CN112034520B - Anisotropic medium dynamic focusing beam offset imaging method and system - Google Patents

Anisotropic medium dynamic focusing beam offset imaging method and system Download PDF

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CN112034520B
CN112034520B CN202010921448.2A CN202010921448A CN112034520B CN 112034520 B CN112034520 B CN 112034520B CN 202010921448 A CN202010921448 A CN 202010921448A CN 112034520 B CN112034520 B CN 112034520B
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刘强
李振春
张敏
崔立杰
张凯
徐学成
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China University of Petroleum East China
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28Processing seismic data, e.g. for interpretation or for event detection
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    • G01V1/306Analysis for determining physical properties of the subsurface, e.g. impedance, porosity or attenuation profiles
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28Processing seismic data, e.g. for interpretation or for event detection
    • G01V1/36Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
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    • G01MEASURING; TESTING
    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
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    • G01V2210/50Corrections or adjustments related to wave propagation
    • G01V2210/51Migration
    • G01V2210/512Pre-stack
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    • G01MEASURING; TESTING
    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
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    • G01V2210/626Physical property of subsurface with anisotropy
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    • G01MEASURING; TESTING
    • G01VGEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
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Abstract

The invention discloses an anisotropic medium dynamic focusing beam offset imaging method and system. An anisotropic medium ray tracing algorithm based on a Cartesian coordinate system is provided by deducing a kinematics and dynamics ray tracing equation, the kinematics and dynamics ray tracing equation is introduced into offset imaging, a Gaussian beam propagation operator is modified into a dynamic focusing beam propagation operator, and an anisotropic dynamic focusing beam offset method based on the Cartesian coordinate system is provided. The imaging method and the imaging system provided by the invention can better keep the form and the energy of the ray beam in propagation, improve the imaging effect of the medium-deep layer under the condition of not reducing the imaging quality of the shallow layer, and are favorable for eliminating the influence of the initial beam width in the conventional Gaussian beam offset on offset imaging. The imaging method and the imaging system provided by the invention can solve the problem of complex anisotropic medium structure imaging and provide a solution for the exploration problem of deep geological targets.

Description

Anisotropic medium dynamic focusing beam offset imaging method and system
Technical Field
The invention relates to the field of seismic data processing, in particular to an anisotropic medium dynamic focusing beam migration imaging method and system.
Background
Seismic migration imaging, one of three seismic processing techniques, plays an important role in oil and gas exploration. In the traditional geophysical research, the earth medium is assumed to be isotropic, the earth medium is usually anisotropic, and the isotropic migration algorithm adopted in the anisotropic medium can cause the problems of inaccurate migration imaging homing, incomplete diffracted wave convergence, unfocused energy and the like, so that the follow-up work of seismic data interpretation, reservoir prediction, oil reservoir description and the like is influenced. Therefore, there is a need to develop anisotropic medium migration imaging methods to provide more reliable seismic imaging profile data for oil and gas exploration.
Disclosure of Invention
The invention aims to provide an anisotropic medium dynamic focusing beam offset imaging method and system to eliminate the influence of initial beam width on offset imaging in conventional Gaussian beam offset and improve the imaging effect of a deep anisotropic medium complex geological structure.
In order to achieve the purpose, the invention provides the following scheme:
an anisotropic media dynamic focused beam shift imaging method, comprising:
acquiring an initial velocity field, an anisotropic medium anisotropy parameter field and an anisotropic medium seismic record; the initial velocity field is used for acquiring velocity information required in ray tracing; the anisotropic parameter field of the anisotropic medium is used for acquiring anisotropic parameter information required in ray tracing; the anisotropic medium seismic record is used for acquiring total travel time equal wave field information from a seismic source to a wave detection point;
determining phase velocity, group velocity and phase slowness according to the velocity information, the anisotropic parameter information and the emergent ray phase velocity angle information; determining a kinematic ray tracing equation in the anisotropic medium and an anisotropic medium dynamic ray tracing equation based on a Cartesian coordinate system according to the phase velocity, the group velocity, the phase slowness and the travel time information;
determining the travel time and path information of the central ray according to the kinematic ray tracing equation in the anisotropic medium based on the Cartesian coordinate system;
determining a dynamic ray parameter of a complex value according to the anisotropic medium dynamic ray tracing equation based on the Cartesian coordinate system;
determining the amplitude of a dynamic focusing beam according to the ray path, the dynamic ray parameters of the complex value, the initial velocity field and the anisotropic parameter field of the anisotropic medium, and expressing a seismic source displacement wave field by using the dynamic focusing beam;
determining an imaging value corresponding to single-shot seismic data by utilizing the dynamic focusing beam displacement wave field based on the forward continuation of the seismic source displacement wave field and the backward continuation of the wave field at the wave detecting point; the imaging value is obtained by performing cross correlation on a forward continuation wave field of the seismic source and a reverse continuation wave field of the wave detection point;
and performing superposition calculation on imaging values corresponding to all the single-shot seismic data, and determining an anisotropic medium dynamic focusing beam migration imaging result.
Optionally, determining an anisotropic medium kinematic ray tracing equation based on a cartesian coordinate system and an anisotropic medium kinematic ray tracing equation based on the cartesian coordinate system according to the phase velocity, the group velocity, and the phase slowness specifically includes:
according to the formula
Figure BDA0002666882100000021
Determining a kinematic ray tracing equation in an anisotropic medium; wherein, UiRepresenting the propagation direction of the energy flow for a group velocity i component in a Cartesian coordinate system (i is 1 and 3); t is travel time; x is the number ofiAre coordinates in a cartesian coordinate system; p is a radical ofiIs the slowness; etaiIs the component of the time derivative of slowness in a Cartesian coordinate system;
according to the formula dQi/dT=AijQj+BijPj、dPi/dT=CijQj+DijPjDetermining an anisotropic medium dynamic ray tracing equation based on a Cartesian coordinate system; wherein Q isi,Qj,PiAnd PjKinetic ray parameters representing complex values; i is 1, 3; j is 1, 3; a. theij,Bij,Cij,DijRepresenting the corresponding calculation coefficients, respectively:
Figure BDA0002666882100000022
Figure BDA0002666882100000023
optionally, determining a seismic source displacement wave field according to the ray path, the complex-valued dynamic ray parameter, the initial velocity field, and the anisotropic medium anisotropy parameter field, and representing the seismic source displacement wave field by using a dynamic focused beam, specifically including:
using formulas
Figure BDA0002666882100000031
Determining a seismic source displacement wave field; wherein v (r) is the phase velocity at the position r of the calculated point, v (r ') is the phase velocity at the position r' of the ray exit point, omega is the angular frequency, r 'represents the position of the ray exit point, and p' represents the slowness vector at the ray exit point; q1(r ') is the corresponding complex-valued kinetic ray-tracing parameter for the plane wave at the exit point r', Q1(r) is a kinetic ray tracing parameter, Q, obtained under the initial strip of the plane wave at the position r of the calculated point2(r) calculating the dynamic ray tracing parameters obtained by the initial conditions of the point source wave field at the point position r; epsilon (r) is a complex value parameter corresponding to the dynamic focusing beam, and tau (r) is the travel time of the central ray at r; m (r) is the second partial derivative of the travel time at r with respect to the ray center coordinate system coordinate q, qTRepresenting the transpose of q.
Optionally, the determining, based on the seismic source displacement wave field forward continuation, the wave field backward continuation received at the wave detection point, and the imaging value corresponding to the single-shot seismic data by using the dynamic focus beam displacement wave field specifically includes:
determining a displacement vector caused by the seismic source at r' received at the q point by using the dynamic focusing beam;
determining a wave field of forward continuation of the dynamic focusing beam and a wave field of reverse continuation of the dynamic focusing beam according to the displacement vector;
determining a displacement wave field after the forward continuation of the anisotropic medium according to the wave field of the forward continuation of the dynamic focusing beam;
determining the displacement of the backward continuation emergent from the center of the detection point beam according to the wave field of the backward continuation of the dynamic focusing beam;
and determining an imaging value corresponding to the single-shot seismic data according to the wave field after the forward continuation of the anisotropic medium and the wave field after the backward continuation by utilizing a cross-correlation imaging condition.
An anisotropic media dynamic focused beam offset imaging system, comprising:
the parameter acquisition module is used for acquiring an initial velocity field, an anisotropic parameter field and an anisotropic medium seismic record; the initial velocity field is used for acquiring velocity information required in ray tracing; the anisotropy parameter field is used for acquiring anisotropy parameter information required in ray tracing; the anisotropic medium seismic record is used for acquiring total travel time equal wave field information from a seismic source to a wave detection point;
the ray tracing equation determining module is used for determining phase velocity, group velocity and phase slowness according to the velocity information, the anisotropic parameter information and ray emergent phase velocity angle information; the system comprises a Cartesian coordinate system-based kinematic ray tracing equation and an anisotropic medium dynamic ray tracing equation, wherein the Cartesian coordinate system-based kinematic ray tracing equation and the anisotropic medium dynamic ray tracing equation are used for determining the anisotropic medium according to the phase velocity, the group velocity, the phase slowness and the anisotropic parameter field information;
the central ray travel time and path determining module is used for determining the travel time and path of the central ray according to the kinematic ray tracing equation in the anisotropic medium based on the Cartesian coordinate system;
the dynamic ray parameter determination module is used for determining a complex dynamic ray parameter according to the anisotropic medium dynamic ray tracing equation based on the Cartesian coordinate system;
the seismic source displacement wave field determining module is used for determining a seismic source displacement wave field according to the ray path, the complex-valued dynamic ray parameters, the initial velocity field and the anisotropic parameter field and representing the seismic source displacement wave field by using a dynamic focusing beam;
the single-shot imaging value determining module is used for determining an imaging value corresponding to single-shot seismic data by utilizing the dynamic focusing beam displacement wave field based on the forward continuation of the seismic source displacement wave field and the backward continuation of the wave field at the wave detecting point; the imaging value is obtained by performing cross correlation on a forward continuation wave field of the seismic source and a reverse continuation wave field of the wave detection point;
and the anisotropic medium dynamic focusing beam migration imaging result determining module is used for performing superposition calculation on the imaging values corresponding to all the single-shot seismic data and determining the anisotropic medium dynamic focusing beam migration imaging result.
Optionally, the ray tracing equation determining module specifically includes:
an anisotropic medium kinematic ray tracing equation determination unit based on Cartesian coordinate system and used for determining the anisotropic medium kinematic ray tracing equation according to the formula
Figure BDA0002666882100000041
Determining a kinematic ray tracing equation in an anisotropic medium; wherein, UiRepresenting the propagation direction of the energy flow for a group velocity i component in a Cartesian coordinate system (i is 1 and 3); t is travel time; x is a radical of a fluorine atomiAre coordinates in a cartesian coordinate system; p is a radical ofiIs the slowness; etaiIs the component of the time derivative of slowness in a Cartesian coordinate system;
an anisotropic medium dynamics ray tracing equation determination unit based on Cartesian coordinate system for determining the equation dQ according to the formulai/dT=AijQj+BijPj、dPi/dT=CijQj+DijPjDetermining an anisotropic medium dynamic ray tracing equation based on a Cartesian coordinate system; wherein Qi,Qj,PiAnd PjKinetic ray parameters representing complex values; i is 1, 3; j is 1, 3; a. theij,Bij,Cij,DijRepresenting the corresponding calculation coefficients, respectively:
Figure BDA0002666882100000042
Figure BDA0002666882100000043
optionally, the seismic source displacement wavefield determination module specifically includes:
seismic source displacement wave field determination unit for using formula
Figure BDA0002666882100000051
Determining a seismic source displacement wave field; wherein v (r) is the phase velocity at the position r of the calculated point, v (r ') is the phase velocity at the position r ' of the ray exit point, omega is the angular frequency, and r ' representsThe position of the ray exit point, p' represents the slowness vector at the ray exit point; q1(r ') is the corresponding complex-valued kinetic ray-tracing parameter for the plane wave at the exit point r', Q1(r) is a kinetic ray tracing parameter, Q, obtained under the initial strip of the plane wave at the position r of the calculated point2(r) calculating the dynamic ray tracing parameters obtained by the initial conditions of the point source wave field at the point position r; epsilon (r) is a complex value parameter corresponding to the dynamic focusing beam, and tau (r) is the travel time of the central ray at r; m (r) is the second partial derivative of the travel time at r with respect to the ray center coordinate system coordinate q, qTRepresenting the transpose of q.
Optionally, the determining, based on the forward continuation of the seismic source displacement wave field and the backward continuation of the wave detection point, an imaging value corresponding to the single-shot seismic data by using the dynamic focusing beam specifically includes:
the displacement vector determining unit is used for determining a displacement vector received at the r point and caused by the seismic source at the r' position by using the dynamic focusing beam;
the dynamic focusing beam forward continuation wave field and reverse continuation displacement field determining unit is used for determining the dynamic focusing beam forward continuation wave field and the dynamic focusing beam reverse continuation displacement wave field according to the displacement vector;
and the imaging value determining unit corresponding to the single-shot seismic data is used for determining the imaging value corresponding to the single-shot seismic data according to the anisotropic medium reverse continuation displacement wave field and the forward continuation displacement wave field by utilizing the cross-correlation imaging condition.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides a method and a system for imaging anisotropic medium dynamic focused beam offset, which realize the dynamic focused beam Gaussian beam offset in an anisotropic medium by using an anisotropic medium ray tracing equation based on phase velocity, group velocity and phase slowness; the method can better keep the beam shape and energy in propagation, and improve the imaging effect of the middle and deep layers under the condition of not reducing the imaging quality of the shallow layer, which is favorable for solving the problem of poor compatibility of the imaging quality of the shallow layer and the middle and deep layers in the conventional Gaussian beam deviation.
Compared with an isotropic method, the anisotropic medium dynamic focusing beam offset imaging method and system provided by the invention can enable the reflected wave of the complex anisotropic medium to be accurately returned, the diffracted wave is better converged, and the energy is more focused. Compared with the traditional anisotropic medium Gaussian beam deflection based on elastic parameters, the anisotropic medium dynamic focusing beam deflection imaging method and system provided by the invention have advantages in computational efficiency and imaging precision, can solve the problem of complex anisotropic medium structure imaging, and can provide a solution for the problem of deep geological target exploration.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a dynamic focusing beam shift imaging method for anisotropic media according to the present invention;
FIG. 2 is a schematic diagram of a velocity field and an anisotropy parameter field of a VTI medium complex structure model provided by the present invention; wherein, FIG. 2(a) shows the longitudinal wave velocity v of the VTI medium complex structure model provided by the present inventionPA schematic diagram; FIG. 2(b) is a schematic diagram of anisotropy parameter ε of a complex structure model of a VTI medium provided by the invention; FIG. 2(c) is a schematic diagram of anisotropy parameter δ of a complex-structure model of a VTI medium provided by the present invention;
FIG. 3 is a schematic diagram of seismic beams of different forms of a VTI medium complex structural model provided by the invention; FIG. 3(a) is a schematic Gaussian beam diagram of a complex construction model of VTI medium provided by the present invention; FIG. 3(b) is a schematic focusing beam diagram of a VTI medium complex construction model provided by the present invention; 3(c) is a dynamic focusing beam schematic diagram of the VTI medium complex construction model provided by the invention;
FIG. 4 is a schematic view of the present inventionThe velocity field and the anisotropy parameter field of the VTI medium Hess model are shown schematically; FIG. 4(a) is a longitudinal wave velocity v of a Hess model of VTI medium provided by the present inventionPA schematic diagram; FIG. 4(b) is a schematic diagram of anisotropy parameter ε of a Hess model of a VTI medium provided by the present invention; FIG. 4(c) is a schematic diagram of anisotropy parameter δ of a Hess model of VTI medium provided by the present invention;
FIG. 5 is a schematic diagram of an anisotropic VTI medium Hess model seismic record provided by the present invention;
FIG. 6 is a schematic diagram of the Hess model offset result of the VTI medium provided by the present invention; FIG. 6(a) is a schematic diagram of a dynamic focused beam prestack depth migration imaging result obtained by using an isotropic media algorithm according to the present invention; FIG. 6(b) is a schematic diagram of a conventional Gaussian beam prestack depth migration imaging result obtained by applying an anisotropic medium algorithm according to the present invention; FIG. 6(c) is a diagram illustrating the result of the anisotropic media dynamic focused beam shift imaging method and system provided by the present invention;
FIG. 7 is a schematic diagram of a VTI medium win model provided by the present invention; FIG. 7(a) is the longitudinal wave velocity field v of VTI medium win model provided by the present inventionPFig. 7(b) is a schematic diagram of an anisotropy parameter field epsilon of a VTI medium winning model provided by the invention, and fig. 7(c) is a schematic diagram of an anisotropy parameter field delta of a VTI medium winning model provided by the invention;
FIG. 8 is a schematic diagram of a VTI medium win model seismic record provided by the present invention;
FIG. 9 is a diagram illustrating the deviation result of the VTI medium win model provided by the present invention; FIG. 9(a) is a schematic diagram of a dynamic focused beam prestack depth migration imaging result obtained by using an isotropic media algorithm according to the present invention; FIG. 9(b) is a diagram illustrating the result of prestack depth migration imaging obtained by the anisotropic medium Gaussian beam migration imaging method provided by the present invention; FIG. 9(c) is a schematic diagram of the pre-stack depth migration imaging result obtained by the anisotropic medium dynamic focused beam migration imaging method and system provided by the present invention.
FIG. 10 is a partially enlarged schematic view of the deviation result of the VTI medium win model provided by the present invention; FIG. 10(a) is a partially enlarged schematic view of a dynamic focused beam prestack depth migration imaging result obtained by using an isotropic media algorithm according to the present invention; FIG. 10(b) is a partially enlarged schematic view of the pre-stack depth migration imaging result obtained by the anisotropic medium Gaussian beam migration imaging method provided by the present invention; fig. 10(c) is a partially enlarged schematic view of the pre-stack depth shift imaging result obtained by the anisotropic medium dynamic focused beam shift imaging method and system provided by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide an anisotropic medium dynamic focusing beam offset imaging method and system to eliminate the influence of initial beam width on offset imaging in conventional Gaussian beam offset and improve the imaging effect of a deep anisotropic medium complex geological structure.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
The key to realizing the anisotropic medium dynamic focusing beam offset and the system is to realize the anisotropic medium kinematics and dynamic ray tracing. On the basis of the previous research, the invention further deduces the kinematics and dynamics ray tracing equation suitable for the anisotropic medium by introducing parameters such as group velocity, phase slowness and the like, effectively simplifies the operation on the form and the realization, provides an anisotropic medium ray tracing algorithm, and applies the algorithm to the deduced anisotropic medium dynamic focusing beam imaging formula. The anisotropic medium dynamic focusing beam offset imaging method is realized by the following steps.
Fig. 1 is a flowchart of an anisotropic media dynamic focused beam offset imaging method provided by the present invention, and as shown in fig. 1, the anisotropic media dynamic focused beam offset imaging method includes:
step 101: acquiring an initial velocity field, an anisotropic parameter field and an anisotropic medium seismic record; the initial velocity field is used for acquiring velocity information required in ray tracing; the anisotropy parameter field is used for acquiring anisotropy parameter information required in ray tracing; and the anisotropic medium seismic record is used for acquiring total travel time equal wave field information from a seismic source to a wave detection point.
Inputting an initial velocity field, an anisotropic parameter field and an anisotropic medium seismic record;
step 102: determining phase velocity, group velocity and phase slowness according to the velocity information, the anisotropic parameter information and the emergent ray phase velocity angle information; and determining a kinematic ray tracing equation in the anisotropic medium and an anisotropic medium dynamic ray tracing equation based on a Cartesian coordinate system according to the phase velocity, the group velocity, the phase slowness and the travel time information.
Acquiring travel time and a ray path by using an anisotropic medium kinematics ray tracing equation;
in the invention, on the basis of an anisotropic medium ray tracing equation based on elastic parameters researched by the predecessor, an anisotropic medium kinematic tracing equation is further deduced:
Figure BDA0002666882100000081
Figure BDA0002666882100000082
in the formula: u shapeiRepresenting the propagation direction of the energy flow for a group velocity i component in a Cartesian coordinate system (i is 1 and 3); t is travel time; x is the number ofiAre coordinates in a cartesian coordinate system; p is a radical ofiIs the slowness; etaiIs the component of the time derivative of slowness in a cartesian coordinate system.
Step 103: and determining the travel time and the path information of the central ray according to the kinematic ray tracing equation in the anisotropic medium based on the Cartesian coordinate system.
Step 104: and determining a complex-valued kinetic ray parameter according to the anisotropic medium kinetic ray tracing equation based on the Cartesian coordinate system.
The invention calculates the differential of the ray coordinate system parameter gamma for the formulas (1) and (2) to obtain the dynamic ray tracing equation under the Cartesian coordinate system:
Figure BDA0002666882100000091
Figure BDA0002666882100000092
in the formula, Qi,Qj,PiAnd PjKinetic ray parameters representing complex values; i is 1, 3; j is 1, 3; a. theij,Bij,Cij,DijRepresents the corresponding calculation coefficient, and the specific calculation is given by equation (5):
Figure BDA0002666882100000093
the present invention utilizes the conversion matrix between the Cartesian coordinate system and the ray center coordinate system to convert the dynamic ray tracing parameters of complex values in the Cartesian coordinate system to the ray center coordinate system directly without complicated ray center coordinate system for calculation.
Step 105: and determining the amplitude of the dynamic focusing beam according to the ray path, the complex-valued dynamic ray parameters, the initial velocity field and the anisotropic parameter field of the anisotropic medium, and expressing a seismic source displacement wave field by using the dynamic focusing beam.
And (3) obtaining a complex-valued kinetic ray parameter by utilizing an anisotropic medium kinetic ray tracing equation and using the complex-valued kinetic ray parameter for calculating the dynamic focusing beam.
On the basis of ray tracing, a ray center coordinate system (q) can be further calculated1,q2S) complex travel time of the central ray:
Figure BDA0002666882100000094
in the formula, a 2 x 2 complex-valued matrix M is a travel-time wave field with respect to a coordinate q1And q is2The second partial derivative of (A) is M ═ PQ-1,Q-1Is the inverse of the complex-valued matrix Q, t(s) is the real-valued travel time at the s position, s being the position of the central ray.
Where the complex value M(s) is the second partial derivative of the travel-time wavefield with respect to coordinate n, and can be represented in a two-dimensional medium as shown by the following equation:
Figure BDA0002666882100000101
in the formula, epsilon(s)0) Is a complex constant, P1(s) and Q1(s) is a dynamic ray tracing parameter, P, obtained under the initial condition of plane waves2(s) and Q2(s) dynamic ray tracing parameters obtained under the initial condition of a point source wave field, wherein P(s) and Q(s) are complex-valued dynamic ray tracing parameters obtained by dynamic ray tracing, and the expression is as follows:
Figure BDA0002666882100000102
representing a seismic source wave field and a wave field at the beam center by a dynamic focusing beam, further obtaining a Gaussian beam displacement vector expression which is emitted from an origin r' and passes through a calculation point r under a ray center coordinate system in an anisotropic medium:
Figure BDA0002666882100000103
wherein v (r) is the phase velocity at the position r of the calculated point, v (r ') is the phase velocity at the position r' of the ray exit point, omega is the angular frequency, r 'represents the position of the ray exit point, and p' represents the slowness vector at the ray exit point; q1(r ') is the corresponding complex-valued kinetic ray-tracing parameter for the plane wave at the exit point r', Q1(r) is a kinetic ray tracing parameter, Q, obtained under the initial strip of the plane wave at the position r of the calculated point2(r) calculating the dynamic ray tracing parameters obtained by the initial conditions of the point source wave field at the point position r; tau (r) is the central ray travel time at r; m (r) is the second partial derivative of the travel time at r with respect to the ray center coordinate system coordinate q, qTRepresenting the transpose of q, ∈ (r) is a complex-valued parameter corresponding to the dynamic focused beam, and can be expressed in the form:
Figure BDA0002666882100000104
in the formula, ωrefFor the reference frequency, L (r) is the beam waist width at a certain calculated point r in the ground.
Step 106: determining an imaging value corresponding to single-shot seismic data by utilizing the dynamic focusing beam displacement wave field based on the forward continuation of the seismic source displacement wave field and the backward continuation of the wave field at the wave detecting point; and the imaging value is obtained by performing cross correlation on the forward continuation wave field of the seismic source and the backward continuation wave field of the wave detection point.
According to previous studies, the seismic wavefield generated by the seismic source at point r' can be high frequency approximated at point r, using a dynamically focused beam of the form:
Figure BDA0002666882100000111
in the formula, a vector p 'represents the phase slowness at the seismic source point r', uDFB(r, r ', p '; [ omega ]) is the dynamically focused beam excited at the source point r '.
And (3) carrying out forward continuation on a seismic source wave field, carrying out reverse continuation on different types of received wave fields at a detection point, and carrying out cross correlation to obtain an imaging value.
Equation (11) requires that the initial position of the central ray be coincident with the source, so that r is near the source r' when the beam center is not at the source r0Where a phase shift factor needs to be inserted in the integration to compensate for the effect of the phase shift (Hill, 2001), the green function represented by the dynamic focused beam can be expressed in the form:
Figure BDA0002666882100000112
according to the research of Nowack et al, the common shot domain prestack dynamic focusing beam offset imaging formula is known as follows:
Figure BDA0002666882100000113
in the formula, pdIs the phase slowness vector at the beam center, D (L, r', p)dω) is a local oblique superposition of Gaussian time windows, C is a constant coefficient, U (r, r', L, p)dω) is the dynamic focused beam imaging operator for the common shot domain, as follows:
Figure BDA0002666882100000114
in the formula, psIs the phase slowness vector at the source,
Figure BDA0002666882100000115
and
Figure BDA0002666882100000116
the dynamic focus beams are the corresponding underground wave field at the seismic source and the wave detecting point respectively.
Step 107: and performing superposition calculation on imaging values corresponding to all the single-shot seismic data, and determining an anisotropic medium dynamic focusing beam migration imaging result.
And adding all the imaging values to obtain a final anisotropic medium dynamic focusing beam offset imaging result.
In order to illustrate the correctness and the effectiveness of the method, the method adopts an anisotropic VTI medium complex construction model, a VTI medium Hess model and a VTI medium victory model to carry out an offset imaging test.
FIG. 2 is a schematic diagram of a velocity field and an anisotropy parameter field of a VTI medium complex-structured model provided by the present invention; FIG. 3 is a schematic diagram of seismic beams of different forms of a VTI medium complex structural model provided by the invention; FIG. 4 is a schematic diagram of a velocity field and an anisotropy parameter field of a Hess model of a VTI medium provided by the present invention; FIG. 5 is a schematic diagram of an anisotropic VTI medium Hess model seismic record provided by the present invention; FIG. 6 is a schematic diagram of the Hess model offset result of the VTI medium provided by the present invention; FIG. 7 is a schematic diagram of a VTI medium win model provided by the present invention; FIG. 8 is a schematic diagram of a VTI medium win model seismic record provided by the present invention; FIG. 9 is a diagram illustrating the deviation result of the VTI medium winning model provided by the present invention; fig. 10 is a partially enlarged schematic view of the deviation result of the VTI medium win model provided by the present invention.
1) And (3) a VTI medium complex construction model. As shown in fig. 2, the model has horizontal sampling points 351 with a sampling interval of 10m, sampling points in the depth direction of 1000, and a sampling interval of 5 m; FIG. 2(a) shows longitudinal wave velocity v of VTI medium complex structure model provided by the present inventionPA schematic diagram; FIG. 2(b) is a schematic diagram of anisotropy parameter ε of a complex structure model of a VTI medium provided by the invention; FIG. 2(c) is a schematic diagram of anisotropy parameter δ of a complex-structure model of a VTI medium provided by the present invention;
FIG. 3 is a schematic diagram of seismic beams of different forms of a VTI medium complex structural model provided by the invention; FIG. 3(a) is a schematic Gaussian beam diagram of a complex structure model of VTI medium provided by the present invention; FIG. 3(b) is a schematic focusing beam diagram of a VTI medium complex construction model provided by the present invention; 3(c) is a dynamic focusing beam schematic diagram of the VTI medium complex construction model provided by the invention;
the comparison can find that: as shown in fig. 3(a), the gaussian beam diverges morphologically faster as the propagation distance increases, and particularly when the initial beam width is narrower, the beam width of the gaussian beam increases rapidly as the propagation distance increases, which results in a decrease in energy delivered to a deep portion of the beam. While the focused beam shown in fig. 3(b) is at a location in the ground (e.g., 2500 m), the beam at that location can be converged within the beam waist width, thereby making the energy at that point more focused and the diffracted wave energy more convergent. In the process of propagation, the dynamic focused beam of the invention shown in fig. 3(c) constrains the beam within a certain range near the central ray, and the beam width does not rapidly diverge with the increase of the propagation distance, so that the energy keeps converging, which helps to solve the problem that the energy of the shallow layer and the medium-deep layer in the gaussian beam shift cannot be compatible.
2) And (4) trial calculation of an anisotropic VTI medium Hess model. The number of horizontal sampling points of the model is 3617, the sampling interval is 6.096m, the number of sampling points in the depth direction is 1500, and the sampling interval is 6.096 m; the seismic data is subjected to forward modeling in a left-side excitation and single-side receiving mode and a finite difference mode, wherein 720 cannons are counted, and the cannon spacing is 30.480 m; the track spacing was 12.192 m; the seismic recording sampling time was 7.992s, and the time sampling interval was 6 ms. FIG. 4 is a schematic diagram of a velocity field and an anisotropy parameter field of a Hess model of a VTI medium provided by the present invention; FIG. 4(a) is a schematic longitudinal wave velocity diagram of a Hess model of a VTI medium provided by the present invention; FIG. 4(b) is a schematic diagram of anisotropy parameters of a Hess model of a VTI medium provided by the present invention; fig. 4(c) is a schematic diagram of the anisotropy parameters of the Hess model of the VTI medium provided by the present invention.
FIG. 5 is a schematic diagram of the anisotropic VTI medium Hess model seismic record provided by the invention.
FIG. 6 is a schematic diagram of the Hess model offset result of the VTI medium provided by the present invention; FIG. 6(a) is a schematic diagram of a dynamic focused beam prestack depth migration imaging result obtained by using an isotropic media algorithm according to the present invention; FIG. 6(b) is a schematic diagram of a conventional Gaussian beam prestack depth migration imaging result obtained by applying an anisotropic medium algorithm according to the present invention; FIG. 6(c) is a schematic diagram of the result obtained by the anisotropic medium dynamic focused beam shift imaging method and system provided by the present invention.
By contrast, it can be found that, because the influence of the anisotropic parameters is ignored, reflected waves of an imaging section obtained by isotropic dynamic focusing beam deflection shown in fig. 6(a) are not accurately returned, diffracted waves are not completely converged, the continuity of the in-phase axis is poor, the energy focusing performance is not ideal, obvious noise interference exists, and the overall quality is poor. The anisotropic Gaussian beam shown in FIG. 6(b) and the offset profile obtained by the method shown in FIG. 6(c) have clear in-phase axis, enhanced continuity and obviously improved imaging quality. Compared with the anisotropic Gaussian beam migration (figure 6(b)), the method provided by the invention is superior to the Gaussian beam migration in deep energy focusing property, reflected waves can be more accurately returned, diffracted waves are better converged, faults, high-speed salt domes and lithologic pinchout are well imaged, but the phenomenon of incomplete convergence still exists in individual places under the influence of seismic data noise and the like.
3) And (4) trial calculation of the anisotropic VTI medium complex construction model. The number of horizontal sampling points of the model is 1000, the sampling interval is 10m, the number of sampling points in the depth direction is 550, and the sampling interval is 8 m; the seismic data are 250 shots in total, the shot interval is 40m, and the channel interval is 10 m; the sampling time of the seismic record is 4s, the sampling interval is 0.8ms, and a full-receiving mode is adopted. FIG. 4 is a schematic diagram of a velocity field and an anisotropy parameter field of a Hess model of a VTI medium provided by the present invention; FIG. 4(a) is a schematic longitudinal wave velocity diagram of a Hess model of a VTI medium provided by the present invention; FIG. 4(b) is a schematic diagram of anisotropy parameters of a Hess model of a VTI medium provided by the present invention; FIG. 4(c) is a schematic diagram of anisotropy parameters of a Hess model of a VTI medium provided by the present invention.
FIG. 7 is a schematic diagram of a VTI medium win model provided by the present invention; fig. 7(a) is a schematic diagram of a longitudinal wave velocity field of a VTI medium winning model provided by the present invention, fig. 7(b) is a schematic diagram of an anisotropic parameter field of a VTI medium winning model provided by the present invention, and fig. 7(c) is a schematic diagram of an anisotropic parameter field of a VTI medium winning model provided by the present invention.
Fig. 8 is a schematic diagram of a VTI medium win model seismic record provided by the present invention.
FIG. 9 is a diagram illustrating the deviation result of the VTI medium winning model provided by the present invention; FIG. 9(a) is a schematic diagram of a dynamic focused beam prestack depth migration imaging result obtained by using an isotropic media algorithm according to the present invention; FIG. 9(b) is a schematic diagram of the imaging result of prestack depth migration obtained by the anisotropic medium Gaussian beam migration imaging method provided by the present invention; fig. 9(c) is a schematic diagram of the pre-stack depth migration imaging result obtained by the anisotropic medium dynamic focused beam migration imaging method and system provided by the present invention.
The contrast imaging result can find that: as can be seen from fig. 9, as shown in fig. 9(a), the result obtained by applying the isotropic dynamic focusing beam shift is affected by anisotropy, and the structures such as fracture zones and faults are not clearly imaged and the imaging quality is poor in both shallow layers and intermediate layers. The anisotropic Gaussian beam applied in FIG. 9(b) and the anisotropic dynamic focusing beam shifting method provided by the invention in FIG. 9(c) have obviously improved continuous in-phase axis and better imaging of complex structures such as fault and fracture zone. To more effectively illustrate the advantages of the anisotropic media dynamic focused beam offset imaging and system of the present invention, the image in FIG. 9 is shown enlarged partially, resulting in the result shown in FIG. 10. FIG. 10(a) is a partially enlarged schematic view of a dynamic focused beam prestack depth migration imaging result obtained by using an isotropic media algorithm according to the present invention; FIG. 10(b) is a partially enlarged schematic view of the pre-stack depth migration imaging result obtained by the anisotropic medium Gaussian beam migration imaging method provided by the present invention; fig. 10(c) is a partially enlarged schematic view of the pre-stack depth shift imaging result obtained by the anisotropic medium dynamic focused beam shift imaging method and system provided by the present invention.
As shown in fig. 10(a), in the isotropic dynamic focusing method, the reflected wave cannot be accurately returned, the diffracted wave is not completely converged, and the energy is not completely converged; the reflected wave homing is more accurate and the overall imaging quality is obviously improved by applying the results obtained by the anisotropic Gaussian beam (figure 10(b)) and the dynamic focusing beam offset (figure 10(c)) provided by the invention; however, the imaging result obtained by the anisotropic VTI medium dynamic focused beam shift imaging method according to the present invention (fig. 10(c)) is superior to the anisotropic gaussian beam shift method in energy focusing property, because the deep layer in-phase axis amplitude energy is stronger. The result of model trial calculation further illustrates the adaptability of the anisotropic medium dynamic focusing beam migration imaging method to deep complex geological structures, and can provide a solution for solving the exploration problem of deep geological targets.
The anisotropic medium dynamic focusing beam offset imaging method based on the Cartesian coordinate system has the advantages which are not possessed by other methods, and the specific advantages and the characteristics are shown in the following aspects:
firstly, the method of the invention realizes the dynamic focus beam shift in the anisotropic medium by using the anisotropic medium kinematics and the dynamic ray tracing algorithm. The method can realize the anisotropic medium dynamic focusing beam migration imaging method by using the dynamic focusing type propagation operator, and the dynamic focusing type propagation operator is used for well maintaining energy, eliminating the influence of the initial beam width in the conventional Gaussian beam migration on migration imaging and improving the imaging effect of the deep anisotropic medium complex geological structure.
Compared with an isotropic method, the method provided by the invention can enable the reflected wave of the complex anisotropic medium to be accurately returned, the diffracted wave is better converged, and the energy is more focused. Compared with the traditional anisotropic medium Gaussian beam deviation based on the elastic parameters, the method has more advantages in computational efficiency and imaging accuracy. Therefore, the method can solve the problem of complex anisotropic medium structure imaging and provide a solution for the exploration problem of deep geological targets.
According to the method, the anisotropic medium dynamic focusing beam migration imaging method based on the Cartesian coordinate system is realized on the basis of effectively simplifying the operation by deducing the anisotropic medium kinematic ray tracing equation and further deducing the anisotropic medium dynamic ray tracing equation suitable for the Cartesian coordinate system. The method is an effective imaging method for processing complex anisotropic medium seismic data, and has obvious advantages in the aspects of calculation efficiency and imaging precision compared with an isotropic method and an anisotropic medium Gaussian beam method based on elastic parameters. The method can promote the research of the deep complex anisotropic imaging method in seismic exploration, and further provide important technical support for deep complex structure oil-gas exploration.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the description of the method part.
The principle and the implementation mode of the present invention are explained by applying specific examples in the present specification, and the above descriptions of the examples are only used to help understanding the method and the core idea of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (4)

1. An anisotropic media dynamic focused beam offset imaging method, comprising:
acquiring an initial velocity field, an anisotropic medium anisotropy parameter field and an anisotropic medium seismic record; the initial velocity field is used for acquiring velocity information required in ray tracing; the anisotropic parameter field of the anisotropic medium is used for acquiring anisotropic parameter information required in ray tracing; the anisotropic medium seismic record is used for acquiring total travel time wave field information from a seismic source to a wave detection point;
determining phase velocity, group velocity and phase slowness according to the velocity information, the anisotropic parameter information and the emergent ray phase velocity angle information; determining a kinematic ray tracing equation in the anisotropic medium and an anisotropic medium dynamic ray tracing equation based on a Cartesian coordinate system according to the phase velocity, the group velocity, the phase slowness and the travel time information, and specifically comprising the following steps of:
according to the formula
Figure FDA0003650371840000011
Determining kinematic ray tracing in anisotropic mediaAn equation; wherein, UiRepresenting the propagation direction of the energy flow for a group velocity i component in a Cartesian coordinate system; t is travel time; x is the number ofiAre coordinates in a cartesian coordinate system; p is a radical ofiIs the slowness; etaiIs the component of the time derivative of slowness in a Cartesian coordinate system;
according to the formula dQi/dT=AijQj+BijPj、dPi/dT=CijQj+DijPjDetermining an anisotropic medium dynamic ray tracing equation based on a Cartesian coordinate system; wherein Q isi,Qj,PiAnd PjKinetic ray parameters representing complex values; i is 1, 3; j is 1, 3; a. theij,Bij,Cij,DijRepresenting the corresponding calculation coefficients, respectively:
Figure FDA0003650371840000012
Figure FDA0003650371840000013
determining the travel time and path information of the central ray according to the kinematic ray tracing equation in the anisotropic medium based on the Cartesian coordinate system;
determining a dynamic ray parameter of a complex value according to the anisotropic medium dynamic ray tracing equation based on the Cartesian coordinate system;
determining the amplitude of a dynamic focusing beam according to the ray path, the dynamic ray parameters of the complex value, the initial velocity field and the anisotropic parameter field of the anisotropic medium, and expressing a seismic source displacement wave field by using the dynamic focusing beam, which specifically comprises the following steps:
using formulas
Figure FDA0003650371840000021
Determining a seismic source displacement wave field; wherein, I represents an imaginary number unit, v (r) is the phase velocity at the position r of a calculated point, v (r ') is the phase velocity at the position r' of a ray exit point, omega is an angular frequency, r 'represents the position of the ray exit point, and p' represents a raySlowness vectors at the exit points; q1(r ') is the corresponding complex-valued kinetic ray-tracing parameter for the plane wave at the exit point r', Q1(r) is a kinetic ray tracing parameter, Q, obtained under the initial condition of plane waves at the position r of the calculated point2(r) calculating the dynamic ray tracing parameters obtained by the initial conditions of the point source wave field at the point position r; epsilon (r) is a complex value parameter corresponding to the dynamic focusing beam, and tau (r) is the travel time of the central ray at r; m (r) is the second partial derivative of the travel time at r with respect to the ray center coordinate system coordinate q, qTRepresents a transpose of q;
determining an imaging value corresponding to single-shot seismic data by utilizing the dynamic focusing beam displacement wave field based on the forward continuation of the seismic source displacement wave field and the backward continuation of the wave field at the wave detecting point; the imaging value is obtained by performing cross correlation on a forward continuation wave field of the seismic source and a reverse continuation wave field of the wave detection point;
and superposing and calculating imaging values corresponding to all the single-shot seismic data, and determining an anisotropic medium dynamic focusing beam migration imaging result, wherein the dynamic focusing beam migration imaging is an improvement of conventional Gaussian beam migration and can eliminate the influence of initial beam width on the Gaussian beam migration imaging.
2. The anisotropic medium dynamic focus beam migration imaging method of claim 1, wherein the determining the imaging value corresponding to the single shot seismic data by using the dynamic focus beam displacement wave field based on the forward continuation of the source displacement wave field and the backward continuation of the wave field at the wave detection point comprises:
determining a displacement vector caused by the seismic source at r' received at the q point by using the dynamic focusing beam;
determining a wave field of forward continuation of the dynamic focusing beam and a wave field of reverse continuation of the dynamic focusing beam according to the displacement vector;
determining a displacement wave field after the forward continuation of the anisotropic medium according to the wave field of the forward continuation of the dynamic focusing beam;
determining the displacement of the backward continuation emergent from the center of the detection point beam according to the wave field of the backward continuation of the dynamic focusing beam;
and determining an imaging value corresponding to the single-shot seismic data according to the wave field after the forward continuation of the anisotropic medium and the wave field after the backward continuation by utilizing a cross-correlation imaging condition.
3. An anisotropic media dynamic focused beam shift imaging system, comprising:
the parameter acquisition module is used for acquiring an initial velocity field, an anisotropic medium anisotropy parameter field and an anisotropic medium seismic record; the initial velocity field is used for acquiring velocity information required in ray tracing; the anisotropic parameter field of the anisotropic medium is used for acquiring anisotropic parameter information required in ray tracing; the anisotropic medium seismic record is used for acquiring total travel time wave field information from a seismic source to a wave detection point;
the ray tracing equation determining module is used for determining phase velocity, group velocity and phase slowness according to the velocity information, the anisotropic parameter information and the emergent ray phase velocity angle information; the system comprises a Cartesian coordinate system-based kinematic ray tracing equation and an anisotropic medium dynamic ray tracing equation, wherein the Cartesian coordinate system-based kinematic ray tracing equation and the anisotropic medium dynamic ray tracing equation are used for determining the anisotropic medium according to the phase velocity, the group velocity, the phase slowness and the travel time information;
the central ray travel time and path determining module is used for determining the travel time and path of the central ray according to the kinematic ray tracing equation in the anisotropic medium based on the Cartesian coordinate system;
the dynamic ray parameter determination module is used for determining a complex dynamic ray parameter according to the anisotropic medium dynamic ray tracing equation based on the Cartesian coordinate system;
the seismic source displacement wave field determining module is used for determining the amplitude of a dynamic focusing beam according to the ray path, the dynamic ray parameters of the complex value, the initial velocity field and the anisotropic parameter field of the anisotropic medium, and expressing a seismic source displacement wave field by using the dynamic focusing beam;
the single-shot imaging value determining module is used for determining an imaging value corresponding to single-shot seismic data by utilizing the dynamic focusing beam displacement wave field based on the forward continuation of the seismic source displacement wave field and the backward continuation of the wave field at the wave detecting point; the imaging value is obtained by performing cross correlation on a forward continuation wave field of the seismic source and a reverse continuation wave field of the wave detection point;
the anisotropic medium dynamic focus beam migration imaging result determining module is used for carrying out superposition calculation on imaging values corresponding to all the single shot seismic data and determining the anisotropic medium dynamic focus beam migration imaging result, wherein the dynamic focus beam migration imaging is an improvement of conventional Gaussian beam migration and can eliminate the influence of initial beam width on Gaussian beam migration imaging;
the ray tracing equation determining module specifically includes:
an anisotropic medium kinematic ray tracing equation determination unit based on Cartesian coordinate system and used for determining the anisotropic medium kinematic ray tracing equation according to the formula
Figure FDA0003650371840000041
Determining a kinematic ray tracing equation in an anisotropic medium; wherein, UiRepresenting the propagation direction of the energy flow for a group velocity i component in a Cartesian coordinate system; t is the travel time; x is the number ofiAre coordinates in a cartesian coordinate system; p is a radical of formulaiIs the slowness; etaiIs the component of the time derivative of slowness in a Cartesian coordinate system;
an anisotropic medium dynamics ray tracing equation determination unit based on Cartesian coordinate system for determining the equation dQ according to the formulai/dT=AijQj+BijPj、dPi/dT=CijQj+DijPjDetermining an anisotropic medium dynamic ray tracing equation based on a Cartesian coordinate system; wherein Q isi,Qj,PiAnd PjKinetic ray parameters representing complex values; i is 1, 3; j is 1, 3; a. theij,Bij,Cij,DijRepresenting the corresponding calculation coefficients, respectively:
Figure FDA0003650371840000042
Figure FDA0003650371840000043
the seismic source displacement wave field determination module specifically comprises:
seismic source displacement wave field determination unit for using formula
Figure FDA0003650371840000044
Determining a seismic source displacement wave field; wherein v (r) is the phase velocity at the position r of the calculated point, v (r ') is the phase velocity at the position r' of the ray exit point, omega is the angular frequency, r 'represents the position of the ray exit point, and p' represents the slowness vector at the ray exit point; q1(r ') is the corresponding complex-valued kinetic ray-tracing parameter for the plane wave at the exit point r', Q1(r) is a kinetic ray tracing parameter, Q, obtained under the initial condition of plane waves at the position r of the calculated point2(r) calculating the dynamic ray tracing parameters obtained by the initial conditions of the point source wave field at the point position r; epsilon (r) is a complex value parameter corresponding to the dynamic focusing beam, and tau (r) is the travel time of the central ray at r; m (r) is the second partial derivative of the travel time at r with respect to the ray center coordinate system coordinate q, qTRepresenting the transpose of q.
4. The anisotropic media dynamic focus beam migration imaging system of claim 3, wherein the determining the imaging value corresponding to the single shot seismic data using the dynamic focus beam displacement wave field based on the forward continuation of the source displacement wave field and the backward continuation of the wave field at the wave detection point comprises:
the displacement vector determining unit is used for determining a displacement vector received at the r point and caused by the seismic source at the r' position by using the dynamic focusing beam;
the dynamic focusing beam forward continuation wave field and reverse continuation displacement field determining unit is used for determining the dynamic focusing beam forward continuation wave field and the dynamic focusing beam reverse continuation displacement wave field according to the displacement vector;
and the imaging value determining unit corresponding to the single-shot seismic data is used for determining the imaging value corresponding to the single-shot seismic data according to the anisotropic medium reverse continuation displacement wave field and the forward continuation displacement wave field by utilizing the cross-correlation imaging condition.
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