shown, there is a stack of layers generally indicated at 100, i.e., layers l, 2, 3,,,,n, a portion of which represents the overburden. Solid line 101 indicates the ray path of an incident P-wave generated by a source at coordinate SP at the earth's surface 102, and a con-verted P- to Sv-wave that is reflected from interface 103 of layer n at reflection point 104. That reflection is recorded at a receiver located at location D.
For a given receiver-offset distance X between the source coordinate (SP~ and receiver coordinate ~D), the coordinates of the ray is to be determined, and the reflection offset distance Xr can be determined. The Sv-P
conversion problem is a mirror image of that depicted in FIG. 8 but has the same general solution for incident angles in each layer.

~2~329 Briefly, in order to find the incident angles to map the ray, the invention revamps ray tracing fro~
05 solving a reflection problem to solvin~ a transmission problem. This can be done in FIG. 8 by constructing a mirror image of the reflected Sv rays about interface 103. In that wayl the total path of the ray appears to be equivalent o~ downward transmission through two sets of layers, i.e., layers l,...n and layers n+l, n+2,...2n before reflection at reflection point 105 occurs. That is, along the downward segmnents of solid line 101 and dash-dotted line 106 as shown.
Note the upper set of layers is associated with P-wave overburden velocities only, while the lower set of layers is related to Sv velocities only.
If the layers are numbered from top to bottom as shown and assigned the correct velocities, angles ard thicknesses total offset distance X and travel time T for the ray is:

2n i-l ( 1 ) 2n -1 T = ~ hicos a i/Vi (2) To find the angles of incidence a 1~ 92~ i in the layers, the travel time T for the path is minimized by the con-straint that the offset X be fixed. This will determine the ray parameter p from which all angles can be computed by Snell's law.
In this regard, Taner and Koehler (1966) described a technique for tracing conventional reflections only (but not for converted waves and not by transmission paths) that is of interest ("VELOCITY SP~CTRA-DIGITAL
COMPUTER DERIVATION AND APPLICATIONS OF VELOCITY
FUNCTIONS", Geophysics, Vol. 34, pp. 859-881.) The functional (F) is next defined.

121!~3;2~3 .

F = T - pX (3) F = ~ (hivi [{(tan2si ~ 1)/2 - p vitan ~i} (4) where p is a variational parameter.
To minimize T with a fixed offset X, the differ-ential of F is taken and set to equal to 0, i.e.

ôF = ~ (hi~vi) ~tan 6i/(tan2~i + 1)~2 - p vi} Otan ~i i=l This is possible for arbitrary angle differentials only if P Vi = 1 / (1 + cot29i)/2- sin ei (5) i.e., Snell's Law applies, where p is the ray parameter with units of apparent horizontal slowness. This can also be written as sin 9i = P Vi = Vi/c (6) where c is the unknown horizontal velocity of the ray.
Substituting this for the angles in equation 1 a single equation for c is obtained.

X = ~ hi Vi /(c2 - v2i)/2 (7) This equation has no algebraic solution for c, but is solvable numerically by iteration, requiring an initial guess for the ray path which will allow the method to iterate to a solution. In accordance with the present invention, the hyperbolic moveout formula gives surpris-ingly good starting values for c in the ~anner set forth below.
Referring again to FIG~ 8, total transmission path through the two sets of layers is seen to be simply half of a two-way conventional reflection path down to interface 2n and back up to the surface. The upgoing 32~3 reflection would arrive at offset 2X. Standard NMO
formulas can estimate arrival times and slownesses in 05 terms of rms velocities down to interface 2n. One-way times to interface 2n at offset X are obtained from the same moveout formula by just dividing the distance and time variables by two.
Thus, for our converted reflection problem, the approximate formula is T2 ~ T2 + (X/Vps)2 (8) ps where Tps is the two-way zero offset time for the con-verted reflections equal to 2n Ps i~l hi/vi , (9) and Vps is the rms velocity equal to 2n 2n Vps = ~i~l Vi ti)/l~lti)] 2 l10) In expression (10) the ti's are one-way layer time~ given by ti = hi/Vi ( 11 ) where P times are obtained for i fro~. 1 to n and Sv times for i from n+l to 2n.
From equation (8) an initial guess of cO can be made for the apparent horizontal velocity of ~he ray. Or, cO = dX/dT = Vps [T2 + (x/vpS)2]~2/ (X/Vps) (12 Note that cO is infinity at zero offset and decreases asymptotically to Vps as X goes to infinity.

~2~Z9 To find the exact value of c for the layeredmodel cO is substitute cO into equation (7) and iterations 05 are made toward as accurate a solution as required.
With c determine~, the reflection point offset Xr can be calculated by equation t7) but summing i only up to n, provides, r iE1 hi Vi / tc vi) 2 (13) The converted wave rms velocity can be related to the separate P and Sv rms velocities measured on the separate unconverted reflections. If Tp and TS are the two-way, zero offset times for the unconverted events, then the converted wave rms velocity in equation (103 can be written as Vps = {(TpV2 + TS V2 )~(Tp + Ts)}~2 (14) where Vp and Vs are the rms velocities for P- and Sv-waves, respectively, down to interface n, obtained from cores of adjacent wells or by other conventional means.
Expression (14) shows that Vps is a weighted average of the mean squared velocities v2 and Vs~ so that in principle, correlations between conventional P and Sv phases and converted velocities and times for identifica-tion purposes, can be made.
Note also that the converted wave problem has n~w been replaced by an equivalent conventional moveout problem. Velocity variations are quite extreme since P
and Sv velocities are a mixed function.
It is of interest that for a single layer case equation (14) can be further reduced. Since the rms velo-cities for small offsets equal the true P and Sv veloci-ties, hl = Tp Vp = Ts Vs. Substituting these equalities into equation (14) YpS varies in accordance with 4~ Vps = (Vp vS)~2 (15) 12~329 for the converted wave r~s velocity to be used in equation (12).
05 Coordinates of the reflection points can now be estimated. The lateral shift fro~ the midpoint is prefer-able used for a single layer using Snell's Law.
If the hori~ontal o~fset X from the source coor-dinate (D) to detector position (SP) is defined as j i (16) then the actual reflection point offset Xr, can be defined in terms of a ratio of these two quantities:
R = Xr /(X/2) = 2 tan ap/(tan 3p + tan 9sv) ~17) where gp is the angle of incidence and ~sv is the angle of reflection. Multiplying top and bottom by cos sp and using Snell's Law, yields: -R - 2 (Vp / Vs)/(Vp / Vs ~ cos ~p/cos ~sv) (18) Talcing a power series expansion for each cosine term and using Snell's Law and simplifying R = 2 (Vp/Vs)/{(Vp/Vs + 1 - (3p2/2)(1 - (Vp/Vs 2)} (19) where ~p is the incident angle in radians.
The approximate ratio of reflection point offset Xr to midpoint offset X/2 is accurate up to ~p = ~/4 = 45 degrees. For offsets X less than the reflector depth the term in a p can be ignored, so that R = 2 (Vp/Vs) / (Vp/Vs + 1) (20) Note that the ratio R depends only on the (Vp/Vs) ratio for all reflectors deeper than the offset distance.
Expression (20) hence can be used to gather traces associated with selected pairs of source-receiver pairs haviny events thereon which sample the same point on an interface in the following manner.
Recall that for conventional waves for which angles ap and ~sv are equal so that the reflection point CRPi,; = SPi + .5 (Dj - SPi) = .5 (Dj + SPi) (21) 1;;~1~3~9 For converted P to Sv reflections the reflection point 05 offset is CRPi,j = SPi + 5 R (Dj - spi) The above transformation can be thought of as a process for determining the reflection point coordinate projected to the horizontal datum plane via multiplying a constant (k) that takes into account the velocity ratio of the overburden times the (SP) and (D) coordinates of respective source-receiver pairs in accordance ~ith = kDj + (l-k)SPi (22) where k = R/2 = (Vp/Vs)/(vp/v5 + 1) (23) From equation (22) it can be seen that the actual reflection points for converted waves e~ual a weighted average of source and detector location coordi-nates where the weights add up to unity. For conventionalreflections the weights are each .5 and sum to 1. Because of Expressions (22) and (23), traces that are associated with pairs of source and detectors coordinates can he gathered for a known reflection point ]ocation CRP.
From Expressions (22) and (23) note that k is only a function of Vp/Vs ratio for the earth above the reflector, i.e., the Vp/Vs ratio of the overburden, if that reflector is flat. However, if the reflector is dipping at an angle ~ with a horizontal line normal to the earth's gravitational field (instead of being flat), then the formulas for the reflection point coordinates CRP
are more complex.
RAY TRACING CONVENTIONAL AND CONVERTED
WAVES FOR DIPPING REFLECTORS
FIG. 9 shows the geometrical relationships of reflection points CRP's for converted waves off a dipping layer 110. The parameter k for this case depends on two factors, dip angle ~, and offset to depth ratio X/h. An exact formula for k is k = 1/2 [1 + (X/2h) sin ~] (24) ~2~33Z9 Ol -26-tne expression (24), supra, being developed as follows.
A source is at position coordinate (SP) shooting 05 down dip into a receiver at receiver position ~D). Whilefor conventional reflections the incident and reflected angles at the dipping interface 110 are equal, they are not so for converted waves. Purpose of the following expressions: To find a relation between the actual reflection point offset Xr' along the interface 110 and the midpoint offset X'/2 along the same interface as measured from coordinates s' and d' which are the image points on that interface llO projected from the surface points SP and d, respectively.
R can be defined as the ratio of reflection point offset to midpoint offset at the earth's surface as 112 actualy recorded. By geometry the same ratio in dipping coordinates along the interface 110 is equal to R = Xr/~X/2) = Xr'~(X'/2) (25~
If the dip angle ~ were zero, Xr' = X'/2 and R would equal 1 as expected. From the geometry in F~G. 9 since Xr' = h tan ~p X' = (2 h + X sin ) tan ~p (26) Substituting these expressions yields k as k - R/2 = 1/2[1 + (X/2 h) sin ~] (27) as set forth above in equation (24).
For zero dip equation expression (27) reduces to k = 1/2, which means that the true reflection point equals the midpoint location between source and receiver. For non-zero dip this equation is convenient to use for estimatin~ t~e location of the true reflection point as a coupled function of dip, offset and depth.
Then since k = R/2, according to Expressin (22), the true reflection points CRPi j for conventional waves can be stated as CRPi j = kDj + (l-k)~P;

12~33Z9 But expression (27) deals only with conventional reflections at interface 110, and does not involve con-Q5 verted reflections.
FIG~ 10 illustrates the geometrical relation-ships of converted ray paths with respect to a dipping interface 115.
In this case the parameter k depends on three factors, Vp/Vs ratio, dip angle ~, and offset to depth ratio X/h. An exact formula for k is thus:

( Vp/Vs ) . ..
{(Vp/Vs) + [1 + (X~h) sin a] ~1 + fl 1'~} (28) where [(Vp/Vs) 1] IX~h2) cos 2 ~ ~29 [ ( Vp/Vs ) + 1 ]

the total Expression ~28), supra, being developed as follows.
Note first in FIG. 10 that the angle of incidence (sp) and the angle of reflection (3sv) are no longer equal. Hence Xr' = h tan sp (30) and X' = h tan sp + (h + X sin a) tan gsv ~31)

3 X' - h tan sp (1 + (1 + (X/h) sin a) tan gsv/tan sp) Substituting these into equation (25) yields R = 2/{1 + ~1 + (X/h) sin ] tan ssv/tan gp} (32) Except for the ratio of tangents this formula is similar to that derived for conventional reflections.
Equation (32) is exact, but the tangent ratio cannot be determined exactly without an iterative ray tracing. However, a simple approximation can be made whic~ gives very close answers.
If the reflection point is moved from CRP' to CRP" as in EIG. 11, then both incident and reflection ~LZ~32~

angles increase from ~p to ~p" and from 9sv to 9sv"respectively. However, the ratio of tangent angles 05 changes very slightly so that to a good approximation tan 3SvJtan ~p ~ tan 3sv /tan 3p As the reflector depth increases, this approxi~ation becomes more accurate. Then from FIG. ll, cos ~p" = h/(h2 + Xr"2) l/2 (34~

sin ~p" = Xr"/(h2 + Xr"2) 1/2 (35) where (for deep layers) Xr" = (Vp/Vs)X cos /(Vp/Vs + l) (36) Snell's Law states that incident and reflected angles are related by sin ~sv" = tVs/Vp) sin ~ pN ( 37) Using Snell's Law twice, the ratio of tangents for the perturbed angles can he calculated by tan ~5vN/tan 3p" = (Vs/Vp) cos ~p"/cos ~sv"

= (Vs/Vp) cos sp" [1-(Vs/Vp)2 sin29p"]~1/2 (38) Substituting (34) and (35) into this equation for cos ~p" and sin ~p" after algebraic simplification, yields:

tan ~5v"/tan ~p" = (Vs/Vp~ [1 + f]-1/2 139 where f = (Xr''/h)2(1-(VS/Vp)2) (40) ~L21~329 To express f in terms of surface offset dis-tances X substitute (36) into this equation, which yields:

[(Vp/Vs) 11 (X/h)2 cos2a ~41) Finally, the parameter k = R/2 is obtained by substituting the tangent ratio of (39) into (32), thus giving ( Vp/Vs ) 1/2 (42) {(Vp/Vs) + [1 + (X/h)sin a] [1 + f] }
From this derivation, it is observed that equa tions (41) and (42) verify the formulas originally stated in equations (29~ and ~28).
Although the formula for k is complex, it is also quite general and reduces to simpler forms for both converted and conventional waves, in conjunction with and without dipping reflectors.
By setting (Vp/Vs) to be equal to 1, yields the conventional wave formula for k in the dipping layer case (because the incident and reflected waves are the same type). From equation (41) it is seen that f goes to 0~, hence k in (42) reduces to k = 1/2[1 + (X/2h) sin a] (43) which agrees with (24), previously derived for conven-tional waves.
For converted waves, setting the dip angle a = O
reduces the parameter k to the formula:

(Vp/Vs) {(Vp/Vs) + [1 +fj-1~2}

where lZ~329 [ ~ Vp/VS ) - 1 ]
f = - (X/h)2 (45) ~ ( V~,/Vs ~ + 1 ]

The effect o~ ~ in this expression is to correct for off-set variations in X which become important when X is as larye as the depth to reflector h.
If the user is interested in onl~ near offset conditions, where the X/h ratio is much less than 1, then f can be set equal to 0, causiny k to be further simpli-~ied to k ~ Vp/Vs/(Vp/VS + 1) (46) which i5 the least complex approxima,ion in the method of 0 the present invention, useful for short offsets in zero dip areas. This expression for k was developed earlier for equation (~3).
From the above development it is also seen that the parameter k can be calculated for conventional and converted waves including the effects of offset to deuth ratio ~X/h) dip an~le a, and velocity ratio Vp/Vs. Thus, k is a ~eneral function of these three parameters k = k ( X/h, Vp/Vs, a ) ( 47 ) wnich can be calculated for any case o~ interest. A5 aescri~ed earlier, k is re~uired to calculate the common reflection points (CR~) for each type of wave.
DETAILED DESCRIPTION O~ THE PRE~ENT INVENTION
Now, having a firm theoretical foundation, the steps for carrying out the metho~ can be set forth in detail in con~unction with FIGS. 12, 13, 14 and 15.

FIG. 12 illustrates how transformation of a series of field traces in accordance with the present 05 invention occurs. It represents an overall viewpoint.
As shown, flow chart 199 sets forth the desired sequence of steps controlling the operation of a digital computer, such as an IBM Model 3n33, involving at least the transformation ~nd reordering of converted traces associated with source-detector pairs of known source-point-detector station coordinate locations (SP,D), using an equation of transformation for associated co~mon reflection points (CRP's) selected from the group comprising:

CRP = kD + (l-k)SP : for conversions of P-waves to Sv-waves at the target;
CRP = (l-k~D + kSP : for conversions of Sv-waves to P-waves at the target;
2~
where k = - ~ (Vp/Vs) [(Vp/Vs) + {1 + (X/h)sin ~}(l+f) 1/2 [(Vp/Vs) - 1] 2 2 [ (Vp/VS) + 1]

Vp and Vs are the P-wave and Sv-wave velocities, respectively, of the overburden;
X is the source-receiver offset distance;
h is the depth of the target reflector;
a is the dip angle of the target reflector; and SP and D are source and detector coordinates, respec-tively, along the line of survey.
As a result of evaluation centering on the determination of the ahove constant "k" as a function of velocity ratios in the overburden, the dip angle and depth (h) of the target reflector and the source-receiver of.set ~2~3Z9 distance X, transformation easily occurs whereby signals of greater intelligibility and clarity for geophysical oS interpretation, are subsequently provided. ~ote that while chart 199 sets forth the method of the present invention in general terms, a programmer of ordinary skill in conventional CMP collection and processing techniques in addition to the aforementloned transformation equa-tions, can program most convention computers in a rathershort time span to carry out the goals and objects of the invention. Typical programming language, is FORTRAN.
Although instruction 20~ i9 the key to the transforming of source (SP) and receiver (D) coordinates to CRP coordinates via evaluation of the above equations, it is assumed that the data has been collected as set forth at step 201, supra, by common midpoint (CMP) methods. That is to say, it is taken as fact that the data at step 201 has been sequentially generated by a conventional seismic source located at a series of source-point locations (SP), and then redundantly collected as converted traces at a series of detectors positioned at known detector locations (D) along the line of survey.
Since the converted traces are each associated with a source-detector pair of known sourcepoint-detector station coordinate locations (SP,D), subsequent processing in accordance with step 200 produces their easy transforma-tion in terms of true common reflection point coordinates.
That is, step 200 establishes CRP coordinates for a gather of converted traces so as to time-correct each of tha converted trace for (i) any elevational differences that may have existed between its sourcepoint-detector station coordinates at the time that the trace was derived (static corrections), as well as (ii) moveout differences associ-3~ ated with the travel paths of the energy (dynamic correc-tions). Result: the final traces represent an imaginary collection sequence as if a source associated with a given trace was placed at each C~P and activated followed imme-diately by the relocation of a detector at the CRP and the reception of converted phases of the generated wave. In ~21~3Z9 that way, the CRP's associated with each gather of con-verted traces (in ~erms of (SP,D) locations of each oS source-detector pair, and an evaluated ~k" constant) account for nonsymmetrical travel paths of the incident and reflected rays, as well as the dip and depth of the target reflector. Thereafter, the converted waves are stacked via instruction 202 in terms of CRP coordinates and then gathers displayed in accordance with instruction 203 as a ~ero offset seismic section of converted traces.
FIG. 13 is of further interest, in explaining instruction 200 wherein a simplified stacking chart 204 is depicted and is discussed in connection with the collec-lS tion system of FIG. 7.
As shown, each point on the diagram 204 has asource coordinate (SP~ along axi~ 205 corresponding to the location of the source that gave rise to the trace corre-sponding to that point. The same point also has a (D)-2U coordinate along axis 206 corresponding to the location ofthe receiver whose output is also associated with traces in the same manner. In other words, the diagram 204 is a plot of the SP- and ~-coordinates of all of the traces comprising a CMP seismic collection sequence. Location of the origin of the seismic line is at the instruction ~07 of the axes 205, 206, viz., at D = SP = 0. The example shown in FIG. 13 is a seismic line consisting of six 13-trace seismograms, which were recorded with an end-on layout geometry, wherein the incremental spacing of points as depicted on the diagram 204, viz., ~SP and ~D are made equal to each other.
For a given ofset, as along axis 208, conven-tional common gather lines generally indicated at 209, interesect axis 208 at right angles. Consequently, coor-dinates (i.e. ~addresses") of gatherable traces (alignedalong such gather lines 209) are easily evaluated via the equation CMP = kD ~ (l-k)SP
where k is dstermined to be equal to .5.
~0 ~L21~33~9 01 ~34~

That is to say, for conventional flat reflectors without mode conversion, the reflection points of the 05 reflector are vertical projections of the midpoints between associated source-receiver pair locations produc-ing the trace. ~ence, a com~on reflection point on a target reflector is vertically associated with a pair of known (SP) and ~D) coordinates~ For example, for coordi-nates (SP) and (D) equal six (in conjunc~ion with offsetaxis 208), the relevant traces for a proper gather would be aligned along dashed-dotted gather line 209a at right angles to the axis 208. Furthermore, within the gather of defined traces occurring along the line 209a, the source to receiver offset distance associated with any one trace of the gather, is also determinable because of the fact that the longest offset trace coordinates is a direct function of its sourcepoint (SP) and receiver sta~ion ~) coordinates. In the above example (involving gather line 20~a), it would, of course, occur at coordinates (SP) = 2 and (D) = 10.
For converted waves incident on flat reflectors, gather lines are no longer along the 45-degree diagonals indicated at 209 of FIG. 13 but instead they are altered along sets of gather lines keyed to the evaluation of the constant "k" based on the type of elastic wave conversion that occurred and to a selected Vp/Vs ratio of the over-burden above the target reflector, viz., either ~i) along solid lines 211a, 211b, associated with P-wave to Sv-wave conversion, or (ii) along solid lines 212a, 212b, associ-ated with Sv-wave to P-wave conversion.
Slopes of lines 211a, 211b and 212a, 212b for a selected Vp/Vs ratio, say Vp/Vs = 24, are identified by "k" evaluations wherein the latter was found to equal to 0.73; and l-k was found to be equal to 0.24. Thus, the coordinates for common reflection points on a flat target are found via evaluation of:
CRP = .73D + ~27 SP and CRP = .27D + .73 SP
for P-to-Sv and Sv-to-P conversions, respectively, so as 01 _35_ to provide the sets of lines 211a, 211b and 212a, 212b o~
FIG. 13~
05 Note that the sets of resulting gather lines 211a, 211b and 212a and 212b, while not being conincident with conventional midpoint gather lines, nevertheless can be stacked using a stacking algorithm defined by the above-mentioned equations augmented to search in (SP vs. D) coordinates about each defined gather lines, say along a two-dimensional "fairway" path. In this regard, the following two-dimensional tolerance for limiting the search area so as to include only those transformed traces whose addreses places them within a selected "bin" of each defined fairway path, has been found to be adequate.
~nclusion = < ~ 1/2 ~D, ~ 1/2 ~SP
Hence, for a gather about a common reflection point, say, one having coordinates of (SP) and (D) equal to 6, (tolerance range: aD = ~SP = 5-1/2 to 6-1/2), traces associated with the line 211a meeting the above inclusion tolerance have source-receiver coordinates as set forth in Table I, below.
TABLE I
SP = 7, D = 6;
SP = 6, D = 6;
SP = 5, D = 6;
SP = 4, D = 7;
SP = 3, ~ = 7;
SP = 2, D = 8.
The above-described "binning'l procedure is also ~seful in processing conventional data because of the fact that irregularities often occur in the field due to inter-ference of roads, streams and cultural obstacles with desired shot and recording positions. The former prevent the exact sequence of shot and detector positions shown in FIG. 13, from occurring, viz., wherein common gather lines can be established along lines 209 of FIG. 13.
For dipping reflectors, several additional vari-ables associated wi~h evaluation of the constant "k" are ~2~329 ascertained in the manner previously indicated, viz., thedip angle of the reflector, and the depth of that reflec-05 tion point via evaluation of the simultaneously collectedconventional traces.
FI~S. 14 and 15 illustrate how the present invention can directl~ associate the conventional CMP
seismic data to account for dipping reflectors.
Return now to the description of the transforma-tion of coordinates equations with respect ~o a dipping reflector. It should be apparent from FIGS. 14 and 15 that events in the conventional traces recorded as a func-tion of source (SP) and receiver ;D) coordinates are first evaluated. Then the determined dip and depth of target reflectors are used in the processing of the converted traces of interest. Dip and depth evaluation of events of interest is machine-oriented. Key to such determinations:
maximi~iny signal response as dip angle of the event is systematically changed.
With reference to FIG. 13, the gathering and stacking of the conventional traces from flat targets would be along the diagonal lines 209. Hence, the true dip of any reflector in manner previously described with reference to the theoretical equations forming the founda-tion of the present invention, would only change the slope of those lines at the particular event of interest. It should be specifically noted that since the normal projec-tions of the reflection points are themselves coded and stored in accordance with processing commands, the depth and dip of such events can likewise be easily included in stored codes for latter use in processing converted traces.
Now, in more detail, in FIG. 14, the field traces are first read in. Instruction 300 then assumes command and sorts the conventional traces as a function of source-receiver pair coordinates from which respective traces were derived. That is to say, the traces are sorted to form the trace funct;on W(SP,D), but midpoint ~2~L!33Z9 and offset addres~ coordinates of such traces are also made of record.
05 Next, instruction 30I transforms 'he previously sor'ed traces into terms of reflection points t~at ~re vertical projections of the midpoints o~ particular source-receiver pairs associated ~ith the traces of interest over a series of particular time window w wl. That is to say, each trace is transformed initially as a function of a midpoint coordinate value to form the trace function W(y,t) for a fixed offset coordinate (X).
The series of trace windows identified with same fixed offset (X) are then dynamically and statically corrected via instruction 302 after which the traces are initially stacked as a function of the common midpoints (CMP's) of respective source-receiver pairs via instruction 303.
Ater decisional step 304 is negatively answered as a function of individual sample points along the trace windo~, a dip estimate is provided via instruction 306.
Using a velocity function, its depth is also estimated.
Next, at instruction 30~, the coordinates of the reflections of the trace are re-estimated as a function of ~i) dip of the target reflector, (ii) the SP and D coordi-nates of the perpendicular projection of the reflectionpoint to a preselected horizon; and (iii) the depth h of the reflection point. Simultaneously, note the operations of instruction 309. That instruction is activated to store the aforementioned, SP and D coordinates of the projection and the dip angle ~ and depth h of the target reflector, as the search for maximum signal response con-tinues.
Iteration in loop 310 occurs until the decisional step 304 is affirmatively answered based upon whether (or not) signal response has been maximized.
3uring such iteration, instruction 309 merely bufers the interim dip, depth and surface coordinate data until step 304 releases loop 310 from active operations. At that time, the last-in buffered data is simultaneously released to tape recorder 307 to aid in latter processing o the ~2~93~9 converted data as described below. As the latter data is recorded at 307, the buffer is erased.
05 Instruction 311 next assumes control. Instruc-tion 311 determines if the time window w...wl is the last window for trace evaluation. If instruction 311 is answered negatively, instruction 312 increments the time window by one, and the loop 313 is entered to repeat the 10 process. If instruction 311 is answered affirmatively, instruction 313 assumes control. Instruction 313 incre-ments operations by advancing the process to the next gather coordinate. If the prior offset coordinate was (X), the next in time fixed offset coordinate woulcl thus 15 be offset coordinate X+l.
Loop 312 is again entered. Operations via instructions 301-312 as previously described, are sequen-tially activated to account for the dip, depth and projec-tion data for the new gather of traces over windows 20 w...wl. In that way, the process can be made to repeat and then re-repeat itself so as to generate a series of gathers at different offset coordinates along with desired dip, depth and projection data.
At the same time that instruction 313 is incre-25 menting the 2rocess to generate new gathers at a progres-sively increasing offset coordinates, instructions 314 and 315 are also placed in sequential operations to (i) store the gathers as a function of offset and ~ii) then generate a stack of such gathers as a conventional seismic sec-3(~ tions. The process terminates when decisional step 316 isa.firmatively answered.
Now, with reference to FIG. 15, note that the nethod of producing the converted zero offset section is similar to that shown in FIG 14. There are a few 35 variances, however. For example, after the converted traces on tape 320 have been inputted and sorted at instruction 321, the interpreter presets the source to key, via instruction 322, the selection of the equation of coordinate transformation at operations 323 or 324. As ~21~329 01 _39_ previously indicated, such equations are selected from the group comprising:
05 CRP = kD + (l-k)SP: (for P-wave to Sv-wave conversions);
and C~P = (l-k)D + kSP: (for Sv-wave to P-wave conversions).
In more detail, while operation 321 sorts the converted traces as a function source-receiver pair coor-dinates, viz., SP and ~ coordinates, note that offsetaddresses of such traces are also made of record. I.e., as the traces are sorted to form the trace function W(SP,~), offset coordinates for a series of particular time windows w...wl are also part and parcel, of each lS trace address.
Instructions 323, 324 transform the previously sorted traces in terms of common reflection points (CRP) coordinates that are surface projections associated with traces of particular source-receiver pairs, over the series of ti~le windows w...w/ and offset addresses coor-dinates X...XL.
After the trace segments identified with the following ~viz. the same fixed offset ~, the identical time window w, and the same CRP coordinates), have been statically corrected, such trace segments are stacked at instruction 325. Such stacking, of course, takes into account reflector dip, reflector depth and reflector off-set coordinate information, such data being supplied via tape 307 to the operations 323, 324 as shown in FIG. 15.
In regard to instruction 325, note that the transformed traces are summed along gather lines that have been altered by ~k" factor evaluation, augmented by a "bin" searching principle that searches in two dimensions along the selected "k" evaluated fairway gather path, as previously mentioned. In that way, transformed traces that have been determined by "k" factor evaluation and whose addresses placed such traces within the examined "bin", are summed. Such sum~ing steps were praviously discussed.

!

lZ~3~:9 01 ~40-Decisional instruction 326 next assumes control to either continue processing the data via iteration loop 05 327 or to allow instruction 329 to assume command. That is to say, process iteration via loop 327 continues until the decisional instruction 32~ is affirmatively answered based upon whether or not the data associated with the last window wl has been processed. That is, instruction 1~ 326 determines if the processed data is associated with the last window wl. If it is, instruction 329 assumes control; if it is not, i.e., if instruction 326 is answered negatively, instruction 328 increments the time window by one, and the loop 327 is entered to repeat the lS process. ~hen instruction 329 does assume control, it increments operations by advancing the process to the next gather coordinate. If the prior offset coordinate was (X), the next in time fixed offset coordinate would thus be offset coordinate X+l. Loop 327 is again entered.
Operations via instructions 322-326 as previously described, thus are sequentially activated, to provide correctly transformed stacked converted data.
That is the process repeats and then re-repeats itself so as to generate a series of stacked gathers at different offset coordinates along with desired dip, depth and CRP
projection coordinator.
At the same time that instruction 329 is incre-menting the process to generate new stacked gathers at a progressively increasing offset coordinates, instructions 330 and 331 are also placed in sequential operations to (i) store the stacksd gathers as a function of offset and (ii) generate a section of such gathers as a converted seismic section. The process terminates when decisional step 333 is affirmatively answered.
EXAMPLE
A field trial was undertaken in the Sacxamento Valley of California. ~ibrator, receiver and recording parameters are as set forth below in Table II.

-01 . -41-TABLE II
P-wave Source; ~ertz Model 9 Vibrators oS A. Sweep Pattern: 3 Vibs x 20 Sweeps over 230' B. Vibrator Separation: 55' C. Move-up: 6' D. Sweep Frequencies: 6-56 Hz, Upsweep E. Sweep Time: 16 sec + 8 sec Listen Recording Configuration A. Coverage: 2400~
B. Spread: V.P. - 960' - 6600' C. Group Interval: 120' D. Geophone Interval: 10' E. Geophone Array: In-line Boxcar Recording Instrumentation A~ Gain: Binary B. Sample Interval: 4 msec C. Record Length: 24 sec D. Preamp Gain: 2**7 E. Filters:
1. Low Cut: Out 2. ~igh Cut: 83.5 Hz 3. Notch: In, 60 Hz F. Number of Channels: 4 x ~48 Data + 4 Auxl S-Wave Source: Mertz Model 13/609 Vibrators A. Sweep Pattern: 3 Vibs x 20 Sweeps over 230' B. Vibrator Separation: 55' C. Move-up: 6' D. Sweep Frequencies: 6-2S Hz, Upsweep E. Sweep Time: 16 sec + 8 sec Listen FIG. 16 is a conventional zero offset section derived ~rom the field data of that test.
~0 l.Z~ 9 From the section, initially note that production is gaseous hydrocarbons from a Winters sandstone generally 05 indicated within boxed area 403. Interpretations further indicate the sandstone is overlain by deltaic shales which form an impenetratable closure. Bright spots 404, 405 twithin boxed area 403) indicate the location of the trapped gas.
Additional events of interest are identified at 400, 401 and 402. Event 400 is formed within a tertiary sedimentary complex. Event 401 is at the base of that complex. Event 402 is from a low velocity shale just above the Winters sandstone of interest.
lS FIGS. 17 and 18 are zero offset stacked sections of the converted data; in FIG. 17, a P-wave sound was used; in FIG. 18, an Sv-wave source was e~ployed. The resulting P-Sv and Sv-P wave converted sections, respec-tively, were processed in accordance with the method of the present invention depicted in FIG. 15.
In brief, note from these Figures that the low velocity shale just above the Winters sandstone, viz., event 402 of FIG. 16, has been dramatically extended in the lateral direction of the sections, say, in the region outlined by solid line 410. ~ore remarkab1e, events 400, 401 and 402 in FIG. 18, show outstanding resolution even through the amplitude level of Sv-P wave conversion is theoretically much lower than that of the P-Sv wave con-version shown in FIG. 17.
~ Improvement in resolution of events in the sec-tions set forth in FIGS. 17 and 18 is a direct function of the Vp/Vs ratio of the overburden. Hence, correct deter-mination of the P- and Sv-wave velocities is required in order to provide accurate, true zero offset sections.
~ven with such data, evaluations of the stacking horizontal velocity required when using the equations of coordinate transformation of the present invention, requires a good initial guess of that value. In t~is regard, employment ~f the geometric mean of known ~- and ~2~3329 01 ~43~

Sv-wave velocities, has been found to be very helpful, viz. Vps = l/Vp Vs.
05 Agree~ent bet~een the geometric ~ean oE P- and S-wave velocities and the final stacki~g velocitie~s for events 401, 402 of ~IGS. 16-18, is good. In FIG. 19, for event 401, only a small discrepancy of a few hundred feet per second appears. Similarly, in FIG. 20, for event 402, similar good results are evident. Note also that dis-crepancies appear to decrease going from FIG. 19 to FIG. 20. This is predictable since the offset to depth ratio of the reflectors of interest, viz., event 401 vis-a-vis event 402, decrease as a function of offset.
The invention is not limited to the above combi-nations alone, but is applicable to other anomalous cir-cumstances as known to those skilled in the art. It should thus be understood that the invention is not limited to any specific embodiments set forth herein, as variations are readily apparent. Thus, the invention is to be given th~e~ broadest possible interpretation within the terms of the following claims.

Claims (24)

THE EMBODIMENTS OF THE INVENTION IN WHICH AN EXCLUSIVE
PROPERTY OR PRIVILEGE IS CLAIMED ARE DEFINED AS FOLLOWS:

1. In a method of improving resolution of seismic data collected by conventional common midpoint collection (CMP) methods including sequentially activating a conven-tional seismic source at a series of sourcepoint locations (SP) along a line of survey and redundantly collecting reflections of both the conventional waves and the con-verted phases thereof via a series of multicomponent detectors at a plurality of detector stations (D) along said line of survey, wherein each resulting convention and converted traces is associated with a sourcepoint-detector station pair of known (SP,D) coordinates, the improvement thereof related to processing both conventional and con-verted traces in a systematic manner whereby resulting conventional and converted gathers of such traces each samples a reflection point of a target reflector in the subsurface common to each gather irrespective of dip and depth of said target reflector, comprising the steps of (i) generating seismic field records including at least separate conventional and converted seismic records, by positioning and employing an array of source and multi-component detectors such that individual sourcepoint-detector station coordinates can be redundantly associated with a selected number of conventional and converted traces of said records, said converted and conventional traces being the simultaneous output of said detectors, (ii) establishing for said conventional and con-verted traces a series of separate common reflection points (CRP's), each CRP being for gathering traces common thereto as is a source associated with a given trace of a common gather was placed at said each CRP and activated followed immediately by the relocation of a detector at said each CRP and the reception of conventional or con-verted waves comprising said conventional or converted trace;
(iii) each CRP associated with said common gather of conventional traces being made to account for different travel paths of the wave due to depth and dip of each target reflector;
(iv) each CRP associated with said common gather of converted traces undergoing dynamic sourcepoint-detector station coordinate transformation to account for nonsym-metrical travel paths of incident and reflected ray, dip as well as depth of said target reflectors, wherein the equation of coordinate transformation is selected from the group comprising:

CRP = kD + (l-k)SP : for conversions of P-waves to Sv-waves at said target CRP - (l-k)D + kSP : for conversions of Sv-waves to P-waves at said target;

where Vp and Vs are the P-wave and Sv-wave velocities, respectively, of the overburden;
X is the source-receiver offset distance;
h is the depth of the target reflector;
.alpha. is the dip angle of the target reflector; and SP and D are source and detector coordinates, respec-tively, along the line of survey.

2. Improvement of Claim 1 in which said dip and depth values employed by said selected equation of coor-dinate transformation are provided as a by-product of transformation and enhancement processing of said conven-tional traces.

3. Improvement of Claim 2 in which said transforma-tion and enhancement processing of said conventional traces involve the substeps of:
establishing common midpoint coordinates for said conventional traces as a function of each traces source-point-detector station (SP,D) coordinates, gathering said traces along established common midpoint gather lines, stacking said gathered traces to form finite offset sec-tions, then estimating depth and dip from said sections for events therealong, and then after re-estimating true CRP's from said dip and depth data, regathering said con-ventional traces along altered gather lines to establish said true CRP's therefor, and restacking said regathered traces until a true zero offset section is formed, said final estimates of depth and dip of said events being subsequently employed in said selected equation of coordinate transformation of step (iv).

4. Improvement of Claim 3 with the additional step of:
(v) stacking said converted traces associated with each established CRP in sequence to form a true zero con-verted section having insignificant horizontal smearing of high-intensity events therealong.

5. Improvement of Claim 3 in which said substep of regathering and restacking said conventional traces until a true zero offset section is formed, is an iteration operation that terminates when the signal response for each of said events of interest, is maximum.

6. Improvement of Claim 1 in which said step (ii) includes the step of statically correcting said conven-tional and converted traces to normalize said sourcepoint and detector station coordinates to a common horizontal elevational plane coextensive with said line of survey.

7. Improvement of Claim 1 in which said target reflector is substantially parallel to said horizontal datum plane wherein an equation coordinate of transforma-tion for said conventional traces is in accordance with CRPconvent. = .5SP + .5D
where Vp/Vs of the overburden is unity, and SP, D are sourcepoints and detector station coor-dinates, respectively.

8. Improvement of Claim 7 wherein said k constant of said selected equation of coordinate transformation for said converted traces is in accordance with:

k = where Vp/Vs of the overburden is determined by experimental or empirical data.

9. Improvement of Claim 2 in which said dip and depth values of said target reflector interrelate such that said k constant of said selected equation of dynamic transformation for converted traces can be approximated in accordance with:

k =

10. A method of improving resolution of seismic data collected by conventional common midpoint collection (CMP) methods including sequentially activating a conventional seismic source at a series of sourcepoint locations (SP) along a line of survey and redundantly collecting reflec-tions of both the conventional waves and the converted phases thereof via a series of multicomponent detectors at a plurality of detector stations (D) along said line of survey, whereby resulting conventional and converted gathers of such traces each systematically samples a reflection point of a target reflector in the subsurface common to each gather irrespective of dip and depth of said target reflector, comprising the steps of (i) generating seismic field records including at least separate conventional and converted seismic records, by positioning and employing an array of source and multi-component detectors such that individual sourcepoint-detector station (SP,D) coordinates can be redundantly associated with a selected number conventional and con-verted traces of said records, said converted and conven-tional traces being the simultaneous output of said detectors, (ii) separately establishing for said conventional and converted traces a series of common reflection point (CRP) coordinates each associated with a gather of traces as if a source associated with a given trace was placed at said each CRP and activated followed immediately by the relocation of a detector at said each CRP and the recep-tion of conventional or converted waves comprising said conventional or converted trace, (iii) each CRP associated with conventional traces being made to account for different travel paths of the wave, due to depth and dip of each target reflector;
(iv) each CRP associated with converted traces undergoing at least dynamic sourcepoint-detector station coordinate transformation to account for nonsymmetrical travel paths of incident and reflected ray, dip as well as depth of said target reflectors, using an equation of coordinate transformation selected from the group comprising:

CRP = kD + (1-k)SP : for conversions of P-waves to Sv-waves at the target;
CRP = (1-k)D + kSP : for conversions of Sv-waves to P-waves at the target;

where Vp and Vs are the P-wave and Sv-wave velocities, respectively, of the overburden;
X is the source-receiver offset distance, h is the depth of the target reflector:
.alpha. is the dip angle of the target reflector; and SP and D are source and detector coordinates, respec-tively, along the line of survey.

11. Method of Claim 10 in which said dip and depth values employed by said selected equation of coordinate transformation are provided as a by-product of transforma-tion and enhancement processing of said conventional traces.

12. Method of Claim 11 in which said transformation and enhancement processing of said conventional traces involve the substep of:
establishing common midpoint coordinates for said conventional traces as a function of each traces source-point-detector station (SP,D) coordinates, gathering said traces along established common midpoint gather lines, stacking said gathered traces to form a finite offset sections, then estimating depth and dip from said sections for events therealong, and then after re-estimating true CRP's from said dip and depth data, regathering said con-ventional traces along altered gather lines and restacking said regathered traces until a true zero offset section is formed, said final estimates of depth and dip of said events being subsequently employed in said equation of coordinate transformation of step (iv).

13. Method of Claim 12 with the additional step of:
(v) stacking said converted traces associated with each established CRP in sequence to form a true zero con-verted section having insignificant horizontal smearing of high-intensity events therealong.

14. Method of Claim 12 in which said substep of regathering and restacking said conventional traces until a true zero offset section is formed, is an iteration operation that terminates when the signal response of said event of interest, is maximum.

15. Method of Claim 10 in which said step (ii) includes the step of statically correcting said conven-tional and converted traces to normalize said sourcepoint and detector station coordinates to a common horizontal elevational plane coextensive with said line of survey.

16. Method of Claim 15 in which said target reflec-tor is substantially parallel to said horizontal datum plane wherein an equation of coordinate transformation for said conventional traces is in accordance with CRPconvent. = .5SP + .5D
where Vp/Vs of the overburden is unity, and SP, D are sourcepoints and detector station coor-dinates, respectively.

17. Method of Claim 16 wherein said k constant of said selected equation of coordinate transformation for said converted traces is in accordance with:

18. Method of Claim 10 in which said dip and depth values of said target reflector interrelate such that said k constant of said selected equation of dynamic transfor-mation for converted traces can be approximated in accordance with:

19. In a method of increasing resolution of ampli-tude events in seismic records provided by CMP collection methods involving generating conventional waves by a con-ventional seismic source at a series of sourcepoint loca-tions (s), and redundantly collecting converted phases of said conventional waves as converted traces at a series of detectors positioned at known detector locations (d) along a line of survey, the improvement thereof related to pro-cessing said converted traces in an efficient manner whereby nonsymmetrical travel paths of incident and reflected rays of said generated conventional waves are taken into account prior to trace stacking, comprising (i) sequentially activating said conventional source at said series of sourcepoint locations;
(ii) reducdantly collecting at least converted phases of said conventional waves at said known detector stations (d) via said series of detectors so as to provide a series of converted traces each associated with a source-detector pair of known sourcepoint-detector station coordinate locations (s,d);
(iii) processing said converted traces as to define a series of common reflection point (CRP'S) coordinates each associated with a gather of converted traces as if a source associated with a given trace was placed at said each CRP and activated followed immediately by the reloca-tion of a detector at said each CRP and the reception of converted phases of said generated wave comprising said trace, said each CRP undergoing at least dynamic source-point-detector station coordinate transformation to account for nonsymmetrical travel paths of incident and reflected rays, dip as well as depth of the target reflec-tor wherein the equation of coordinate transformation is selected from the group comprising:

CRP = kd + (1-k)s : for conversions of P-waves to Sv-waves at said target;
CRP = (1-k) + ks : for conversions of Sv-waves to P-waves at said target;

where ;

Vp and Vs are the P-wave and Sv-wave velocities, respectively, of the overburden;
X is the-source-receiver offset distance;
h is the depth of the target reflector;
.alpha. is the dip angle of the target reflector; and s and d are source and detector coordinates, respec-tively, along the line of survey.

20. Improvement of Claim 19 in which said dip and depth of said target reflector interrelate such that said constant "k" of said selected equation of dynamic trans-formation is approximated by:
.

21. Improvement of Claim 19 in which said target reflector is substantially parallel to said horizontal datum plane wherein said constant "k" of said selected equation of transformation is in accordance with

22. Improvement of Claim 19 with the additional steps of (a) establishing a series of imaginary common gather fairway paths across a conventional stacking chart that identifies traces by orthogonal sourcepoint-detector station coordinates, each fairway path having a slope substantially defined by said equation of coordinate transformation, and (b) gathering in sequence along each path said statically corrected traces whose sourcepoint-detector station coordinates place them therewithin to thereby provide a series of gathers of corrected converted traces.

23. Improvement of Claim 22 with the further addi-tional step of stacking traces of each of said series of gathers to form a true zero offset, stacked seismic sec-tion of converted traces.

24. A method of increasing resolution of amplitude events in seismic records provided by CMP collection methods involving generating conventional waves by a con-ventional seismic source at a series of sourcepoint loca-tions (s), and redundantly collecting converted phases of said conventional waves as converted traces at a series of detectors positioned at known detector locations (d) along a line of survey, whereby nonsymmetrical travel paths of incident and reflected rays of said generated conventional waves are taken into account prior to trace stacking, comprising:
(i) sequentially activating said conventional source at said series of sourcepoint locations;

(ii) redundantly collecting at least converted phases of said conventional waves at said known detector stations (d) via said series of detectors so as to provide a series of converted traces each associated with a source-detector pair of known sourcepoint-detector station coordinate (s,d) locations;
(iii) establishing for each of said converted traces common reflection point (CRP's) coordinates whereby a gather of converted traces can be likewise associated therewith, as if a source indexed to a given converted trace was placed at said CRP and activated followed imme-diately by the relocation of a detector at said CRP and the reception of converted phases of said generated wave comprising said trace, said each CRP undergoing at least dynamic sourcepoint-detector station coordinate trans-formation to account for nonsymmetrical travel paths of incident and reflected rays, dip as well as depth of the target reflector wherein the equation of coordinate trans-formation is selected from the group comprising:

CRP - kd + (l-k)s : for conversions of P-waves to Sv-waves at said target;
CRP = (l-k) + ks : for conversions of Sv-waves to P-waves at said target;

where Vp and Vs are the P-wave and Sv-wave velocities, respectively, of the overburden;
X is the source-receiver offset distance;
h is the depth of the target reflector .alpha. is the dip angle of the target reflector; and s and d are source and detector coordinates, respec-tively, along the line of survey.