CN111999770B - TTI medium conversion PS wave precise beam offset imaging method and system - Google Patents

TTI medium conversion PS wave precise beam offset imaging method and system Download PDF

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CN111999770B
CN111999770B CN202010915044.2A CN202010915044A CN111999770B CN 111999770 B CN111999770 B CN 111999770B CN 202010915044 A CN202010915044 A CN 202010915044A CN 111999770 B CN111999770 B CN 111999770B
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CN111999770A (en
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韩建光
严加永
刘志伟
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Chinese Academy of Geological Sciences
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
    • G01V1/30—Analysis
    • G01V1/301—Analysis for determining seismic cross-sections or geostructures
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
    • G01V1/36—Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
    • G01V1/362—Effecting static or dynamic corrections; Stacking
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/50—Corrections or adjustments related to wave propagation
    • G01V2210/51—Migration
    • G01V2210/512—Pre-stack
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/50—Corrections or adjustments related to wave propagation
    • G01V2210/58—Media-related
    • G01V2210/586—Anisotropic media
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/70—Other details related to processing
    • G01V2210/74—Visualisation of seismic data

Abstract

The invention discloses a TTI medium converted PS wave precise beam offset imaging method and a system, firstly, converted PS wave common shot point gather seismic record data, anisotropic medium parameters and offset ray parameters of the TTI medium to be offset imaged are obtained; accordingly, ray tracing of P waves and S waves in the TTI medium is respectively carried out; then, calculating a forward wave field of each shot point and a reverse wave field of each wave detection point; finally, imaging the forward wave field of each shot point and the reverse wave field of each wave detection point; and superposing the converted PS wave prestack depth migration profile of the TTI medium of each shot point to obtain a converted PS wave depth domain migration imaging profile of the TTI medium. The method fully considers the influence of anisotropic factors on the converted PS wave seismic wave field, can accurately offset and restore the underground structure with the TTI medium, overcomes the influence of the anisotropic factors on the converted PS wave offset, and improves the precision of the pre-stack depth offset imaging section of the converted PS wave in the acquired TTI medium.

Description

TTI medium conversion PS wave precise beam offset imaging method and system
Technical Field
The invention relates to the technical field of seismic exploration, in particular to a TTI medium conversion PS wave precise beam offset imaging method and system.
Background
Compared with single longitudinal wave seismic exploration, the combined conversion PS wave seismic data can obtain more underground medium information, and better exploration effects can be obtained for underground structure imaging, lithology estimation, fluid detection and reservoir monitoring. Because of the asymmetry of the propagation path from the source to the detector, the imaging process of converting PS waves is very difficult, and the conventional superposition process and post-stack migration means cannot obtain accurate imaging results. Although the pre-stack time migration of the converted PS wave can obtain a relatively good imaging effect, in areas with complex geological structures and large speed change, imaging errors often exist in the pre-stack time migration, and the pre-stack depth migration is an effective technical means for solving the problem of accurate imaging of the converted PS wave under the condition of the underground complex geological structures.
Seismic anisotropy exists in most sedimentary rocks in the ground, if a seismic migration method based on isotropic assumption is used for processing seismic data in anisotropic media, obvious imaging errors can be caused, and phenomena such as energy unfocusing and the like can occur in migration sections, so that subsequent seismic interpretation work can be seriously influenced. Therefore, with the increasing requirements of seismic exploration precision, it is increasingly important to consider the effects of anisotropy on seismic offset imaging. Transverse Isotropy (TI) media is a commonly used anisotropic media model in practical applications, most sedimentary rocks can be described as TI media, where TTI media with tilted symmetry axes are a general form of TI media. The technology for researching the offset in the TTI medium has important application value for eliminating the influence of anisotropy in the seismic wave propagation process and realizing high-precision imaging of complex structures. The effect of anisotropy on S-waves is more pronounced than P-waves, and anisotropy is more important and not negligible for offset imaging of converted PS-waves. At present, the research on the pre-stack time migration of the converted PS wave in an anisotropic medium is mature, but the conventional pre-stack time migration method cannot obtain an ideal converted PS wave migration imaging profile for an underground complex structure.
Disclosure of Invention
The invention aims to provide a method and a system for precisely imaging beam deflection of converted PS waves of a TTI medium, which are used for overcoming the influence of anisotropy on the deflection of the converted PS waves and improving the precision of a pre-stack depth deflection imaging section of the converted PS waves in the obtained TTI medium.
In order to achieve the above object, the present invention provides the following solutions:
a TTI media converted PS wave precise beam offset imaging method, the imaging method comprising the steps of:
acquiring converted PS wave common shot point gather seismic record data, anisotropic medium parameters and offset ray parameters of a TTI medium to be offset imaged;
according to the anisotropic medium parameters and the offset ray parameters, respectively carrying out ray tracing on P waves and S waves in a TTI medium by utilizing a two-dimensional anisotropic ray tracing equation set to obtain anisotropic Gaussian beam complex value amplitude and complex value time of the P waves emitted by each shot point and anisotropic Gaussian beam complex value amplitude and complex value time of the S waves emitted by each detection point;
constructing a forward wave field of each shot according to the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot;
according to the anisotropic Gaussian beam complex amplitude and complex time of the S wave emitted by each wave detector, carrying out reverse prolongation on the converted PS wave common-shot gather seismic record data of each shot to obtain a reverse wave field of each wave detector;
Imaging the forward wave field of each shot and the backward wave field of each detector based on the cross-correlation migration imaging condition to obtain a converted PS wave prestack depth migration profile of the TTI medium of each shot;
and superposing the converted PS wave prestack depth migration profile of the TTI medium of each shot point to obtain a converted PS wave depth domain migration imaging profile of the TTI medium.
Optionally, acquiring anisotropic medium parameters of the TTI medium to be offset imaged specifically includes:
acquiring Thomsen parameters (V) of an anisotropic media model of a TTI media to be offset imaged P0 ,V S0 Epsilon, delta); wherein V is P0 、V P0 The vertical velocities of the P-wave and S-wave, respectively, epsilon and delta being a first dimensionless factor and a second dimensionless factor representing the strength of anisotropy of the VTI medium;
according to the relation between Thomsen parameters and VTI medium elasticity parameters, the formula is utilized
Calculating VTI medium density normalization elastic matrixElastic parameter element->And->
Normalizing elasticity parameter elements in an elasticity matrix according to VTI media densityUsing Bond transformation formula->Calculating a normalized elastic matrix of the TTI medium density>Anisotropic elastic parameter element a in (a) 11 ,a 33 ,a 55 ,a 13 ,a 15 And a 35 ；
Wherein,and->Are elastic parameter elements in the normalized elastic matrix of the VTI medium density, < > >a 11 、a 12 、a 13 、a 15 、a 22 、a 23 、a 25 、a 33 、a 35 、a 44 、a 46 、a 55 、a 66 Are anisotropic elastic parameter elements theta in the TTI medium density normalized elastic matrix 0 Is the inclination of the symmetry axis of the TTI medium.
Optionally, according to the anisotropic medium parameter and the offset ray parameter, the two-dimensional anisotropic ray tracing equation set is used to respectively trace the P-wave and the S-wave rays in the TTI medium, so as to obtain an anisotropic gaussian beam complex value amplitude and a complex value time of the P-wave emitted from each shot point and an anisotropic gaussian beam complex value amplitude and a complex value time of the S-wave emitted from each detector point, which specifically includes:
solving the equation function equation by Newton's iteration methodObtaining initial first ray parameters p 10 And a third ray parameter p 30 A first component p being an initial slowness vector of a two-dimensional anisotropic ray tracing equation set 1 And a third component p 3 ；
Wherein, kappa 1 ,κ 2 ,κ 3 ,κ 4 ,κ 5 Representing the first coefficient, the second coefficient, the third coefficient, the fourth coefficient and the fifth coefficient of the equation of the program respectively,
the first component p of the initial slowness vector 1 And a third component p 3 Inputting initial ray position coordinates into a two-dimensional anisotropic ray tracing equation set, and solving the two-dimensional anisotropic ray tracing equation set by using a Dragon-Gregory tower method to obtain path information and travel time information of central rays of P waves and S waves emitted by each shot point and each detector point;
According to the path information and travel time information of the central rays of the P wave and the S wave emitted by each shot point and each wave detection point, solving an anisotropic dynamic ray equation set to obtain dynamic parameters of the central rays of the P wave and the S wave emitted by each shot point and each wave detection point;
and calculating the anisotropic Gaussian beam complex amplitude and complex time of the P wave emitted by each shot point and the anisotropic Gaussian beam complex amplitude and complex time of the S wave emitted by each detector point according to the path information, travel time information and dynamic parameters of the central rays of the P wave and the S wave emitted by each shot point.
Optionally, the constructing a forward wave field of each shot according to the anisotropic gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot specifically includes:
according to the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot point, constructing a forward wave field of each shot focus as follows:
wherein G (x, x) s ω) is shot point x s Is used for the forward wave field of (a),and->Respectively shot points x s Complex amplitude and complex time of emergent P-wave anisotropic Gaussian beam, ω is angular frequency, ++>For shot x s Emergent P-wave ray offset parameter vector, +. >Is the horizontal component of the P-wave ray offset parameter vector; />Is the vertical component of the P-wave ray offset parameter vector; x represents the position vector of any point in the subsurface.
Optionally, the reverse continuation is performed on the converted PS wave common shot gather seismic record data according to the anisotropic gaussian beam complex value amplitude and complex value time of the S wave emitted by each wave detector to obtain a reverse wave field of each wave detector, which specifically includes:
according to the anisotropic Gaussian beam complex amplitude and complex time of the S wave emitted by each wave detector, using a formulaCarrying out reverse continuation on the converted PS wave common shot point gather seismic record data of each shot to obtain a reverse wave field of each wave detection point;
wherein R (x, x) r ω) represents the detector point x r Is a reverse wave field of u PS (x r ,x s ω) is shot point x s And detector point x r Is converted from PS wave common shot gather seismic record data,and->Respectively the wave detection points x r Complex amplitude and complex time of outgoing S-wave anisotropic Gaussian beam, +.>For the detector point x r Emergent S-wave ray offset parameter vector, +.>Is the horizontal component of the S-wave ray offset parameter vector; />Offset the vertical component of the parameter vector for the S-wave ray; x represents the position vector of any point in the subsurface.
Optionally, the imaging the forward wave field and the backward wave field of the wave detection point of each gun focus based on the cross-correlation offset imaging condition to obtain a converted PS wave pre-stack depth offset section of each gun TTI medium specifically includes:
based on the cross-correlation offset imaging condition, the formula is utilized
Imaging the forward wave field of each shot and the reverse wave field of each wave detection point to obtain a converted PS wave prestack depth migration section of the TTI medium of each shot;
wherein,representing shot x s Is a PS wave shift profile; sgn (x) r -x s ) Sign function representing the phenomenon of polarity inversion correcting converted PS wave seismic recordings, +.>u PS (x r ,x s ω) is shot point x s And detector point x r Is converted from PS wave common shot gather seismic record data,>and->Respectively the wave detection points x r Complex amplitude and complex time of outgoing S-wave anisotropic Gaussian beam, +.>And->Respectively shot points x s Complex amplitude and complex time of the outgoing P-wave anisotropic Gaussian beam, i representing complex units, +.>Is the horizontal component of the P-wave ray shift parameter vector, < >>Is the horizontal component of the S-wave ray offset parameter vector; x represents the position vector of any point in the subsurface,ω is the angular frequency.
Optionally, the overlapping the converted PS-wave prestack depth migration profile of the TTI medium of each shot point to obtain a converted PS-wave depth domain migration imaging profile of the TTI medium specifically includes:
Using the formulaOverlapping the converted PS wave prestack depth migration profile of the TTI medium of each shot point to obtain a converted PS wave depth domain migration imaging profile of the TTI medium;
wherein N represents the number of shots of the converted PS wave common shot gather seismic record, I PS (x) Representing the final TTI media transition PS wave depth domain offset imaging profile, x representing the position vector of any point in the subsurface.
A TTI media converted PS wave precise beam offset imaging system, the imaging system comprising:
the parameter acquisition module is used for acquiring converted PS wave common shot point gather seismic record data, anisotropic medium parameters and offset ray parameters of the TTI medium to be imaged in an offset mode;
the ray tracing module is used for respectively carrying out ray tracing on the P wave and the S wave in the TTI medium by utilizing a two-dimensional anisotropic ray tracing equation set according to the anisotropic medium parameters and the offset ray parameters to obtain the anisotropic Gaussian beam complex value amplitude and the complex value time of the P wave emitted by each shot point and the anisotropic Gaussian beam complex value amplitude and the complex value time of the S wave emitted by each wave point;
the forward wave field construction module is used for constructing a forward wave field of each shot point according to the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot point;
The reverse wave field construction module is used for carrying out reverse continuation on the converted PS wave common shot point gather seismic record data of each shot according to the anisotropic Gaussian beam complex value amplitude and complex value time of the S wave emitted by each wave detection point to obtain a reverse wave field of each wave detection point;
the single shot point conversion PS wave pre-stack depth migration profile calculation module is used for imaging a forward wave field of each shot point and a reverse wave field of each wave detection point based on cross-correlation migration imaging conditions to obtain a conversion PS wave pre-stack depth migration profile of a TTI medium of each shot point;
and the converted PS wave depth domain migration imaging profile calculation module is used for superposing the converted PS wave prestack depth migration profile of the TTI medium of each shot point to obtain the converted PS wave depth domain migration imaging profile of the TTI medium.
Optionally, the parameter obtaining module specifically includes:
a Thomsen parameter acquisition sub-module for acquiring Thomsen parameters (V P0 ,V S0 Epsilon, delta); wherein V is P0 、V P0 The vertical velocities of the P-wave and S-wave, respectively, epsilon and delta being a first dimensionless factor and a second dimensionless factor representing the strength of anisotropy of the VTI medium;
an elastic parameter calculation sub-module of the VTI medium for utilizing a formula according to the relation between Thomsen parameters and the elastic parameters of the VTI medium Calculating VTI medium density normalization elastic matrixElastic parameter element->And->
An elastic parameter calculation sub-module of the VTI medium for normalizing elastic parameter elements in the elastic matrix according to the density of the VTI mediumUsing Bond transformation formula
Calculating a normalized elastic matrix of the TTI medium density>Anisotropic elastic parameter element a in (a) 11 ,a 33 ,a 55 ,a 13 ,a 15 And a 35 ；
Wherein,and->Are elastic parameter elements in the normalized elastic matrix of the VTI medium density, < >>a 11 、a 12 、a 13 、a 15 、a 22 、a 23 、a 25 、a 33 、a 35 、a 44 、a 46 、a 55 、a 66 Are anisotropic elastic parameter elements theta in the TTI medium density normalized elastic matrix 0 Is the inclination of the symmetry axis of the TTI medium.
Optionally, the ray tracing module specifically includes:
an initial parameter acquisition submodule of a two-dimensional anisotropic ray tracing equation set for solving a program function equation by adopting a Newton iteration methodObtaining initial first ray parameters p 10 And a third ray parameter p 30 A first component p being an initial slowness vector of a two-dimensional anisotropic ray tracing equation set 1 And a third component p 3 ；
Wherein, kappa 1 ,κ 2 ,κ 3 ,κ 4 ,κ 5 Respectively represent a first coefficient, a second coefficient, a third coefficient, a fourth coefficient anda fifth coefficient of the number of coefficients of the set,
a path information and travel time information acquisition sub-module for acquiring a first component p of an initial slowness vector 1 And a third component p 3 Inputting initial ray position coordinates into a two-dimensional anisotropic ray tracing equation set, and solving the two-dimensional anisotropic ray tracing equation set by using a Dragon-Gregory tower method to obtain path information and travel time information of central rays of P waves and S waves emitted by each shot point and each detector point;
the dynamic parameter acquisition sub-module is used for solving a dynamic ray equation set according to the path information and the travel time information of the central rays of the P wave and the S wave emitted by each shot point and each detector point to obtain dynamic parameters of the central rays of the P wave and the S wave emitted by each shot point and each detector point;
the complex value amplitude and complex value time calculation sub-module is used for calculating the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot point and the anisotropic Gaussian beam complex value amplitude and complex value time of the S wave emitted by each detector point according to the path information, the travel time information and the kinetic parameters of the central rays of the P wave and the S wave emitted by each shot point.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses a TTI medium conversion PS wave precise beam offset imaging method, which comprises the following steps: acquiring converted PS wave common shot point gather seismic record data, anisotropic medium parameters and offset ray parameters of a TTI medium to be offset imaged; according to the anisotropic medium parameters and the offset ray parameters, respectively carrying out ray tracing on P waves and S waves in a TTI medium by utilizing a two-dimensional anisotropic ray tracing equation set to obtain anisotropic Gaussian beam complex value amplitude and complex value time of the P waves emitted by each shot point and anisotropic Gaussian beam complex value amplitude and complex value time of the S waves emitted by each detection point; constructing a forward wave field of each shot according to the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot; according to the anisotropic Gaussian beam complex amplitude and complex time of the S wave emitted by each wave detector, carrying out reverse prolongation on the converted PS wave common-shot gather seismic record data of each shot to obtain a reverse wave field of each wave detector; imaging the forward wave field of each shot and the backward wave field of each detector based on the cross-correlation migration imaging condition to obtain a converted PS wave prestack depth migration profile of the TTI medium of each shot; and superposing the converted PS wave prestack depth migration profile of the TTI medium of each shot point to obtain a converted PS wave depth domain migration imaging profile of the TTI medium. The method fully considers the influence of anisotropic factors on the converted PS wave seismic wave field, can accurately offset and restore the underground structure with the TTI medium, overcomes the influence of the anisotropic factors on the converted PS wave offset, and improves the precision of the pre-stack depth offset imaging section of the converted PS wave in the acquired TTI medium.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for precisely beam-offset imaging of a TTI medium converted PS wave provided by the invention;
FIG. 2 is a schematic diagram of a horizontal layered TTI medium model provided in accordance with a embodiment of the present invention;
FIG. 3 is a diagram of a single shot converted PS wave seismic trace of a horizontal layered TTI media model provided in accordance with an embodiment of the present invention;
FIG. 4 is a single shot converted PS wave pre-stack depth migration profile of a horizontal layered TTI media model provided in accordance with an embodiment of the present invention; wherein, FIG. 4 (a) shows the offset profile of the horizontal layered TTI medium model obtained by the isotropic offset method, and FIG. 4 (b) shows the offset profile of the horizontal layered TTI medium model obtained by the method of the present invention;
FIG. 5 is a diagram of a reverse-osmosis TTI medium model provided in accordance with a second embodiment of the present invention;
FIG. 6 is a cross section of a multi-shot stacked converted PS wave pre-stack depth migration for a thrust TTI media model provided in accordance with a second embodiment of the present invention; fig. 6 (a) is a profile of offset of a reverse-flow TTI medium model obtained by the isotropic offset method, and fig. 6 (b) is a profile of offset of a reverse-flow TTI medium model obtained by the method of the present invention.
Detailed Description
The invention aims to provide a TTI medium converted PS wave accurate beam deviation imaging method and a system, which are used for overcoming the influence of anisotropy on converted PS wave deviation and improving the accuracy of a pre-stack depth deviation imaging section of converted PS waves in an obtained TTI medium.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
As shown in fig. 1, the present invention provides a TTI medium converted PS wave precise beam offset imaging method, which includes the following steps:
step 101, acquiring converted PS wave common shot gather seismic record data, anisotropic medium parameters and offset ray parameters of a TTI medium to be imaged in an offset mode.
The acquiring anisotropic parameters of the TTI medium to be offset imaged specifically comprises the following steps:
Reading Thomsen parameters (V of anisotropic media model to be offset imaged P0 ,V S0 Epsilon, delta), from the relationship between Thomsen parameters and VTI media elasticity parameters, a normalized elastic matrix of VTI media density characterized by Thomsen parameters can be obtainedElastic parameter element->The method comprises the following steps:
in the formula (1), thomsen parameter V P0 、V P0 Vertical speeds of P wave and S wave respectively, epsilon and delta are dimensionless factors representing the anisotropic strength of the VTI medium;
according to the elastic parameters of the VTI medium density normalization, obtaining a TTI medium density normalization elastic matrix through Bond transformationAnisotropic elastic parameter element a in (a) 11 ,a 33 ,a 55 ,a 13 ,a 15 ,a 35 The method specifically comprises the following steps:
in the formula (2), θ 0 Is the inclination of the symmetry axis of the TTI medium.
Wherein,and->Are elastic parameter elements in the normalized elastic matrix of the VTI medium density, < >>a 11 、a 12 、a 13 、a 15 、a 22 、a 23 、a 25 、a 33 、a 35 、a 44 、a 46 、a 55 、a 66 Are anisotropic elastic parameter elements theta in the TTI medium density normalized elastic matrix 0 Is the inclination of the symmetry axis of the TTI medium. The operation of the present invention only uses +.>And->a 11 、a 33 、a 55 、a 13 、a 15 And a 35 No calculation of other elements is required.
And 102, respectively carrying out ray tracing on the P wave and the S wave in the TTI medium by utilizing a two-dimensional anisotropic ray tracing equation set according to the anisotropic medium parameters and the offset ray parameters, and obtaining the anisotropic Gaussian complex amplitude and the complex time of the P wave emitted by each shot point and the anisotropic Gaussian complex amplitude and the complex time of the S wave emitted by each detector point.
Step 102, according to the anisotropic medium parameter and the offset ray parameter, respectively performing ray tracing of the P-wave and the S-wave in the TTI medium by using a two-dimensional anisotropic ray tracing equation set, to obtain an anisotropic gaussian beam complex value amplitude and a complex value time of the P-wave emitted from each shot point and an anisotropic gaussian beam complex value amplitude and a complex value time of the S-wave emitted from each detector point, which specifically includes:
the two-dimensional anisotropic ray tracing equation set is:
in formula (3), τ is x when traveling along the ray i (i=1, 3) is a coordinate in a rectangular coordinate system,is a component of a slowness vector, a kl ＝c kl ρ (k, l=1, 3, or 5) is the elasticity parameter normalized by the TTI medium density, +.>Is a component of the Christoffel matrix eigenvector. The two-dimensional anisotropic ray tracing equation set (formula (3)) has the same form for the P wave and the S wave in the TTI medium, and m=1 and m=2 respectively represent the P wave and the S wave;
the method for respectively realizing ray tracing of P wave and S wave in TTI medium to obtain complex value amplitude and complex value time of corresponding P wave and S wave anisotropic Gaussian beams comprises the following steps:
(a) According to the equation G of the P wave and S wave in the anisotropic medium m (x i0 ,p i0 ) =1, obtaining the corresponding waveform initial ray parameter p 10 And p 30 The following relation is satisfied:
in (4)
κ 2 ＝(a 15 a 33 -a 13 a 35 )p 10
(b) For the initial ray parameters p described in (a) 10 And p 30 Is solved by Newton's iteration method, for each initial ray parameter p 10 Acquiring corresponding initial ray parameters p 30 And then obtaining corresponding initial conditions of P-wave and S-wave anisotropic ray tracing, which are specifically as follows:
the initial conditions of the two-dimensional anisotropic ray tracing equation set are specifically:
in the formula (6), (x) 10 ,x 30 ) Is the coordinates of the ray tracing initial position, which is known for the P-wave and S-wave ray tracing;
(c) Calculating a two-dimensional anisotropic ray tracing equation set by using a Dragon-Gregory tower method according to the corresponding initial conditions of the P-wave and S-wave anisotropic ray tracing in the step (b), solving the P-wave and S-wave ray tracing in the corresponding TTI medium, and obtaining corresponding path and travel time information of the P-wave and S-wave central rays;
(d) On the P-wave and S-wave central ray paths described in (c), using an anisotropic kinetic ray equation set to calculate the kinetic parameters of the corresponding rays, specifically:
the kinetic ray equation set in the anisotropic medium is:
in the formula (7), P and Q are dynamic parameters of rays, B 1 、B 2 、B 3 Is the characteristic value G of the corresponding waveform Christoffel matrix m For the ray normal direction n and the normal direction ray parameter p n Is a derivative of (2);
(e) Based on the travel time information of the P-wave and S-wave central rays described in (c) and the dynamic parameters of the corresponding rays described in (d), complex-valued amplitude a and complex-valued time T of the corresponding P-wave and S-wave anisotropic gaussian beams are obtained, specifically:
in the formula (8), the amino acid sequence of the compound,is the initial amplitude, where V 0 Group velocity, L, of the corresponding mode of the initial position of the ray 0 Is the initial beam width, omega of the corresponding wave-type anisotropic Gaussian beam r Is the reference frequency; v is the group velocity along the ray path for the corresponding mode and n is the vertical distance from the near ray location to the central ray.
And 103, constructing a forward wave field of each shot point according to the complex amplitude and the complex time of the anisotropic Gaussian beam of the P wave emitted by each shot point.
Step 103, constructing a forward wave field of each shot according to the anisotropic gaussian beam complex value amplitude and complex value time of the P-wave emitted by each shot, which specifically includes:
reading the position coordinates of a seismic source of each shot according to the converted PS wave common shot point gather seismic records, and determining the position of the seismic source;
the forward wave field at the position of the seismic source is constructed by utilizing the P-wave anisotropic Gaussian beam emitted at the position of the seismic source, and the forward wave field at the position of the seismic source is specifically:
In the formula (9), G (x, x) s ω) is the source location x s A forward wave field at the point of the wave,and->Complex amplitude and complex time of P-wave anisotropic Gaussian beam emitted by the seismic source, wherein ω is angular frequency, ">And the P-wave ray parameter vector is emitted by the seismic source.
And 104, carrying out reverse continuation on the converted PS wave common shot gather seismic record data of each shot according to the anisotropic Gaussian beam complex amplitude and complex time of the S wave emitted by each wave detector to obtain a reverse wave field of each wave detector.
Step 104, performing reverse continuation on the converted PS wave common shot gather seismic record data of each shot according to the anisotropic gaussian beam complex value amplitude and complex value time of the S wave emitted by each wave detector to obtain a reverse wave field of each wave detector, which specifically includes:
the precise beam wave field reverse extension formula of the wave detection point is as follows:
in (10)，R(x,x r ω) represents a backward extended wave field, u PS (x r ,x s ω) is converted PS-wave co-shot gather seismic record spectrum in TTI medium,and->Respectively the wave detection points x r Complex amplitude and complex time of outgoing S-wave anisotropic Gaussian beam, +.>And the S-wave ray parameter vector is emitted by the wave detector.
Step 105, based on the cross-correlation migration imaging conditions, imaging the forward wave field of each shot and the backward wave field of each detector, and obtaining a converted PS wave pre-stack depth migration profile of the TTI medium of each shot.
The single gun converted PS wave accurate beam offset imaging formula in the TTI medium is as follows:
in the formula (11), the amino acid sequence of the compound,representing a single shot converted PS wave offset profile; using a sign function sgn (x r -x s ) Correcting the polarity inversion phenomenon of the converted PS wave seismic record, wherein the sign function satisfies the following relation:
and 106, superposing the converted PS wave prestack depth migration profile of the TTI medium of each shot point to obtain a converted PS wave depth domain migration imaging profile of the TTI medium.
Specifically, all single shot offset profiles are overlapped to obtain a converted PS wave depth domain offset imaging profile in a final TTI medium, specifically:
in the formula (13), N represents the shot number of the converted PS wave common shot point gather seismic record, I PS (x) Representing the final TTI media transition PS wave depth domain offset imaging profile.
The invention also provides a TTI medium conversion PS wave precise beam offset imaging system, which comprises:
and the parameter acquisition module is used for acquiring the converted PS wave common shot point gather seismic record data, the anisotropic medium parameters and the offset ray parameters of the TTI medium to be imaged in an offset mode.
The parameter acquisition module specifically comprises:
a Thomsen parameter acquisition sub-module for acquiring Thomsen parameters (V P0 ,V S0 Epsilon, delta); wherein V is P0 、V P0 The vertical velocities of the P-wave and S-wave, respectively, epsilon and delta are first and second dimensionless factors representing the strength of anisotropy of the VTI medium.
An elastic parameter calculation sub-module of the VTI medium for utilizing a formula according to the relation between Thomsen parameters and the elastic parameters of the VTI mediumCalculating a normalized elastic matrix of the density of the VTI medium>Elastic parameter element->And->
VTAn elastic parameter calculation sub-module of the I medium for normalizing elastic parameter elements in the elastic matrix according to the density of the VTI mediumUsing Bond transformation formula
Calculating a normalized elastic matrix of the TTI medium density>Anisotropic elastic parameter element a in (a) 11 ,a 33 ,a 55 ,a 13 ,a 15 And a 35 。
Wherein,and->Are elastic parameter elements in the normalized elastic matrix of the VTI medium density, < >>a 11 、a 12 、a 13 、a 15 、a 22 、a 23 、a 25 、a 33 、a 35 、a 44 、a 46 、a 55 、a 66 Are anisotropic elastic parameter elements theta in the TTI medium density normalized elastic matrix 0 Is the inclination of the symmetry axis of the TTI medium. The operation of the present invention only uses +.>And->a 11 、a 33 、a 55 、a 13 、a 15 And a 35 Without other elementsAnd (5) calculating.
And the ray tracing module is used for respectively carrying out ray tracing on the P wave and the S wave in the TTI medium by utilizing a two-dimensional anisotropic ray tracing equation set according to the anisotropic medium parameters and the offset ray parameters, and obtaining the anisotropic Gaussian complex amplitude and the complex time of the P wave emitted by each shot point and the anisotropic Gaussian complex amplitude and the complex time of the S wave emitted by each detection point.
The ray tracing module specifically comprises:
an initial parameter acquisition submodule of a two-dimensional anisotropic ray tracing equation set for solving a program function equation by adopting a Newton iteration methodObtaining initial first ray parameters p 10 And a third ray parameter p 30 A first component p being an initial slowness vector of a two-dimensional anisotropic ray tracing equation set 1 And a third component p 3 。
Wherein, kappa 1 ,κ 2 ,κ 3 ,κ 4 ,κ 5 Representing the first coefficient, the second coefficient, the third coefficient, the fourth coefficient and the fifth coefficient of the equation of the program respectively,
a path information and travel time information acquisition sub-module for acquiring a first component p of an initial slowness vector 1 And a third component p 3 And inputting the initial ray position coordinates into a two-dimensional anisotropic ray tracing equation set, and solving the two-dimensional anisotropic ray tracing equation set by using a Dragon-Gregory tower method to obtain the path information and travel time information of the central rays of the P wave and the S wave emitted by each shot point and each detector point.
The dynamic parameter acquisition sub-module is used for solving an anisotropic dynamic ray equation set according to the path information and the travel time information of the central rays of the P wave and the S wave emitted by each shot point and each detector point to obtain the dynamic parameters of the central rays of the P wave and the S wave emitted by each shot point and each detector point.
The complex value amplitude and complex value time calculation sub-module is used for calculating the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot point and the anisotropic Gaussian beam complex value amplitude and complex value time of the S wave emitted by each detector point according to the path information, the travel time information and the kinetic parameters of the central rays of the P wave and the S wave emitted by each shot point.
And the forward wave field construction module is used for constructing a forward wave field of each shot point according to the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot point.
And the reverse wave field construction module is used for carrying out reverse continuation on the converted PS wave common shot point gather seismic record data of each shot according to the anisotropic Gaussian beam complex value amplitude and complex value time of the S wave emitted by each wave detection point to obtain a reverse wave field of each wave detection point.
And the single shot point conversion PS wave pre-stack depth migration profile calculation module is used for imaging the forward wave field of each shot point and the reverse wave field of each wave detection point based on the cross-correlation migration imaging condition to obtain the conversion PS wave pre-stack depth migration profile of the TTI medium of each shot point.
And the converted PS wave depth domain migration imaging profile calculation module is used for superposing the converted PS wave prestack depth migration profile of the TTI medium of each shot point to obtain the converted PS wave depth domain migration imaging profile of the TTI medium.
The first embodiment is as follows:
FIG. 2 is a model of a horizontal layered TTI medium provided by the invention, the model anisotropy parameters are shown in FIG. 2, the model grid is 301 x 301, and the longitudinal and transverse grid spacing is 10m. A single explosion source (shot point) is arranged in the middle of the surface of the model, the source wavelet is Ricker wavelet, the main frequency is 30Hz, the sampling time of the seismic record is set to be 3s, and the sampling interval is 2ms. And adopting a middle blasting two-side receiving observation system, wherein the track interval is 10m. FIG. 3 is a single shot converted PS wave seismic record of the horizontal layered TTI media model shown in FIG. 2, and the polarity inversion of the converted PS wave can be clearly seen from FIG. 3. Fig. 4 is a single shot converted PS wave pre-stack depth migration profile of the horizontal layered TTI media model shown in fig. 2, wherein fig. 4 (a) is a migration profile obtained using an isotropic migration method and fig. 4 (b) is a migration profile obtained using the method of the present invention. It can be seen from fig. 4 (a) that the isotropic migration method cannot accurately restore the reflective interface in the model, and there is a significant imaging error in the profile, due to neglecting the effects of anisotropy. It can be seen from fig. 4 (b) that the method of the present invention can fully homing the reflective interface, resulting in an accurate offset imaging profile. The effectiveness of the method is verified by carrying out a single shot converted PS wave offset test on the horizontal layered TTI medium model.
The second embodiment is as follows:
FIG. 5 shows a model of a reverse-impact TTI medium provided by the invention, wherein the anisotropic parameters of the model are shown in FIG. 5, the model grid is 401 x 201, the longitudinal and transverse grid intervals are 10m, and the model has a reverse-impact rock slice structure with different symmetrical axis dip angles. 77 explosion seismic sources are arranged on the surface of the model, the gun spacing is 50m, the seismic source wavelets are Ricker wavelets with the main frequency of 25Hz, each gun receives 401 channels, and the channel spacing is 10m. Fig. 6 is a multi-shot stacked converted PS wave pre-stack depth migration profile of the thrust TTI media model shown in fig. 5, wherein fig. 6 (a) is a migration profile obtained using an isotropic migration method and fig. 6 (b) is a migration profile obtained using the method of the present invention. It can be seen from fig. 6 that for the isotropic offset profile shown in fig. 6 (a), the horizontal interface imaging underlying the thrust rock slice configuration is lifted upwards, the inclined interface imaging location in the thrust rock slice configuration is inaccurate, and there is significant divergent energy and strong noise interference near the reflective interface, as shown by the arrows in fig. 6 (a). As can be seen from FIG. 6 (b), the method of the present invention obtains accurate focusing imaging for the reverse-flow TTI medium model, and eliminates noise interference, and compared with the isotropic migration imaging effect shown in FIG. 6 (a), the method of the present invention has obvious improvement, and further verifies that the method of the present invention is an accurate and effective migration method suitable for converting PS wave seismic data by the TTI medium.
The invention comprises the following steps: acquiring TTI medium conversion PS wave common shot point gather seismic record data, TTI medium anisotropic parameters and offset ray parameters; realizing ray tracing of P wave and S wave in the TTI medium, and obtaining complex value amplitude and complex value time of corresponding P wave and S wave anisotropic Gaussian beams; constructing a forward wave field at each gun focus by using the obtained P-wave anisotropic Gaussian beam complex value amplitude and complex value time; reverse extension is carried out on the PS wave seismic record converted by each gun TTI medium, and the accurate beam reverse extension wave field of each gun corresponding to the wave detection point is obtained; imaging the forward wave field of each gun focus and the backward wave field of the wave detection point to obtain a pre-stack depth migration section of the converted PS wave of each gun TTI medium; and superposing all the single shot migration profiles to obtain a converted PS wave depth domain migration imaging profile in the final TTI medium. By adopting the method, the influence of anisotropy on the shift of the converted PS wave can be effectively solved, and the high-precision pre-stack depth shift imaging profile of the converted PS wave in the TTI medium can be obtained.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
1) The invention fully considers the influence of anisotropic factors on converting the PS wave seismic wave field, and can accurately offset and restore the underground structure with TTI medium; 2) The method is not limited by the strength of the anisotropy, and is suitable for strong anisotropic media; 3) The invention adopts an accurate beam reverse extension wave field formula, does not perform approximate processing in the wave field extension calculation process, and can obtain a high-precision converted PS wave offset imaging section; 4) The method is not limited by an observation system, and is suitable for irregularly acquired converted PS wave seismic data; 5) The invention can be widely used in the field of converted PS wave seismic exploration, and has more obvious imaging effect on complex structures with anisotropic media.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other.
The principles and embodiments of the present invention have been described herein with reference to specific examples, which are intended to be only illustrative of the methods and concepts underlying the invention, and not all examples are intended to be within the scope of the invention as defined by the appended claims.

Claims (4)

1. A TTI media converted PS wave precise beam offset imaging method, the imaging method comprising the steps of:
acquiring converted PS wave common shot point gather seismic record data, anisotropic medium parameters and offset ray parameters of a TTI medium to be offset imaged;
according to the anisotropic medium parameters and the offset ray parameters, respectively carrying out ray tracing on P waves and S waves in a TTI medium by utilizing a two-dimensional anisotropic ray tracing equation set to obtain anisotropic Gaussian beam complex value amplitude and complex value time of the P waves emitted by each shot point and anisotropic Gaussian beam complex value amplitude and complex value time of the S waves emitted by each detection point;
Constructing a forward wave field of each shot according to the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot;
according to the anisotropic Gaussian beam complex amplitude and complex time of the S wave emitted by each wave detector, carrying out reverse prolongation on the converted PS wave common-shot gather seismic record data of each shot to obtain a reverse wave field of each wave detector;
imaging the forward wave field of each shot and the backward wave field of each detector based on the cross-correlation migration imaging condition to obtain a converted PS wave prestack depth migration profile of the TTI medium of each shot;
overlapping the converted PS wave prestack depth migration profile of the TTI medium of each shot point to obtain a converted PS wave depth domain migration imaging profile of the TTI medium;
the method for acquiring the anisotropic medium parameters of the TTI medium to be offset imaged specifically comprises the following steps:
acquiring Thomsen parameters (V) of an anisotropic media model of a TTI media to be offset imaged P0 ,V S0 Epsilon, delta); wherein V is P0 、V S0 Respectively P waveAnd the vertical velocity of the S-wave, epsilon and delta being a first dimensionless factor and a second dimensionless factor representing the strength of anisotropy of the VTI medium;
according to the relation between Thomsen parameters and VTI medium elasticity parameters, the formula is utilized
Calculating VTI medium density normalization elastic matrixElastic parameter element in (a)And->
Normalizing elasticity parameter elements in an elasticity matrix according to VTI media densityUsing Bond transformation formula->Calculating a normalized elastic matrix of the TTI medium density>Anisotropic elastic parameter element a in (a) 11 ,a 33 ,a 55 ,a 13 ,a 15 And a 35 ；
Wherein,and->Are elastic parameter elements in the normalized elastic matrix of the VTI medium density, < >>a 11 、a 12 、a 13 、a 15 、a 22 、a 23 、a 25 、a 33 、a 35 、a 44 、a 46 、a 55 、a 66 Are anisotropic elastic parameter elements in the TTI medium density normalized elastic matrix, and theta 0 is the symmetrical axis inclination angle of the TTI medium;
according to the anisotropic medium parameter and the offset ray parameter, the two-dimensional anisotropic ray tracing equation set is utilized to respectively trace the P wave and the S wave in the TTI medium to obtain the anisotropic Gaussian beam complex value amplitude and the complex value time of the P wave emitted by each shot point and the anisotropic Gaussian beam complex value amplitude and the complex value time of the S wave emitted by each detector point, and the method specifically comprises the following steps:
solving the equation function equation by Newton's iteration methodObtaining initial first ray parameters p 10 And a third ray parameter p 30 A first component p being an initial slowness vector of a two-dimensional anisotropic ray tracing equation set 1 And a third component p 3 ；
Wherein, kappa 1 ,κ 2 ,κ 3 ,κ 4 ,κ 5 Respectively, the first coefficient, the second coefficient, the third coefficient, the fourth coefficient and the fifth coefficient of the equation of the program,
The first component p of the initial slowness vector 1 And a third component p 3 Inputting the initial ray position coordinates into a two-dimensional anisotropic ray tracing equation set, and solving the two-dimensional anisotropic ray tracing equation set by using a Dragon-Gregory tower method to obtain each shot point and each detectionThe path information and travel time information of the central rays of the P wave and the S wave emitted by the point;
according to the path information and travel time information of the central rays of the P wave and the S wave emitted by each shot point and each wave detection point, solving an anisotropic dynamic ray equation set to obtain dynamic parameters of the central rays of the P wave and the S wave emitted by each shot point and each wave detection point;
according to the path information, travel time information and dynamic parameters of the central rays of the P wave and the S wave emitted by each shot point and each detector point, the anisotropic Gaussian beam complex amplitude and complex time of the P wave emitted by each shot point and the anisotropic Gaussian beam complex amplitude and complex time of the S wave emitted by each detector point are calculated, specifically:
in the method, in the process of the invention,is the initial amplitude, where V 0 Group velocity, L, of the corresponding mode of the initial position of the ray 0 Is the initial beam width, omega of the corresponding wave-type anisotropic Gaussian beam r Is the reference frequency; v is the group velocity of the corresponding wave pattern along the ray path, n is the vertical distance from the position near the ray to the central ray, P and Q are the dynamic parameters of the ray, A is the complex amplitude of the anisotropic Gaussian beam, and T is the complex time of the anisotropic Gaussian beam;
The construction of the forward wave field of each shot point according to the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot point specifically comprises the following steps:
according to the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot point, constructing a forward wave field of each shot focus as follows:
wherein G (x, x) s ω) is shot point x s Is used for the forward wave field of (a),and->Respectively shot points x s Complex amplitude and complex time of emergent P-wave anisotropic Gaussian beam, ω is angular frequency, ++>For shot x s Emergent P-wave ray offset parameter vector, +.>Is the horizontal component of the P-wave ray offset parameter vector; />Is the vertical component of the P-wave ray offset parameter vector; x represents a position vector of any point underground, and i is a complex unit;
the method comprises the steps of carrying out reverse continuation on the converted PS wave common shot gather seismic record data of each shot according to the anisotropic Gaussian beam complex amplitude and complex time of the S wave emitted by each wave detector to obtain a reverse wave field of each wave detector, and specifically comprises the following steps:
according to the anisotropic Gaussian beam complex amplitude and complex time of the S wave emitted by each wave detector, using a formulaCarrying out reverse continuation on the converted PS wave common shot point gather seismic record data of each shot to obtain a reverse wave field of each wave detection point;
Wherein R (x, x) r ω) represents the detector point x r Is a reverse wave field of u PS (x r ,x s ω) is shot point x s And detector point x r PS wave conversion co-cannonThe point gather seismic record data,and->Respectively the wave detection points x r Complex amplitude and complex time of outgoing S-wave anisotropic Gaussian beam, +.>For the detector point x r Emergent S-wave ray offset parameter vector, +.>Is the horizontal component of the S-wave ray offset parameter vector; />Offset the vertical component of the parameter vector for the S-wave ray; x represents a position vector of any point in the ground, i is a complex unit, and ω is an angular frequency.
2. The TTI medium converted PS wave precise beam offset imaging method according to claim 1, wherein the imaging of the forward wave field of each shot and the backward wave field of each detector based on the cross-correlation offset imaging condition, to obtain a converted PS wave prestack depth offset profile of the TTI medium of each shot, specifically comprises:
based on the cross-correlation offset imaging condition, the formula is utilized
Imaging the forward wave field of each shot and the reverse wave field of each wave detection point to obtain a converted PS wave prestack depth migration section of the TTI medium of each shot;
wherein,representing shot x s Is a PS wave shift profile; sgn (x) r -x s ) Sign function representing the phenomenon of polarity inversion correcting converted PS wave seismic recordings, +.>u PS (x r ,x s ω) is shot point x s And detector point x r Is converted from PS wave common shot gather seismic record data,>and->Respectively the wave detection points x r Complex amplitude and complex time of outgoing S-wave anisotropic Gaussian beam, +.>And->Respectively shot points x s Complex amplitude and complex time of the outgoing P-wave anisotropic Gaussian beam, i representing complex units, +.>Is the horizontal component of the P-wave ray shift parameter vector, < >>For the horizontal component of the S-wave ray shift parameter vector, x represents the position vector of any point in the subsurface, and ω is the angular frequency.
3. The TTI medium converted PS wave precise beam offset imaging method according to claim 2, wherein the superimposing the converted PS wave prestack depth offset profile of the TTI medium of each shot to obtain the converted PS wave depth domain offset imaging profile of the TTI medium specifically comprises:
using the formulaOverlapping the converted PS wave prestack depth migration profile of the TTI medium of each shot point to obtain a converted PS wave depth domain migration imaging profile of the TTI medium;
wherein N represents the number of shots of the converted PS wave common shot gather seismic record, I PS (x) Representing the final TTI media transition PS wave depth domain offset imaging profile, x representing the position vector of any point in the subsurface.
4. A TTI media converted PS wave precise beam offset imaging system, the imaging system comprising:
the parameter acquisition module is used for acquiring converted PS wave common shot point gather seismic record data, anisotropic medium parameters and offset ray parameters of the TTI medium to be imaged in an offset mode;
the ray tracing module is used for respectively carrying out ray tracing on the P wave and the S wave in the TTI medium by utilizing a two-dimensional anisotropic ray tracing equation set according to the anisotropic medium parameters and the offset ray parameters to obtain the anisotropic Gaussian beam complex value amplitude and the complex value time of the P wave emitted by each shot point and the anisotropic Gaussian beam complex value amplitude and the complex value time of the S wave emitted by each wave point;
the forward wave field construction module is used for constructing a forward wave field of each shot point according to the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot point;
the reverse wave field construction module is used for carrying out reverse continuation on the converted PS wave common shot point gather seismic record data of each shot according to the anisotropic Gaussian beam complex value amplitude and complex value time of the S wave emitted by each wave detection point to obtain a reverse wave field of each wave detection point;
the single shot point conversion PS wave pre-stack depth migration profile calculation module is used for imaging a forward wave field of each shot point and a reverse wave field of each wave detection point based on cross-correlation migration imaging conditions to obtain a conversion PS wave pre-stack depth migration profile of a TTI medium of each shot point;
The converted PS wave depth domain migration imaging profile calculation module is used for superposing converted PS wave prestack depth migration profiles of the TTI medium of each shot point to obtain converted PS wave depth domain migration imaging profiles of the TTI medium;
the parameter acquisition module specifically comprises:
a Thomsen parameter acquisition sub-module for acquiring Thomsen parameters (V P0 ,V S0 Epsilon, delta); wherein V is P0 、V P0 The vertical velocities of the P-wave and S-wave, respectively, epsilon and delta being a first dimensionless factor and a second dimensionless factor representing the strength of anisotropy of the VTI medium;
an elastic parameter calculation sub-module of the VTI medium for utilizing a formula according to the relation between Thomsen parameters and the elastic parameters of the VTI mediumCalculating a normalized elastic matrix of the density of the VTI medium>Elastic parameter element->And->
An elastic parameter calculation sub-module of the VTI medium for normalizing elastic parameter elements in the elastic matrix according to the density of the VTI mediumUsing Bond transformation formula
Calculating a normalized elastic matrix of the TTI medium density>Anisotropic elastic parameter element a in (a) 11 ,a 33 ,a 55 ,a 13 ,a 15 And a 35 ；
Wherein,and->Are elastic parameter elements in the normalized elastic matrix of the VTI medium density, < >>a 11 、a 12 、a 13 、a 15 、a 22 、a 23 、a 25 、a 33 、a 35 、a 44 、a 46 、a 55 、a 66 Are anisotropic elastic parameter elements in the TTI medium density normalized elastic matrix, and theta 0 is the symmetrical axis inclination angle of the TTI medium;
The ray tracing module specifically comprises:
an initial parameter acquisition submodule of a two-dimensional anisotropic ray tracing equation set for solving a program function equation by adopting a Newton iteration methodObtaining initial first ray parameters p 10 And a third ray parameter p 30 A first component p being an initial slowness vector of a two-dimensional anisotropic ray tracing equation set 1 And a third component p 3 ；
Wherein, kappa 1 ,κ 2 ,κ 3 ,κ 4 ,κ 5 Respectively represent the first coefficients of the equation,A second coefficient, a third coefficient, a fourth coefficient, and a fifth coefficient,
a path information and travel time information acquisition sub-module for acquiring a first component p of an initial slowness vector 1 And a third component p 3 Inputting initial ray position coordinates into a two-dimensional anisotropic ray tracing equation set, and solving the two-dimensional anisotropic ray tracing equation set by using a Dragon-Gregory tower method to obtain path information and travel time information of central rays of P waves and S waves emitted by each shot point and each detector point;
the dynamic parameter acquisition sub-module is used for solving an anisotropic dynamic ray equation set according to the path information and the travel time information of the central rays of the P wave and the S wave emitted by each shot point and each detector point to obtain dynamic parameters of the central rays of the P wave and the S wave emitted by each shot point and each detector point;
The complex value amplitude and complex value time calculation sub-module is used for calculating the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot point and the anisotropic Gaussian beam complex value amplitude and complex value time of the S wave emitted by each detector point according to the path information, travel time information and dynamic parameters of the central rays of the P wave and the S wave emitted by each shot point, and specifically comprises the following steps:
in the method, in the process of the invention,is the initial amplitude, where V 0 Group velocity, L, of the corresponding mode of the initial position of the ray 0 Is the initial beam width, omega of the corresponding wave-type anisotropic Gaussian beam r Is the reference frequency; v is the group velocity of the corresponding mode along the ray path, n is the vertical distance from the near-ray location to the central ray, P and Q are the ray dynamics parameters, A is eachComplex amplitude of the anisotropic gaussian beam, T is the complex time of the anisotropic gaussian beam;
the construction of the forward wave field of each shot point according to the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot point specifically comprises the following steps:
according to the anisotropic Gaussian beam complex value amplitude and complex value time of the P wave emitted by each shot point, constructing a forward wave field of each shot focus as follows:
wherein G (x, x) s ω) is shot point x s Is used for the forward wave field of (a),and->Respectively shot points x s Complex amplitude and complex time of emergent P-wave anisotropic Gaussian beam, ω is angular frequency, ++>For shot x s Emergent P-wave ray offset parameter vector, +.>Is the horizontal component of the P-wave ray offset parameter vector; />Is the vertical component of the P-wave ray offset parameter vector; x represents a position vector of any point underground, and i is a complex unit;
the method comprises the steps of carrying out reverse continuation on the converted PS wave common shot gather seismic record data of each shot according to the anisotropic Gaussian beam complex amplitude and complex time of the S wave emitted by each wave detector to obtain a reverse wave field of each wave detector, and specifically comprises the following steps:
according to the anisotropic Gaussian beam complex amplitude and complex time of the S wave emitted by each wave detector, using a formulaCarrying out reverse continuation on the converted PS wave common shot point gather seismic record data of each shot to obtain a reverse wave field of each wave detection point;
wherein R (x, x) r ω) represents the detector point x r Is a reverse wave field of u PS (x r ,x s ω) is shot point x s And detector point x r Is converted from PS wave common shot gather seismic record data,and->Respectively the wave detection points x r Complex amplitude and complex time of outgoing S-wave anisotropic Gaussian beam, +.>For the detector point x r Emergent S-wave ray offset parameter vector, +.>Is the horizontal component of the S-wave ray offset parameter vector; />Offset the vertical component of the parameter vector for the S-wave ray; x represents a position vector of any point in the ground, i is a complex unit, and ω is an angular frequency.
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