CN110927784B - Frequency domain Gaussian beam Green function calculation method based on OpenMP - Google Patents
Frequency domain Gaussian beam Green function calculation method based on OpenMP Download PDFInfo
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Abstract
The invention discloses a frequency domain Gaussian beam Green function calculation method based on OpenMP, wherein in the migration and anti-migration processes of an integral method, a frequency domain Green function is a high-dimensional function with frequency, shot points and underground space as independent variables, and a frequency domain Gaussian beam is a high-dimensional function with frequency, shot points, wave vectors and underground space; based on the characteristics that multiple nodes and multiple cores of nodes share a large memory at present, a frequency domain Gaussian beam Green function calculation method based on OpenMP is developed, the parallel force is ensured, and the outmost layer cycle is parallel; the node shared memory is fully utilized, and the Green function is placed in the memory, so that efficient offset and inversion based on the frequency Green function can be conveniently carried out subsequently; and the circulating logic is reasonably designed, and repeated calculation is avoided.
Description
Technical Field
The invention relates to the field of seismic exploration, in particular to a frequency domain Gaussian beam Green function calculation method based on OpenMP.
Background
In optics, a gaussian beam is a beam that describes monochromatic electromagnetic radiation, the transverse amplitude of which decays with a gaussian function. The earliest gaussian beam was used to describe the propagation of electromagnetic waves, which was then introduced into seismic wave propagation, and is now widely used for seismic wave migration and inversion. Both classical gaussian beam propagation and deviation can be expressed in the frequency domain, and since the computation and storage of the green's function in the frequency domain consumes much current computer resources, gaussian beam deviation is usually performed in the time-space domain. The "implementation and application research of gaussian beam depth migration" in the article by zeijong and the like published in 2012 by the petroleum geophysical prospecting, and the "time domain gaussian beam prestack depth migration" in the doctor article published in 2015 by the Jilin university all adopt a time-space domain implementation mode. With the increasing exploration requirements in the oil and gas industry, inversion imaging based on Gaussian beams has been proposed, and Greens function calculation is a core step required by forward modeling and inversion of Gaussian beams. Geophysics, Yue published in 2019 at 04 and Sava et al, "blast-square Gaussian gain propagation in elastic media" indicate that Gaussian beam frequency domain Green's function computation and inversion thereof remain challenging in terms of computational efficiency.
Inversion imaging based on gaussian beams is generally implemented by integral equations, and least squares reverse time migration based on two-way wave equations is generally implemented by finite differences. However, the inversion imaging method based on reverse time migration still cannot meet the requirement of exploration seismic data processing, and the expression is that the grid is required to be smaller along with the increase of frequency, and the calculation amount of the green function calculation by solving the wave equation in a small grid time-space domain difference mode under the same model increases exponentially. The theory and implementation challenges of Inversion imaging based on a difference equation are described in detail in the book "Seismic Inversion" of Schuster 2017. The Gaussian beam serving as a one-way wave operator has better advantages than a difference classification algorithm in the aspect of controlling the propagation of high-frequency seismic waves. The method has the advantages that the Gaussian beam is utilized to effectively construct the wave propagation Green function of the frequency domain, the Gaussian beam inversion imaging efficiency is improved, the difference inversion imaging algorithm has potential to be integrated, and a new imaging algorithm integrating the advantages of an integral equation and a difference equation is developed.
Disclosure of Invention
In view of this, the present invention provides a frequency domain gaussian beam green function calculation method based on OpenMP.
A frequency domain Gaussian beam Green function calculation method based on OpenMP comprises the following steps:
step 1: generating a green function of a frequency domain, which comprises the following specific steps:
(1) applying a structure array Cells (Nz, Nx) for storing a Green function corresponding to a Gaussian beam in a single direction, applying a Green (Nz, Nx, N omega, Nshot) for storing a Green function array, wherein z and x refer to two-dimensional coordinates of space points, Nz and Nx refer to grid point numbers in the z direction and the x direction respectively, omega refers to frequency, N omega refers to cycle times of the frequency, Nshot refers to cycle times of shot points, and shot refers to shot points;
(2) carrying out shot point circulation, namely carrying out Nshot times circulation on shot points, carrying out parallel processing on the circulation by utilizing OpenMP, privatizing structure body array Cells (Nz, Nx) and related circulation related variables and temporary variables, and sharing Green (Nz, Nx, N omega, Nshot) function array;
(3) performing ray direction circulation, namely performing Np direction circulation on the ray Gaussian beam, performing time-space domain ray Gaussian beam calculation on the ray Gaussian beam in a certain direction Ip to form Cells (Nz, Nx) in the direction, and marking the position with value of the ray Gaussian beam;
(4) performing frequency circulation, namely performing N omega times of circulation on the frequency omega, and calculating a marked ray Gaussian beam with a certain frequency I omega to obtain related information of a frequency domain Green function;
(5) performing model space circulation, wherein the size of the model space is Nx × Nz, and performing integral calculation of Green functions on grid points of Ix and Iz in the model space to obtain Green (Iz, Ix, I omega, Ishot), wherein I is (1, N); z and x refer to two-dimensional coordinates of a spatial point;
step 2: the application of the forward modeling of the seismic wave Born, namely the reverse migration, is realized by using Green (Nz, Nx, Nω, Nshot) functions, and the specific steps are as follows:
(1) applying a single-channel data array Trace (Lt), applying a data array Dat (Lt, Nreceiver, Nshot), wherein Lt refers to the length of discrete seismic recording time t, Nshot and Nreceiver are the number of shot points and shot-geophone points respectively, shot is shot point, and receiver is a seismic wave detector;
(2) performing shot point circulation, namely calculating the seismic data with multiple shots from the number range of 1 to Nshot, calculating Nshot times in total, performing parallel processing on the circulation by utilizing OpenMP, and sharing a data array Dat (Lt, Nreceiver and Nshot) by using private Trace (Lt) and related cycle related variables and temporary variables; lt refers to the length of discrete seismic recording time t, shot refers to shot point, receiver refers to a seismic wave detector, and Nshot and Nreceiver respectively refer to the number of the shot point and the shot point;
(3) carrying out wave detection point circulation, namely carrying out Nreceiver times of circulation on Ireceiver of a wave detector for randomly detecting seismic waves;
(4) performing frequency circulation, namely performing N omega times of circulation on any frequency I omega in the range of the effective frequency band of the seismic waves;
(5) performing model space circulation, wherein the size of the model space is Nx × Nz, and integrating the grid points of Ix and Iz in the seismic wave velocity model space by using known Green (Iz, Ix, I omega, Ishot) to obtain Trace (I omega);
(6) and performing inverse Fourier transform on the Trace (I omega) data to obtain Trace (Lt) and assigning the Trace (Lt) to Dat (Ireceiver, Ishot), so as to finish forward modeling of the seismic wave Born of the Green (Iz, Ix, I omega, Ishot).
Further, in step 1, the frequency domain green function is:
wherein x represents the imaging point coordinates, xsThe coordinates of the point of shot are represented,
representing the initial wave vector direction of local plane waves of the shot point, omega being the seismic wave frequency, uGB(x,xs,psω) represents a gaussian beam in a cartesian coordinate system, a single gaussian beam can be solved by dynamic ray tracing in a ray-center coordinate system, i represents a complex number.
Further, the gaussian beam is represented as follows:
wherein s is the coordinate of the central coordinate system of the Gaussian beam ray along the ray direction, qT＝(q1,q2) For the vertical ray direction coordinates, v(s) and τ(s) denote velocity and time along the ray direction, ω is the seismic wave frequency, P(s) and Q(s) are two dynamic ray tracing parameters along the ray direction, Q(s)0) Is the initial value of Q(s), v(s)0) For the initial value of velocity v(s), the gaussian beam of the ray center coordinate system can be transformed into a gaussian beam in a cartesian coordinate system by coordinate transformation.
Further, the forward or reverse migration formula of the seismic wave Born is as follows:
DBorn(xr,xs,ω)＝2ω2∫Dm(x)G(x,xs,ω)G(x,xr,ω)dx
in the above formula, m (x) and DBorn(xr,xsω) respectively represent the image of the subsurface model space x and the surface shot location (x)r,xs) The seismic wave Born forward data, xrRepresenting the coordinates of the demodulator probe, xsRepresenting shot coordinates, zrRepresenting seismic geophone point depth, where G (x, x)sω) and G (x, x)rω) Green's function of shot and geophone points, respectively, ω being seismic frequency, G*(x,xrW) is G (x, x)rω) conjugation, Ds(xr,xsAnd ω) refers to recorded frequency domain seismic data, D represents data.
The technical scheme provided by the invention has the beneficial effects that: the invention introduces OpenMP for parallelism, can fully utilize the advantage of large node memory, improves the calculation efficiency, and can further improve the parallelism by combining MPI. The seismic wave Gaussian beam least square migration based on the method can accurately correct the amplitude, and can realize the inversion of the high-frequency seismic wave under the condition of linearly increasing the calculation cost.
Drawings
FIG. 1 is a flowchart of a method for calculating a Gaussian beam Green function in a frequency domain based on OpenMP according to an embodiment of the present invention;
FIG. 2 is a plot of the results of a single Gaussian beam (left) and a single stemming function (right) at a frequency of 25Hz in a constant velocity medium;
FIG. 3 is a cross-sectional model view;
FIG. 4 is a graph of the conventional Gaussian beam shift results (left) for the fault model and a graph of the least squares Gaussian beam shift results (right) based on the Green's function of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be further described with reference to the accompanying drawings.
Referring to fig. 1, an embodiment of the present invention provides a frequency domain gaussian beam green function calculation method based on OpenMP.
A frequency domain Gaussian beam Green function calculation method based on OpenMP comprises the following steps:
step 1: generating a green function of a frequency domain, which comprises the following specific steps:
(1) applying a structure array Cells (Nz, Nx) for storing a Green function corresponding to a Gaussian beam in a single direction, applying a Green (Nz, Nx, N omega, Nshot) for storing a Green function array, wherein z and x refer to two-dimensional coordinates of space points, Nz and Nx refer to grid point numbers in the z direction and the x direction respectively, omega refers to frequency, N omega refers to cycle times of the frequency, Nshot refers to cycle times of shot points, and shot refers to shot points;
(2) carrying out shot point circulation, namely carrying out Nshot times circulation on shot points, carrying out parallel processing on the circulation by utilizing OpenMP, privatizing structure body array Cells (Nz, Nx) and related circulation related variables and temporary variables, and sharing Green (Nz, Nx, N omega, Nshot) function array;
(3) performing ray direction circulation, namely performing Np direction circulation on the ray Gaussian beam, performing time-space domain ray Gaussian beam calculation on the ray Gaussian beam in a certain direction Ip to form Cells (Nz, Nx) in the direction, and marking the position with value of the ray Gaussian beam;
(4) performing frequency circulation, namely performing N omega times of circulation on the frequency omega, and calculating a marked ray Gaussian beam with a certain frequency I omega to obtain related information of a frequency domain Green function;
(5) performing model space circulation, wherein the size of the model space is Nx × Nz, and performing integral calculation of Green functions on grid points of Ix and Iz in the model space to obtain Green (Iz, Ix, I omega, Ishot), wherein I is (1, N); z and x refer to two-dimensional coordinates of a spatial point;
step 2: the application of the forward modeling of the seismic wave Born, namely the reverse migration, is realized by using Green (Nz, Nx, Nω, Nshot) functions, and the specific steps are as follows:
(1) applying a single-channel data array Trace (Lt), applying a data array Dat (Lt, Nreceiver, Nshot), wherein Lt refers to the length of discrete seismic recording time t, Nshot and Nreceiver are the number of shot points and shot-geophone points respectively, shot is shot point, and receiver is a seismic wave detector;
(2) performing shot point circulation, namely calculating the seismic data with multiple shots from the number range of 1 to Nshot, calculating Nshot times in total, performing parallel processing on the circulation by utilizing OpenMP, and sharing a data array Dat (Lt, Nreceiver and Nshot) by using private Trace (Lt) and related cycle related variables and temporary variables; lt refers to the length of discrete seismic recording time t, shot refers to shot point, receiver refers to a seismic wave detector, and Nshot and Nreceiver respectively refer to the number of the shot point and the shot point;
(3) carrying out wave detection point circulation, namely carrying out Nreceiver times of circulation on Ireceiver of a wave detector for randomly detecting seismic waves;
(4) performing frequency circulation, namely performing N omega times of circulation on any frequency I omega in the range of the effective frequency band of the seismic waves;
(5) performing model space circulation, wherein the size of the model space is Nx × Nz, and integrating the grid points of Ix and Iz in the seismic wave velocity model space by using known Green (Iz, Ix, I omega, Ishot) to obtain Trace (I omega);
(6) and performing inverse Fourier transform on the Trace (I omega) data to obtain Trace (Lt) and assigning the Trace (Lt) to Dat (Ireceiver, Ishot), so as to finish forward modeling of the seismic wave Born of the Green (Iz, Ix, I omega, Ishot).
In step 1, the green function of the frequency domain is:
wherein x represents the imaging point coordinates, xsThe coordinates of the point of shot are represented,
representing the initial wave vector direction of local plane waves of the shot point, omega being the seismic wave frequency, uGB(x,xs,psω) represents a gaussian beam in a cartesian coordinate system, a single gaussian beam being possible to coordinate at the center of the rayIs obtained by dynamic ray tracing, i represents a plurality.
The gaussian beam is represented as follows:
wherein s is the coordinate of the central coordinate system of the Gaussian beam ray along the ray direction, qT＝(q1,q2) For the vertical ray direction coordinates, v(s) and τ(s) denote velocity and time along the ray direction, ω is the seismic wave frequency, P(s) and Q(s) are two dynamic ray tracing parameters along the ray direction, Q(s)0) Is the initial value of Q(s), v(s)0) For the initial value of velocity v(s), the gaussian beam of the ray center coordinate system can be transformed into a gaussian beam in a cartesian coordinate system by coordinate transformation.
The forward or reverse migration formula of the seismic waves Born is represented as follows:
DBorn(xr,xs,ω)＝2ω2∫Dm(x)G(x,xs,ω)G(x,xr,ω)dx
in the above formula, m (x) and DBorn(xr,xsω) respectively represent the image of the subsurface model space x and the surface shot location (x)r,xs) The seismic wave Born forward data, xrRepresenting the coordinates of the demodulator probe, xsRepresenting shot coordinates, zrRepresenting seismic geophone point depth, where G (x, x)sω) and G (x, x)rω) Green's function of shot and geophone points, respectively, ω being seismic frequency, G*(x,xrW) is G (x, x)rω) conjugation, Ds(xr,xsAnd ω) refers to recorded frequency domain seismic data, D represents data.
To test the effectiveness of the invention, an implementation of the invention was tested in a constant velocity medium, and figure 2 shows the green's function of the superposition of all beams of a 25Hz single gaussian beam and a single shot.
In order to test the effectiveness of the application of the method in the aspect of inversion imaging, the effect and the efficiency condition of least square Gaussian beam migration based on the fault model are shown. Fig. 3 is a fault model, and fig. 4 is a conventional gaussian beam shift result (left) corresponding to the fault model and a least squares gaussian beam shift result (right) based on the green's function of the present invention. Comparing the results in FIG. 4 shows that least squares Gaussian beam migration can give more uniform amplitude information of the subsurface reflection; in order to illustrate the advantages of the algorithm in calculating the high-frequency wave field, table 1 lists the comparison of the calculation efficiency of the scheme of the invention under the conditions of different main frequencies and highest frequencies, and the comparison of the data in table 1 shows that the calculation amount of the algorithm of the invention basically keeps linear increase along with the increase of the frequency, which is superior to the characteristic that the calculation cost index of the fluctuation algorithm increases along with the increase of the frequency in the forward process.
Table 1 efficiency comparison of gaussian beam forward modeling for different frequency band data
The features of the embodiments and embodiments described herein above may be combined with each other without conflict. The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (4)
1. A frequency domain Gaussian beam Green function calculation method based on OpenMP is characterized by comprising the following steps:
step 1: generating a green function of a frequency domain, which comprises the following specific steps:
(1) applying a structure array Cells (Nz, Nx) for storing a Green function corresponding to a Gaussian beam in a single direction, applying a Green (Nz, Nx, N omega, Nshot) for storing a Green function array, wherein z and x refer to two-dimensional coordinates of space points, Nz and Nx refer to grid point numbers in the z direction and the x direction respectively, omega refers to frequency, N omega refers to cycle times of the frequency, Nshot refers to cycle times of shot points, and shot refers to shot points;
(2) carrying out shot point circulation, namely carrying out Nshot times circulation on shot points, carrying out parallel processing on the circulation by utilizing OpenMP, privatizing structure body array Cells (Nz, Nx) and related circulation related variables and temporary variables, and sharing Green (Nz, Nx, N omega, Nshot) function array;
(3) performing ray direction circulation, namely performing Np direction circulation on the ray Gaussian beam, performing time-space domain ray Gaussian beam calculation on the ray Gaussian beam in a certain direction Ip to form Cells (Nz, Nx) in the direction, and marking the position with value of the ray Gaussian beam;
(4) performing frequency circulation, namely performing N omega times of circulation on the frequency omega, and calculating a marked ray Gaussian beam with a certain frequency I omega to obtain related information of a frequency domain Green function;
(5) performing model space circulation, wherein the size of the model space is Nx × Nz, and performing integral calculation of Green functions on grid points of Ix and Iz in the model space to obtain Green (Iz, Ix, I omega, Ishot), wherein I is (1, N); z and x refer to two-dimensional coordinates of a spatial point;
step 2: the application of the forward modeling of the seismic wave Born, namely the reverse migration, is realized by using Green (Nz, Nx, Nω, Nshot) functions, and the specific steps are as follows:
(1) applying a single-channel data array Trace (Lt), applying a data array Dat (Lt, Nreceiver, Nshot), wherein Lt refers to the length of discrete seismic recording time t, Nshot and Nreceiver are the number of shot points and shot-geophone points respectively, shot is shot point, and receiver is a seismic wave detector;
(2) performing shot point circulation, namely calculating the seismic data with multiple shots from the number range of 1 to Nshot, calculating Nshot times in total, performing parallel processing on the circulation by utilizing OpenMP, and sharing a data array Dat (Lt, Nreceiver and Nshot) by using private Trace (Lt) and related cycle related variables and temporary variables; lt refers to the length of discrete seismic recording time t, shot refers to shot point, receiver refers to a seismic wave detector, and Nshot and Nreceiver respectively refer to the number of the shot point and the shot point;
(3) carrying out wave detection point circulation, namely carrying out Nreceiver times of circulation on Ireceiver of a wave detector for randomly detecting seismic waves;
(4) performing frequency circulation, namely performing N omega times of circulation on any frequency I omega in the range of the effective frequency band of the seismic waves;
(5) performing model space circulation, wherein the size of the model space is Nx × Nz, and integrating the grid points of Ix and Iz in the seismic wave velocity model space by using known Green (Iz, Ix, I omega, Ishot) to obtain Trace (I omega);
(6) and performing inverse Fourier transform on the Trace (I omega) data to obtain Trace (Lt) and assigning the Trace (Lt) to Dat (Ireceiver, Ishot), so as to finish forward modeling of the seismic wave Born of the Green (Iz, Ix, I omega, Ishot).
2. The method according to claim 1, wherein the frequency domain gaussian beam green function in step 1 is:
wherein x represents the imaging point coordinates, xsThe coordinates of the point of shot are represented,
representing the initial wave vector direction of local plane waves of the shot point, omega being the seismic wave frequency, uGB(x,xs,psω) represents a gaussian beam in a cartesian coordinate system, a single gaussian beam can be solved by dynamic ray tracing in a ray-center coordinate system, i represents a complex number.
3. The OpenMP-based frequency domain gaussian beam green's function computation method of claim 2, wherein the gaussian beam is represented as follows:
wherein s is the coordinate of the central coordinate system of the Gaussian beam ray along the ray direction, qT＝(q1,q2) For the vertical ray direction coordinates, v(s) and τ(s) denote velocity and time along the ray direction, ω is the seismic wave frequency, P(s) and Q(s) are two dynamic ray tracing parameters along the ray direction, Q(s)0) Is the initial value of Q(s), v(s)0) For the initial value of velocity v(s), the gaussian beam of the ray center coordinate system can be transformed into a gaussian beam in a cartesian coordinate system by coordinate transformation.
4. The OpenMP-based frequency domain gaussian beam green's function calculation method according to claim 1, wherein the seismic wave Born forward or backward migration formula is represented as follows:
DBorn(xr,xs,ω)＝2ω2∫Dm(x)G(x,xs,ω)G(x,xr,ω)dx
in the above formula, m (x) and DBorn(xr,xsω) respectively represent the image of the subsurface model space x and the surface shot location (x)r,xs) The seismic wave Born forward data, xrRepresenting the coordinates of the demodulator probe, xsRepresenting shot coordinates, zrRepresenting seismic geophone point depth, where G (x, x)sω) and G (x, x)rω) Green's function of shot and geophone points, respectively, ω being seismic frequency, G*(x,xrW) is G (x, x)rω) conjugation, Ds(xr,xsAnd ω) refers to recorded frequency domain seismic data, D represents data.
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