CN103091709A - Method and device for acquiring longitudinal wave and converted wave seismic data time matching relation - Google Patents

Method and device for acquiring longitudinal wave and converted wave seismic data time matching relation Download PDF

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CN103091709A
CN103091709A CN2012105706498A CN201210570649A CN103091709A CN 103091709 A CN103091709 A CN 103091709A CN 2012105706498 A CN2012105706498 A CN 2012105706498A CN 201210570649 A CN201210570649 A CN 201210570649A CN 103091709 A CN103091709 A CN 103091709A
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stack velocity
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CN103091709B (en
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李向阳
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China University of Petroleum Beijing
China National Petroleum Corp
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China National Petroleum Corp
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Abstract

The invention provides a method and a device for acquiring a longitudinal wave and converted wave seismic data time matching relation. The method for acquiring the longitudinal wave and converted wave seismic data time matching relation comprises the steps of acquiring longitudinal wave stacking velocity from the longitudinal seismic data of a study area; determining value ranges of converted wave stacking velocity vc2, converted wave vertical double journey reflection propagation time tc0, and the value ranges of the square ratio gamma iso of the longitudinal wave stacking velocity and the converted wave stacking velocity; discretely sampling the value ranges; extracting an asymptotic common conversion point (ACCP) trace gather; for each ACCP trace gather, calculating converted wave reflection travel time of each seismic channel by using values through discrete sampling, and obtaining scan calculation energy data of the ACCP trace gather; determining a position of the maximum value in the scan calculation energy data corresponding to each tc0 value, and collecting the vc2 value and the gamma is value corresponding to the maximum value; calculating the longitudinal wave stacking velocity based on the collected vc2 value and the collected gamma iso value; conducting minimum error matching of the calculated longitudinal wave stacking velocity and the longitudinal wave stacking velocity from longitudinal wave seismic data, and obtaining time matching relation of the converted wave and the longitudinal wave.

Description

Obtain the method and apparatus of compressional wave, transformed wave geological data time match relation
Technical field
The present invention relates to seismic exploration technique, relate in particular to the method and apparatus that obtains compressional wave, transformed wave geological data time match relation.
Background technology
Transformed wave seismic prospecting starts from the 1980s, until middle and later periods nineteen nineties, along with the development of three-component digital geophone, ten thousand road earthquake instruments and mass data storage technology and the progress of acquisition technique, the acquisition cost of transformed wave geological data constantly descends, and the transformed wave seismic prospecting technology obtains application and development more and more widely.The up secondary wave of the outgoing that to be descending primary seismic wave reflect at the subsurface formations interface transformed wave, converted to by the descending primary seismic wave of incident.Also play more and more important effect at lithology identification, fluid detection, Reservoir Fracture in describing based on the vertical shear wave earthquake data interpretation of compressional wave and transformed wave geological data joint interpretation, and the prerequisite of carrying out compressional wave and transformed wave geological data joint interpretation is to complete the vertical double-pass reflection travel-time coupling work of same geologic horizon on compressional wave, transformed wave geological data.
Compressional wave and transformed wave geological data time match refer to the transformed wave double-pass reflection travel-time is converted to compressional wave double-pass reflection travel-time scale, perhaps be converted to transformed wave double-pass reflection travel-time scale the compressional wave double-pass reflection travel-time, be convenient to the comparison of combined analysis of compressional wave and transformed wave seismic section.In case with the reflection line-ups of zone of interest position respectively pick up on compressional wave and converted wave sectional plane complete after, namely can the compressing and converting wave profile, make the transformed wave lineups that pick up be positioned at the time scale of corresponding compressional wave lineups, the precision of time match depends on the reliability of horizon picking.The height of time match precision will determine the success or failure of joint interpretation and joint inversion.
Poststack transformed wave geological data is before layer position coupling work, and layer position of general compressional wave is to demarcate, and that is to say and has given clear and definite geological meaning to layer position of compressional wave.If at this moment demarcation has also been completed in layer position of converted waves data, namely give the clear and definite geological meaning in layer position of transformed wave, mutually mate with corresponding compressional wave layer bit time having with the transformed wave layer bit time of the identical geological meaning in compressional wave layer position so, namely obtain the layer bit time matching relationship of compressional wave transformed wave geological data.
In the oil gas field seismic prospecting, same geologic horizon is corresponding the different vertical double-pass reflection travel-time on transformed wave geological data and longitudinal wave earthquake data, how to find same geologic horizon to show respectively on compressional wave and transformed wave geological data separately the matching relationship of vertical double-pass reflection between the travel-time, significant for compressional wave in oil-gas exploration, transformed wave geological data joint interpretation, joint inversion.But there are many problems in existing layer position matching technique, shows the aspects such as phase correlation difficulty, " the corresponding crest of crest " concept mistake and tracing of horizons contrast life period error; Especially in the situation that lack the SWAL data, vertical shear wave earthquake data time coupling is just more difficult.
Summary of the invention
The present invention proposes in view of the problems referred to above of the prior art.The invention provides a kind of method that obtains accurately and effectively compressional wave, transformed wave geological data time match relation.
Of the present invention by utilizing the two-parameter equation of transformed wave to carry out two-parameter sweep velocity analysis to compressional wave, the transformed wave geological data of stratiform isotropic medium, obtain the transformed wave stack velocity v from the transformed wave geological data c2With compressional wave-transformed wave stack velocity duplicate ratio γ isoThen according to the compressional wave stack velocity v p2, the transformed wave stack velocity v c2With compressional wave-transformed wave stack velocity duplicate ratio γ isoBetween relation, can further calculate the compressional wave stack velocity v p2By the stack velocity v that will calculate from the transformed wave geological data p2With the compressional wave stack velocity v that obtains from the longitudinal wave earthquake data ' p2Carry out the least error the matching analysis (namely based on making v p2And v ' p2The principle of difference minimum is mated), thus time match relation between compressional wave, transformed wave geological data can be obtained, i.e. vertical double-pass reflection travel-time of compressional wave and the matching relationship of the vertical double-pass reflection of transformed wave between the travel-time.
In one aspect of the invention, proposed a kind of method that obtains compressional wave, transformed wave geological data time match relation, the method comprises the following steps:
Steps A: the compressional wave stack velocity from the longitudinal wave earthquake data of obtaining survey region;
Step B: the span of determining the transformed wave stack velocity according to described compressional wave stack velocity, determine the span in the vertical double-pass reflection of transformed wave travel-time according to the degree of depth of the formation at target locations of described survey region and described compressional wave stack velocity, and determine the span of the duplicate ratio of compressional wave stack velocity and transformed wave stack velocity according to the span of described compressional wave stack velocity and the transformed wave stack velocity determined;
Step C: with the span of the span of described transformed wave stack velocity, described compressional wave stack velocity and the duplicate ratio of transformed wave stack velocity and the span in described transformed wave vertical double-pass reflection travel-time respectively discrete sampling be square ratio and K the vertical double-pass reflection of transformed wave travel-time value of M transformed wave stack velocity value, a N compressional wave stack velocity and transformed wave stack velocity, wherein, M, N and K are natural number;
Step D: extract the nearly geophone offset of described survey region and the transformed wave geological data of middle geophone offset, and extract all asymptotic common-conversion point gathers of the transformed wave geological data that extracts;
Step e: carry out following steps for each the asymptotic common-conversion point gather in all asymptotic common-conversion point gathers that extract:
Step e 1: square ratio and described K the vertical double-pass reflection of transformed wave travel-time value that utilize described M transformed wave stack velocity value, a described N compressional wave stack velocity and transformed wave stack velocity, calculate the transformed wave reflection hourage of each seismic trace in this asymptotic common-conversion point gather, and ask after the data acquisition sample value stack of 2L+1 sampled point before and after the transformed wave of each seismic trace in will this asymptotic common-conversion point gather reflection hourage square and cumulative the summation, to obtain the scanning calculating energy data of this asymptotic common-conversion point gather;
Step e 2: for each value in the vertical double-pass reflection of transformed wave travel-time, determine the position of the maximum value in resulting scanning calculating energy data, extract the corresponding value in position of this maximum value as the duplicate ratio of described transformed wave stack velocity and described compressional wave stack velocity and transformed wave stack velocity;
Step F is calculated the compressional wave stack velocity at corresponding conversion ripple vertical double-pass reflection travel-time place based on the duplicate ratio of the transformed wave stack velocity of extracting and compressional wave stack velocity and transformed wave stack velocity; And
Step G, to the compressional wave stack velocity that calculates with carry out the least error coupling from the compressional wave stack velocity of longitudinal wave earthquake data, obtain the matching relationship between vertical double-pass reflection travel-time of transformed wave and the vertical double-pass reflection of compressional wave travel-time.
In another aspect of the present invention, proposed to obtain the device of compressional wave, transformed wave geological data time match relation, this device comprises:
Storage part, longitudinal wave earthquake data and the transformed wave geological data from the longitudinal wave earthquake data of this storage portion stores survey region;
The span determination portion, this span determination portion is determined the span of transformed wave stack velocity according to the described compressional wave stack velocity of storing in described storage part, determine the span in the vertical double-pass reflection of transformed wave travel-time according to the degree of depth of formation at target locations and described compressional wave stack velocity, and the span of the duplicate ratio of definite compressional wave stack velocity and transformed wave stack velocity;
Discrete section, the span of span, described compressional wave stack velocity and the duplicate ratio of transformed wave stack velocity of this discrete the described transformed wave stack velocity that will be determined by described span determination portion and the span in described transformed wave vertical double-pass reflection travel-time discrete sampling respectively are square ratio and K the vertical double-pass reflection of transformed wave travel-time value of M transformed wave stack velocity value, a N compressional wave stack velocity and transformed wave stack velocity, wherein, M, N and K are natural number;
Asymptotic common conversion point gathering section, extract the transformed wave geological data of nearly geophone offset and middle geophone offset in the transformed wave geological data of the survey region that this asymptotic common conversion point gathering section stores from described storage part, and extract all asymptotic transfer point (ACCP) road altogether collection of the transformed wave geological data that extracts;
scanner section, this scanner section utilizes described M transformed wave stack velocity value, square ratio of described N compressional wave stack velocity and transformed wave stack velocity was worth with described K the vertical double-pass reflection of transformed wave travel-time, the transformed wave reflection hourage of each seismic trace of each the asymptotic common-conversion point gather in all asymptotic common-conversion point gathers that calculating is extracted by described asymptotic common conversion point gathering section, and ask after the data acquisition sample value stack with 2L+1 sampled point before and after the transformed wave of each seismic trace in described each asymptotic common-conversion point gather reflection hourage square and cumulative the summation, to obtain the scanning calculating energy data of described each asymptotic common-conversion point gather, wherein, described scanner section is for each value in the vertical double-pass reflection of transformed wave travel-time, determine the position of the maximum value in resulting scanning calculating energy data, extract the corresponding value in position of this maximum value as the duplicate ratio of described transformed wave stack velocity and described compressional wave stack velocity and transformed wave stack velocity,
Compressional wave stack velocity determination portion, this compressional wave stack velocity determination portion are calculated the compressional wave stack velocity at corresponding conversion ripple vertical double-pass reflection travel-time place based on the duplicate ratio of the transformed wave stack velocity of extracting and compressional wave stack velocity and transformed wave stack velocity; And
The matching relationship determination portion, this matching relationship determination portion to the compressional wave stack velocity that calculates with from the longitudinal wave earthquake data the compressional wave stack velocity carry out the least error coupling, obtain the matching relationship between vertical double-pass reflection travel-time of transformed wave and the vertical double-pass reflection of compressional wave travel-time.
According to the present invention, adopt two to control parameters and describe in the stratiform isotropic medium conversion wave reflection hourage to carry out the transformed wave stack velocity analysis, considered that simultaneously asymmetrical paths is on the transformed wave reflection impact of hourage, nearly offset distance, middle common offset transformed wave geological data asymptotic transfer point (ACCP) road altogether collection is carried out two-parameter scanning, can access transformed wave stack velocity model accurately to scanning result analysis.And, utilize transformed wave stack velocity model assessment to go out the compressional wave stack velocity, minimize coupling according to the compressional wave stack velocity of actual measurement and the difference of the compressional wave stack velocity of estimation, realized the time match of compressional wave, transformed wave, reduced the difficulty of compressional wave transformed wave coupling, improve the precision of compressional wave transformed wave time match, therefore had very important using value for conversion rolling land shake data processing in oil-gas exploration.
In order to realize aforementioned and relevant purpose, the present invention includes the feature of after this fully describing and specifically noting in the claims.The following description and drawings have at length been set forth specific exemplary embodiments of the present invention.Yet these embodiments only represent to use several in principle variety of way of the present invention.According to the following detailed description of considering by reference to the accompanying drawings of the present invention, other purposes of the present invention, advantage and novel feature will become clear.
Description of drawings
Fig. 1 shows the process flow diagram of method of acquisition compressional wave, the transformed wave geological data time match relation of first embodiment of the invention;
Fig. 2 shows from the process flow diagram of the method for the duplicate ratio of transformed wave geological data acquisition transformed wave stack velocity and compressional wave stack velocity and transformed wave stack velocity;
Fig. 3 shows the conversion radio frequency channel collection of theoretical synthetic five layers of HORIZONTAL LAYERED MEDIUM WITH HIGH ACCURACY;
Fig. 4 shows the conversion radio frequency channel collection of the synthetic five layers of HORIZONTAL LAYERED MEDIUM WITH HIGH ACCURACY of theory of nearly geophone offset and middle geophone offset scope;
Fig. 5 shows the two-parameter scanning result of the transformed wave of ground floor Tc0=800ms;
Fig. 6 shows the two-parameter scanning result of the transformed wave of second layer Tc0=1426ms;
Fig. 7 shows the two-parameter scanning result of transformed wave to the 3rd layer of Tc0=1954ms;
Fig. 8 shows the two-parameter scanning result of transformed wave to the 4th layer of Tc0=2431ms;
Fig. 9 shows the two-parameter scanning result of the transformed wave of layer 5 Tc0=2875ms;
Figure 10 shows compressional wave, transformed wave geological data time match relation;
Figure 11 shows that in the test of compressional wave, transformed wave geological data time match, (a) P-wave section (b) matches the compressional wave converted wave sectional plane in vertical double-pass reflection travel-time; And
Figure 12 shows the second embodiment of the invention block diagram of the device of given layer shape isotropic medium transformed wave stack velocity really.
Embodiment
For making the purpose, technical solutions and advantages of the present invention clearer, below in conjunction with accompanying drawing, the specific embodiment of the present invention is elaborated.In these descriptions and accompanying drawing, specifically disclose specific implementations more of the present invention, represent to implement some modes of principle of the present invention, but should be appreciated that scope of the present invention is not so limited.
Need to prove at this, for fear of because of unnecessary details fuzzy the present invention, only show in the accompanying drawings and structure closely-related according to the solution of the present invention and/or treatment step, and omitted other details well-known to those skilled in the art, little with relation of the present invention.
In the present invention, the inventor is by comprising (v c2, γ iso) two-parameter model that conversion wave reflection in the stratiform isotropic medium is carried out quantificational description hourage is as follows:
t c 2 = t c 0 2 + x 2 v c 2 2 - ( γ iso - 1 ) γ iso v c 2 2 × ( γ iso - 1 ) x 4 4 t c 0 2 v c 2 2 + ( γ iso - 1 ) x 2 - - - ( 1 )
Wherein, t cBe the travel-time from shot point to geophone station of transformed wave, or claim transformed wave to reflect hourage; t c0Be the vertical double-pass reflection of the transformed wave travel-time; X is offset distance, and namely shot point is to the horizontal range of geophone station position; v c2Be the transformed wave stack velocity; γ isoBe the compressional wave stack velocity v p2With the transformed wave stack velocity v c2Duplicate ratio, that is:
γ iso = v p 2 2 / v c 2 2 - - - ( 2 )
During less than or equal to the twice of the reflection degree of depth, the maximum offset that can reach under satisfying the prerequisite of sufficiently high accuracy requirement in other words and depth ratio are 2.0(x/z≤2.0 as offset distance x) time, formula (1) establishment, at this moment, the transformed wave travel-time is by (v c2, γ iso) two parameters control.These two parameter (v c2, γ iso) be also referred to as transformed wave stack velocity model.
Equation (2) shows if two-parameter v c2And γ isoCan reliably find the solution, according to compressional wave stack velocity v in formula (2) p2, the transformed wave stack velocity v c2With compressional wave stack velocity and transformed wave stack velocity duplicate ratio γ isoBetween relation, can calculate t independently from the transformed wave geological data c0The v at place p2, namely
Figure BDA00002646924000063
Suppose the t that obtains independently from the longitudinal wave earthquake data p0The time stack velocity at place is v ' p2, by minimizing v ' p2And v p2Between the difference of numerical values recited, and contrast v ' p2T of vertical double-pass reflection travel-time of corresponding compressional wave p0And v p2T of vertical double-pass reflection travel-time of corresponding transformed wave c0, can obtain so the time match relation between compressional wave and transformed wave geological data.
Therefore, in the present invention, the inventor utilizes and comprises (v c2, γ iso) the transformed wave two-parameter model the nearly offset distance data of transformed wave prestack in isotropy stratiform medium are carried out two-parameter sweep velocity analysis, obtain the transformed wave stack velocity v from the transformed wave geological data c2With compressional wave stack velocity and transformed wave stack velocity duplicate ratio γ isoThen estimation obtains the compressional wave stack velocity v according to formula (2) p2By the compressional wave stack velocity v that will calculate from the transformed wave geological data p2With from the compressional wave stack velocity v of longitudinal wave earthquake extracting data ' p2Carry out the least error the matching analysis (namely based on making v p2And v' p2The principle of difference minimum is mated), obtain the time match relation of compressional wave, transformed wave geological data, i.e. vertical double-pass reflection travel-time of compressional wave and the matching relationship of the vertical double-pass reflection of transformed wave between the travel-time.
In order to calculate the compressional wave stack velocity v from the transformed wave geological data p2, at first need to obtain the transformed wave stack velocity v from the transformed wave geological data c2With compressional wave stack velocity and transformed wave stack velocity duplicate ratio γ isoTransformed wave stack velocity model has comprised two parameter (v c2, γ iso), by asymptotic transfer point (ACCP:Asymptotic Common Convert Point) the road collection altogether of transformed wave geological data prestack is carried out two-parameter scanning analysis, estimate transformed wave stack velocity model (v in the present invention c2, γ iso), then calculate corresponding compressional wave stack velocity v p2Thereby, obtain compressional wave, transformed wave time match relation.
Fig. 1 shows the process flow diagram of method of acquisition compressional wave, the transformed wave time match relation of first embodiment of the invention, and as shown in Figure 1, the method comprises the following steps S01-S03:
Step S01 obtains from the transformed wave geological data transformed wave stack velocity v that the stratiform isotropic medium is ordered at each ACCP c2And the duplicate ratio γ of compressional wave stack velocity and transformed wave stack velocity iso
Particularly, as shown in Figure 2, this step S01 comprises the steps:
Step S10: the depth z of determining the formation at target locations of survey region.This depth z is the approximate depth value of known zone of interest position.
Step S20: obtain the compressional wave stack velocity v from the longitudinal wave earthquake data of survey region ' p2
The compressional wave stack velocity v of obtaining ' p2Can be the compressional wave stack velocity data v ' from the longitudinal wave earthquake data of survey region that has collected p2Collected compressional wave stack velocity v ' p2Can be for example to extract in advance from the longitudinal wave earthquake data of this survey region of collection by longitudinal wave earthquake data speed analytical approach.
Step S30: determine the transformed wave stack velocity v c2T of vertical double-pass reflection travel-time of span, transformed wave c0The duplicate ratio γ of span, compressional wave stack velocity and transformed wave stack velocity isoSpan.
Particularly, can according to the compressional wave stack velocity v of extracting ' p2Calculate the transformed wave stack velocity v c2Span, the transformed wave stack velocity v c2Span for example can be confirmed as (v ' p2/ 3)≤v c2≤ v ' p2Certainly, based on different accuracy requirements, can reasonably change v c2Span.
Can be according to the depth z of the formation at target locations that will the analyze vertical double-pass reflection of the transformed wave travel-time t with formation at target locations c0Span be defined as known seismologic record time span scope, also can be according to the compressional wave stack velocity v p2, the transformed wave stack velocity v c2Calculate t with the formation at target locations depth z c0Span, for example, t of vertical double-pass reflection travel-time of transformed wave c0Span can be confirmed as Certainly, based on different accuracy requirements, can reasonably change t c0Span.
Determining the transformed wave stack velocity v c2Span after, according to determining the duplicate ratio γ of compressional wave stack velocity and transformed wave stack velocity with following formula (2) isoSpan, the duplicate ratio γ of compressional wave stack velocity and transformed wave stack velocity isoSpan for example can be confirmed as 1≤γ iso≤ 4.
Step S40: with determined transformed wave stack velocity v c2The span discrete sampling be M transformed wave stack velocity value, with the duplicate ratio γ of determined compressional wave stack velocity and transformed wave stack velocity isoThe span discrete sampling be square ratio of N compressional wave stack velocity and transformed wave stack velocity, and with the vertical double-pass reflection of transformed wave travel-time t c0The span discrete sampling be K value of vertical double-pass reflection travel-time of transformed wave.Wherein, M, N and K are natural number.
Step S50: extract the transformed wave geological data in nearly geophone offset and middle geophone offset scope from the transformed wave geological data of survey region, and extract all ACCP road collection of the transformed wave geological data that extracts.
Particularly, extract nearly geophone offset and the interior data of middle geophone offset scope in the transformed wave geological data, that is, extract the data of x/z≤2.0 scopes.Extract all ACCP road collection of transformed wave geological data according to following formula:
X accp = γ 0 1 + γ 0 x - - - ( 3 )
Wherein, X AccpBe the horizontal range of ACCP point apart from shot point, γ 0Be the velocity of longitudinal wave of the destination layer position of survey region actual measurement and the ratio of shear wave velocity, and in formula (3), γ 0Value be for example
Figure BDA00002646924000082
With reference to Fig. 3, show the conversion radio frequency channel collection of theoretical five layers of HORIZONTAL LAYERED MEDIUM WITH HIGH ACCURACY of synthesizing.
In addition, with reference to Fig. 4, Fig. 4 shows the conversion radio frequency channel collection of the synthetic five layers of HORIZONTAL LAYERED MEDIUM WITH HIGH ACCURACY of theory of the nearly geophone offset that extracts and middle geophone offset scope (x/z≤2.0).
In Fig. 3 and Fig. 4, dotted line represents the position in transformed wave travel-time of calculating according to formula (1).In Fig. 3 and 4, dotted line can prove that with the consistance of the theoretical transformed wave geological data that synthesizes equation (1) is accurately and effectively when offset distance reflects the degree of depth less than twice.
Step S60: for all ACCP concentrated two-parameter (v of each ACCP road collection execution in road that extract c2, γ iso) scanning, calculate the transformed wave reflection hourage of each seismic trace, and obtain the scanning calculating energy data of ACCP road collection, determine the position of maximum value in scanning calculating energy data, obtain the transformed wave stack velocity v corresponding to position of this maximum value c2And the duplicate ratio γ of compressional wave stack velocity-transformed wave stack velocity iso, comprise the following steps particularly:
Step S601: utilize square ratio and K the vertical double-pass reflection of transformed wave travel-time value of M transformed wave stack velocity value, a N compressional wave stack velocity and transformed wave stack velocity, by calculate transformed wave reflection t hourage with following formula (1) c
In addition, at transformed wave reflection t hourage that has calculated each seismic trace of concentrating in this ACCP road cAfterwards, ask after the data acquisition sample value stack of 2L+1 sampled point before and after corresponding conversion wave reflection hourage of each seismic trace that this ACCP road is concentrated square and cumulative the summation, to obtain the scanning calculating energy data of this transformed wave ACCP road collection:
E m , n , k = 1 J Σ l = - L L ( Σ j = 1 J s j ( τ l ) ) 2 - - - ( 4 )
Wherein, E M, n, kExpression v c2Get m value, γ isoGet n value, t c0The scanning calculating energy value of the ACCP road collection when getting k value, m=1,2 ..., M, n=1,2 ..., N, k=1,2 ..., K; J is the number of all seismic traces of concentrating of this ACCP road; s jl) τ in the j road that represents to concentrate in this ACCP road lThe discrete sampling value of the transformed wave geological data at discrete time place; τ lBe and (t cThe immediate discrete sampling time of value of+l * dt); L is integer, and span is l ∈ [L, L].
Can be according to known seismic wavelet length T perdurability of survey region WavwletWith the discrete sampling time interval dt of earthquake-capturing record, calculate the value of L by following formula:
L=(0.5×T wavwlet)/dt(5)
Fig. 5 shows the two-parameter scanning result of the transformed wave of ground floor Tc0=800ms, Fig. 6 shows the two-parameter scanning result of the transformed wave of second layer Tc0=1426ms, Fig. 7 shows the two-parameter scanning result of transformed wave to the 3rd layer of Tc0=1954ms, Fig. 8 shows the two-parameter scanning result of transformed wave to the 4th layer of Tc0=2431ms, and Fig. 9 shows the two-parameter scanning result of the transformed wave of layer 5 Tc0=2875ms.
Step S602: the two-parameter scanning result of calculation of determining this ACCP road collection of resulting transformed wave geological data (is t c0Scanning calculating energy data { E when getting k value M, n, k, M=1 ... M, n=1 ... N) in the position at maximum value place, extract the corresponding v in position of this maximum value c2And γ isoValue as the transformed wave stack velocity v c2And the duplicate ratio γ of compressional wave stack velocity and transformed wave stack velocity iso, that is, survey region is at the two-parameter stack velocity model of transformed wave at this ACCP point place { t c 0 k , v c 2 k , γ iso k } , k=1,2,…K。
By the ACCP road collection repeating step S60 to all transformed wave geological datas, can obtain the two-parameter stack velocity model of transformed wave at all ACCP points place of survey region
Figure BDA00002646924000093
K=1,2 ... K.
Following table 1 shows the comparative analysis of theoretical value with the actual computation value that obtains according to first embodiment of the invention of five layers of horizontal model.
Table 1
Layer position T c0(ms) γ iso * iso Error (%) v c2(m/s) v * c2(m/s) Error (%)
1 800 3.00 2.78 7.3 1155 1196 3.7
2 1426 2.80 2.70 3.6 1281 1255 1.8
3 1954 2.64 2.63 0.4 1390 1388 0.1
4 2431 250 2.52 0.8 1478 1522 0.3
5 2875 2.40 2.45 2.1 1552 1536 1.0
Tc0 in table 1 represents the vertical double-pass reflection travel-time of the transformed wave of five layers of every one deck in horizontal model; γ isoWith v c2It is the theoretical value of modelling; γ * isoWith v * c2That the transformed wave geological data synthetic according to theory uses the method for first embodiment of the invention to carry out the value that two-parameter scanning analysis obtains.
As shown in table 1, the step S01 method of given layer shape isotropic medium transformed wave stack velocity really adopts two to control parameters and describe in the stratiform isotropic medium conversion wave reflection hourage to carry out the transformed wave stack velocity analysis, considered that simultaneously asymmetrical paths is on the transformed wave reflection impact of hourage, nearly offset distance, middle common offset transformed wave geological data ACCP road collection is carried out two-parameter scanning, can access transformed wave stack velocity model accurately to scanning result analysis.
At step S02, the transformed wave stack velocity v at each ACCP point place that determines based on step S01 c2And the duplicate ratio γ of compressional wave stack velocity and transformed wave stack velocity iso, calculate the compressional wave stack velocity at each ACCP point place.
Comprising step S10-S60 based on above-mentioned steps S01() determined the transformed wave stack velocity v at each ACCP point place c2And the duplicate ratio γ of compressional wave stack velocity-transformed wave stack velocity isoAfterwards, just can calculate at step S02 the compressional wave stack velocity v at the corresponding conversion ripple vertical double-pass reflection travel-time value place at each ACCP point place according to formula (2) p2
And by to the ACCP road collection repeating step S02 of all transformed wave geological datas, just finally obtain the two-parameter (v of transformed wave at all ACCP points of survey region place c2, γ iso) and the compressional wave stack velocity v p2
At step S03, to the compressional wave stack velocity v from the longitudinal wave earthquake data of survey region ' p2The compressional wave stack velocity v that calculates with transformed wave geological data according to survey region p2Carry out the least error coupling, obtain the compressional wave stack velocity v that is complementary p2And v ' p2Each self-corresponding vertical double-pass reflection travel-time t c0And t p0Between matching relationship, i.e. time match relation between compressional wave, transformed wave.
Each ACCP t that calculates from the transformed wave geological data of ordering relatively c0The v at place p2With the t that extracts from the longitudinal wave earthquake data p0The v ' at place p2, with the minimized v of difference p2And v ' p2Be complementary, thus the v that acquisition is complementary p2And v ' p2Corresponding t c0And t p0Between matching relationship, and the time match relation between transformed wave and compressional wave.
Following table 2 shows isotropy stratiform dielectric model parameter list.
Table 2. isotropy stratiform dielectric model parameter list
Figure BDA00002646924000101
As in table 2, z kThe thickness of theoretical synthetic model k layer isotropic medium, k=1,2 ...., 5; v pkAnd v skVelocity of longitudinal wave and the shear wave velocity of theoretical synthetic model k layer isotropic medium; t p0It is the vertical double-pass reflection of the compressional wave travel-time according to theoretical synthetic model calculation of parameter; t c0It is the vertical double-pass reflection of the transformed wave travel-time according to theoretical synthetic model calculation of parameter; v c2It is the transformed wave stack velocity that obtains according to theoretical synthetic model calculation of parameter; γ isoBy equation (2) definition, obtained by theoretical synthetic model calculation of parameter; v’ p2According to according to well-known theory synthetic model calculation of parameter t p0The compressional wave stack velocity at place; v p2The t that calculates from converted waves data according to theoretical synthetic model c0The compressional wave stack velocity at place.
Figure 10 shows compressional wave, the transformed wave geological data time match relation that obtains according to the data in table 2.
With reference to Figure 10, spider represents t of vertical double-pass reflection travel-time of compressional wave p0The speed v at place ' p2Round dot is t of vertical double-pass reflection travel-time of transformed wave c0The speed v at place p2(t p0, v ' p2), (t c0, v p2) value list in table 2.The match point of marking shows t c0The v at place p2And t p0The v ' at place p2The difference of value is minimum, has obtained thus the time match relation between compressional wave and transformed wave geological data.The line of link round dot and cross represents t c0With t p0Between the time match relation.
Figure 11 shows the converted wave sectional plane that (a) P-wave section and (b) in the test of compressional wave, transformed wave geological data time match match the vertical double-pass reflection of the compressional wave travel-time.From Figure 11 as seen, based on the coupling work in the vertical double-pass reflection travel-time on compressional wave and transformed wave geological data of same geologic horizon, can utilize the joint interpretation of compressional wave and transformed wave geological data, more effectively carry out lithology identification, fluid detection and Reservoir Fracture and describe.
The method of the acquisition compressional wave of embodiment of the present invention, transformed wave time match relation utilizes the two-parameter equation of transformed wave to carry out computational analysis to compressional wave, the transformed wave geological data of stratiform isotropic medium, and by two compressional wave stack velocity values that obtain are independently carried out the least error the matching analysis, thereby obtain compressional wave, transformed wave geological data time match relation from longitudinal wave earthquake data and transformed wave geological data.
Utilize the two-parameter equation of transformed wave to realize compressional wave, transformed wave time match, reduced the difficulty of compressional wave transformed wave coupling, improved the precision of compressional wave transformed wave time match.
Figure 12 shows the block diagram of device of acquisition compressional wave, the transformed wave time match relation of second embodiment of the invention.
As shown in figure 12, comprise storage part 10, span determination portion 20, discrete 30, ACCP road collection extracting part 40, scanner section 50, compressional wave stack velocity determination portion 60 and matching relationship determination portion according to the device of the geological data time match relation of the acquisition compressional wave of second embodiment of the invention, transformed wave.
Storage part 10 storage from the compressional wave stack velocity v of the longitudinal wave earthquake data of survey region ' p2And transformed wave geological data.This compressional wave stack velocity v ' p2It can be for example the compressional wave stack velocity from the longitudinal wave earthquake data of collecting in advance.
Span determination portion 20 according in storage part 10 storage the compressional wave stack velocity v from the longitudinal wave earthquake data ' p2Calculate the transformed wave stack velocity v c2Span, according to the compressional wave stack velocity v ' p2, the transformed wave stack velocity v c2Calculate the vertical double-pass reflection of the transformed wave travel-time t of formation at target locations with the depth z of the formation at target locations of survey region c0Span, according to determine the duplicate ratio γ of compressional wave stack velocity and transformed wave stack velocity with following formula (2) isoSpan.
The transformed wave stack velocity v c2Span can be confirmed as (v ' p2/ 3)≤v c2≤ v ' p2, t of vertical double-pass reflection travel-time of transformed wave c0Span can be confirmed as
Figure BDA00002646924000121
The duplicate ratio γ of compressional wave stack velocity and transformed wave stack velocity isoSpan can be confirmed as 1≤γ iso≤ 4.Certainly, based on different accuracy requirements, can reasonably change v c2, t c0, γ isoSpan.
Discrete 30 will be by the definite transformed wave stack velocity v of span determination portion 20 c2The duplicate ratio γ of span, compressional wave stack velocity and transformed wave stack velocity isoT of vertical double-pass reflection travel-time of span, transformed wave c0Span respectively discrete sampling be square ratio and K the vertical double-pass reflection of transformed wave travel-time value of M transformed wave stack velocity value, a N compressional wave stack velocity and transformed wave stack velocity, wherein, M, N and K are natural number.
Can be according to known seismic wavelet length T perdurability of survey region WavwletWith the discrete sampling time interval dt of earthquake-capturing record, by calculate the value of L with following formula (5).
Extract the transformed wave geological data of nearly geophone offset and middle geophone offset scope the transformed wave geological data of the survey region that ACCP road collection extracting part 40 is stored from storage part 10, and extract the ACCP road collection of the transformed wave geological data that extracts.
Particularly, the nearly geophone offset in extraction transformed wave geological data and the data of middle geophone offset scope namely, are extracted the data of x/z≤2.0 scopes.According to all ACCP road collection that extracts the transformed wave geological data with following formula (3).
With reference to Fig. 3, show the conversion radio frequency channel collection of theoretical synthetic five layers of HORIZONTAL LAYERED MEDIUM WITH HIGH ACCURACY.
In addition, with reference to Fig. 4, Fig. 4 shows the conversion radio frequency channel collection by the synthetic five layers of HORIZONTAL LAYERED MEDIUM WITH HIGH ACCURACY of theory of the nearly geophone offset of ACCP road collection extracting part 40 extractions and middle geophone offset scope (x/z≤2.0).
In Fig. 3 and Fig. 4, dotted line represents the position in transformed wave travel-time of calculating according to formula (1).
Each ACCP road collection that scanner section 50 is concentrated for all ACCP road that is extracted by ACCP road collection extracting part 40, utilization is worth with K the vertical double-pass reflection of transformed wave travel-time by square ratio of M transformed wave stack velocity value, a N compressional wave stack velocity and the transformed wave stack velocity of discrete 30 discrete samplings, by calculate transformed wave reflection t hourage with following formula (1) and formula (2) c
In addition, at transformed wave reflection t hourage that has determined each seismic trace that this ACCP road is concentrated cAfterwards, ask after the scanner section 50 data acquisition sample value stack according to 2L+1 sampled point before and after corresponding conversion wave reflection hourage of each seismic trace of this ACCP road being concentrated with following formula (4) square and cumulative the summation, to obtain the scanning calculating energy data of this transformed wave ACCP road collection.
Fig. 5 shows the two-parameter scanning result of the transformed wave of ground floor Tc0=800ms, Fig. 6 shows the two-parameter scanning result of the transformed wave of second layer Tc0=1426ms, Fig. 7 shows the two-parameter scanning result of transformed wave to the 3rd layer of Tc0=1954ms, Fig. 8 shows the two-parameter scanning result of transformed wave to the 4th layer of Tc0=2431ms, and Fig. 9 shows the two-parameter scanning result of the transformed wave of layer 5 Tc0=2875ms.
After the scanning calculating energy data that obtain this transformed wave ACCP road collection, scanner section 50 is determined the t of this ACCP road collection of resulting transformed wave geological datas c0Scanning calculating energy data { E when getting k value M, n, k, M=1 ... M, n=1 ... NIn the position at maximum value place, extract the corresponding value in position of this maximum value as the transformed wave stack velocity v c2And the duplicate ratio γ of compressional wave stack velocity and transformed wave stack velocity iso, that is, and the two-parameter stack velocity model of transformed wave at this ACCP point place
Figure BDA00002646924000131
K=1,2 ... K.
Compressional wave stack velocity determination portion 60 calculates the compressional wave stack velocity based on the transformed wave stack velocity of scanner section 50 extractions and the duplicate ratio of compressional wave stack velocity and transformed wave stack velocity according to formula (2).
The compressional wave stack velocity that 70 pairs of matching relationship determination portions calculate with carry out least error coupling from the compressional wave stack velocity of longitudinal wave earthquake data, obtain t of vertical double-pass reflection travel-time of transformed wave c0With the vertical double-pass reflection of compressional wave travel-time t p0Between matching relationship.
The device of the acquisition compressional wave of embodiment of the present invention, transformed wave geological data time match relation utilizes the two-parameter equation of transformed wave to carry out computational analysis to compressional wave, the transformed wave geological data of stratiform isotropic medium, and by two compressional wave stack velocity values that obtain are independently carried out the least error the matching analysis, thereby obtain time match relation between compressional wave, transformed wave geological data from longitudinal wave earthquake data and transformed wave geological data.
Utilize the two-parameter equation of transformed wave to realize time match between compressional wave, transformed wave geological data, reduced the difficulty of compressional wave transformed wave geological data time match, improved the precision of compressional wave transformed wave geological data time match.
Should be appreciated that and to realize a plurality of parts of the embodiment of the present invention with hardware, software, firmware or their combination.
Above-described embodiment is for helping to understand purpose of the present invention, technical scheme and beneficial effect; be understood that; the above is only the specific embodiment of the present invention; the protection domain that is not intended to limit the present invention; within the spirit and principles in the present invention all; any modification of making, be equal to replacement, improvement etc., within protection scope of the present invention all should be included in.

Claims (12)

1. method that obtains compressional wave, transformed wave geological data time match relation, the method comprises the following steps:
Steps A: the compressional wave stack velocity from the longitudinal wave earthquake data of obtaining survey region;
Step B: the span of determining the transformed wave stack velocity according to described compressional wave stack velocity, determine the span in the vertical double-pass reflection of transformed wave travel-time according to the degree of depth of the formation at target locations of described survey region and described compressional wave stack velocity, and determine the span of the duplicate ratio of compressional wave stack velocity and transformed wave stack velocity according to the span of described compressional wave stack velocity and the transformed wave stack velocity determined;
Step C: with the span of the span of described transformed wave stack velocity, described compressional wave stack velocity and the duplicate ratio of transformed wave stack velocity and the span in described transformed wave vertical double-pass reflection travel-time respectively discrete sampling be square ratio and K the vertical double-pass reflection of transformed wave travel-time value of M transformed wave stack velocity value, a N compressional wave stack velocity and transformed wave stack velocity, wherein, M, N and K are natural number;
Step D: extract the nearly geophone offset of described survey region and the transformed wave geological data of middle geophone offset, and extract all asymptotic common-conversion point gathers of the transformed wave geological data that extracts;
Step e: carry out following steps for each the asymptotic common-conversion point gather in all asymptotic common-conversion point gathers that extract:
Step e 1: square ratio and described K the vertical double-pass reflection of transformed wave travel-time value that utilize described M transformed wave stack velocity value, a described N compressional wave stack velocity and transformed wave stack velocity, calculate the transformed wave reflection hourage of each seismic trace in this asymptotic common-conversion point gather, and ask after the data acquisition sample value stack of 2L+1 sampled point before and after the transformed wave of each seismic trace in will this asymptotic common-conversion point gather reflection hourage square and cumulative the summation, to obtain the scanning calculating energy data of this asymptotic common-conversion point gather;
Step e 2: for each value in the vertical double-pass reflection of transformed wave travel-time, determine the position of the maximum value in resulting scanning calculating energy data, extract the corresponding value in position of this maximum value as the duplicate ratio of described transformed wave stack velocity and described compressional wave stack velocity and transformed wave stack velocity;
Step F is calculated the compressional wave stack velocity at corresponding conversion ripple vertical double-pass reflection travel-time value place based on the duplicate ratio of the transformed wave stack velocity of extracting and compressional wave stack velocity and transformed wave stack velocity; And
Step G, to the compressional wave stack velocity that calculates with carry out the least error coupling from the compressional wave stack velocity of longitudinal wave earthquake data, obtain the matching relationship between vertical double-pass reflection travel-time of transformed wave and the vertical double-pass reflection of compressional wave travel-time.
2. method according to claim 1, wherein, the span of described transformed wave stack velocity is:
(v’ p2/3)≤v c2≤v’ p2
Wherein, v c2Be the transformed wave stack velocity; v’ p2Be the compressional wave stack velocity of obtaining,
Wherein, the span in vertical double-pass reflection travel-time of described transformed wave is:
2 z v p 2 ′ ≤ t c 0 ≤ 4 z v p 2 ′
Wherein, t c0Be the vertical double-pass reflection of the transformed wave travel-time; Z is the degree of depth of the formation at target locations of survey region,
Wherein, the span of the duplicate ratio of compressional wave stack velocity and transformed wave stack velocity is:
1≤γ iso≤4
Wherein, γ isoDuplicate ratio for compressional wave stack velocity and transformed wave stack velocity.
3. method according to claim 1, wherein, in described step C, calculate the value of L according to following formula:
L=(0.5×T wavwlet)/dt
Wherein, T WavwletBe seismic wavelet length perdurability in the transformed wave geological data of described survey region; Dt is the discrete sampling time interval of earthquake-capturing record.
4. method according to claim 1, wherein, in described step D, extract the asymptotic common-conversion point gather of the transformed wave geological data that extracts according to following formula:
X accp = γ 0 1 + γ 0 x
Wherein, X AccpBe the horizontal range of asymptotic common transfer point apart from shot point; γ 0Be the formation at target locations velocity of longitudinal wave of survey region actual measurement and the ratio of shear wave velocity; X is that shot point is to the horizontal range of geophone station.
5. method according to claim 1, wherein, in described step e 1, calculate the transformed wave reflection hourage of each seismic trace in asymptotic common-conversion point gather according to following formula:
t c 2 = t c 0 2 + x 2 v c 2 2 - ( γ iso - 1 ) γ iso v c 2 2 × ( γ iso - 1 ) x 4 4 t c 0 2 v c 2 2 + ( γ iso - 1 ) x 2
Wherein, t cBe conversion wave reflection hourage; t c0Be the vertical double-pass reflection of the transformed wave travel-time; X is that shot point is to the horizontal range of geophone station position; v c2Be the transformed wave stack velocity; γ isoDuplicate ratio for compressional wave stack velocity and transformed wave stack velocity.
6. method according to claim 5 wherein, obtains the scanning calculating energy data of asymptotic common-conversion point gather according to following formula:
E m , n , k = 1 J Σ l = - L L ( Σ j = 1 J s j ( τ l ) ) 2
Wherein, E M, n, kExpression v c2Get m value, γ isoGet n value, t c0The scanning calculating energy value of the asymptotic common-conversion point gather when getting k value, m=1,2 ..., M, n=1,2 ..., N, k=1,2 ..., K; J is the number of all seismic traces in this asymptotic common-conversion point gather; s jl) represent the τ in the j road in this asymptotic common-conversion point gather lThe discrete value of the transformed wave earthquake that the discrete sampling time is located; τ lBe and (t cThe immediate discrete sampling time of value of+l * dt); L is integer, and span is l ∈ [L, L].
7. device that obtains compressional wave, transformed wave geological data time match relation, this device comprises:
Storage part, compressional wave stack velocity and the transformed wave geological data from the longitudinal wave earthquake data of this storage portion stores survey region;
The span determination portion, this span determination portion is determined the span of transformed wave stack velocity according to the described compressional wave stack velocity of storing in described storage part, determine the span in the vertical double-pass reflection of transformed wave travel-time according to the degree of depth of formation at target locations and described compressional wave stack velocity, and the span of the duplicate ratio of definite compressional wave stack velocity and transformed wave stack velocity;
Discrete section, the span of span, described compressional wave stack velocity and the duplicate ratio of transformed wave stack velocity of this discrete the described transformed wave stack velocity that will be determined by described span determination portion and the span in described transformed wave vertical double-pass reflection travel-time discrete sampling respectively are square ratio and K the vertical double-pass reflection of transformed wave travel-time value of M transformed wave stack velocity value, a N compressional wave stack velocity and transformed wave stack velocity, wherein, M, N and K are natural number;
Asymptotic common conversion point gathering section, extract the transformed wave geological data of nearly geophone offset and middle geophone offset in the transformed wave geological data of the survey region that this asymptotic common conversion point gathering section stores from described storage part, and extract all asymptotic common-conversion point gathers of the transformed wave geological data that extracts;
scanner section, this scanner section utilizes described M transformed wave stack velocity value, square ratio of described N compressional wave stack velocity and transformed wave stack velocity was worth with described K the vertical double-pass reflection of transformed wave travel-time, the transformed wave reflection hourage of each seismic trace of each the asymptotic common-conversion point gather in all asymptotic common-conversion point gathers that calculating is extracted by described asymptotic common conversion point gathering section, and ask after the data acquisition sample value stack with 2L+1 sampled point before and after the transformed wave of each seismic trace in described each asymptotic common-conversion point gather reflection hourage square and cumulative the summation, to obtain the scanning calculating energy data of described each asymptotic common-conversion point gather, wherein, described scanner section is determined the position of the maximum value of corresponding value of vertical double-pass reflection travel-time of each transformed wave in resulting scanning calculating energy data, extract the corresponding value in position of this maximum value as the duplicate ratio of described transformed wave stack velocity and described compressional wave stack velocity and transformed wave stack velocity,
Compressional wave stack velocity determination portion, this compressional wave stack velocity determination portion are calculated the compressional wave stack velocity at corresponding conversion ripple vertical double-pass reflection travel-time place based on the duplicate ratio of the transformed wave stack velocity of extracting and compressional wave stack velocity and transformed wave stack velocity; And
The matching relationship determination portion, this matching relationship determination portion with the compressional wave stack velocity that calculates with carry out the least error coupling from the compressional wave stack velocity of longitudinal wave earthquake data, obtain the matching relationship between vertical double-pass reflection travel-time of transformed wave and the vertical double-pass reflection of compressional wave travel-time.
8. device according to claim 7, wherein, the span of described transformed wave stack velocity is:
(v’ p2/3)≤v c2≤v’ p2
Wherein, v c2Be the transformed wave stack velocity; v' p2Be the compressional wave stack velocity of obtaining,
Wherein, the span in vertical double-pass reflection travel-time of described transformed wave is:
2 z v p 2 ′ ≤ t c 0 ≤ 4 z v p 2 ′
Wherein, t c0Be the vertical double-pass reflection of the transformed wave travel-time; Z is the degree of depth of the formation at target locations of survey region,
Wherein, the span of the duplicate ratio of compressional wave stack velocity and transformed wave stack velocity is:
1≤γ iso≤4
Wherein, γ isoDuplicate ratio for compressional wave stack velocity and transformed wave stack velocity.
9. device according to claim 7, wherein, described discrete the value of calculating L according to following formula:
L=(0.5×T wavwlet)/dt
Wherein, T WavwletSeismic wavelet length perdurability for described survey region; Dt is the discrete sampling time interval of earthquake-capturing record.
10. device according to claim 7, wherein, described asymptotic common conversion point gathering section extracts the asymptotic common-conversion point gather of the transformed wave geological data that extracts according to following formula:
X accp = γ 0 1 + γ 0 x
Wherein, X AccpBe the horizontal range distance of asymptotic common transfer point apart from shot point; γ 0Be the formation at target locations velocity of longitudinal wave of survey region actual measurement and the ratio of shear wave velocity; X is that shot point is to the horizontal range of geophone station.
11. device according to claim 7, wherein, described scanner section calculates the transformed wave reflection hourage of each seismic trace in asymptotic common-conversion point gather according to following formula:
t c 2 = t c 0 2 + x 2 v c 2 2 - ( γ iso - 1 ) γ iso v c 2 2 × ( γ iso - 1 ) x 4 4 t c 0 2 v c 2 2 + ( γ iso - 1 ) x 2
Wherein, t cBe conversion wave reflection hourage; t c0Be the vertical double-pass reflection of the transformed wave travel-time; X is that shot point is to the horizontal range of geophone station position; v c2Be the transformed wave stack velocity; γ isoDuplicate ratio for compressional wave stack velocity and transformed wave stack velocity.
12. device according to claim 11, wherein, described scanner section obtains the scanning calculating energy data of asymptotic common-conversion point gather according to following formula:
E m , n , k = 1 J Σ l = - L L ( Σ j = 1 J s j ( τ l ) ) 2
Wherein, E M, n, kExpression v c2Get m value, γ isoGet n value, t c0The scanning calculating energy value of the asymptotic common-conversion point gather when getting k value, m=1,2 ..., M, n=1,2 ..., N, k=1,2 ..., K; J is the number of all seismic traces of concentrating of this ACCP road; s jl) represent the τ in the j road in this asymptotic common-conversion point gather lThe discrete value of the transformed wave earthquake that the discrete sampling time is located; τ lBe and (t cThe immediate discrete sampling time of value of+l * dt); L is integer, and span is l ∈ [L, L].
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