Three-dimensional undulating surface seismic wave field forward modeling method, device and equipment and storage medium

Abstract

The invention discloses a three-dimensional undulating surface seismic wave field forward modeling method, device and equipment and a storage medium. The method comprises the following steps: constructing an air layer region surface and an underground layer region surface according to surface region space coordinates corresponding to a target surface region surface and a target space grid node planning model; determining an underground layer sound wave field value corresponding to the surface of the underground layer region and an air layer pseudo sound wave field value corresponding to the surface of the air layer region according to the seismic source information, a finite difference algorithm and the underground layer region space coordinates corresponding to the surface of the underground layer region; and according to the underground layer sound wave field value and the air layer pseudo sound wave field value, carrying out three-dimensional undulating surface seismic wave field finite difference simulation and implicitly realizing the surface free surface boundary condition, thereby reducing the data error in the three-dimensional undulating surface seismic wave field numerical simulation process, improving the seismic wave field numerical simulation precision, and improving the seismic wave field simulation accuracy. The data calculation cost is effectively reduced, and the practicability is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of earthquake numerical simulation, and in particular to a forward modeling method, device, equipment and storage medium for a three-dimensional undulating surface earthquake wave field. Background Art

[0002] Seismic wave field forward modeling can simulate the propagation process of seismic waves underground and serve the entire stage of seismic data acquisition, processing and interpretation.

[0003] At present, the mainstream numerical determination methods of earthquakes in the industry are based on the finite difference method, pseudo-spectral method, finite element method, spectral element method, etc. to solve and calculate partial differential wave equations. In the numerical determination of land earthquakes, in order to adapt to the undulating surface morphology, the finite element method and spectral element method using irregular grids can be better applied to the grid division under irregular surface conditions. This type of method can directly generate a spatial discrete grid system that adapts to the surface morphology, and can realize variable grids from fine to coarse to adapt to the changes in the velocity of the underground medium. However, the computational cost of these two methods is higher than that of the finite difference method and pseudo-spectral method, which also increases the difficulty of industrial-level application of full waveform inversion and imaging.

[0004] The more mainstream numerical simulation methods that take into account both computational efficiency and accuracy are the finite difference method and the pseudo-spectral method. However, in the determination of undulating surfaces, the finite difference method usually uses rectangular grids to divide the calculation area, and the real irregular surface boundaries are approximately truncated to the grid endpoints of the rectangular division, thus forming a "step-like" surface morphology. These grid endpoints will act as diffraction points to generate diffraction waves during the wave field propagation process, causing errors in the travel time of seismic waves. When considering the real three-dimensional undulating surface, the simulation error caused by the numerical algorithm is even greater. Summary of the invention

[0005] The present invention provides a forward modeling method, device, equipment and storage medium for three-dimensional undulating surface seismic wavefield, so as to reduce data errors in the numerical simulation process of three-dimensional undulating surface seismic acoustic wavefield, improve the accuracy of determining the seismic acoustic wavefield value, effectively reduce data calculation costs and improve practicality.

[0006] According to one aspect of the present invention, a method for forward modeling of seismic wave fields on a three-dimensional undulating surface is provided. The method comprises:

[0007] According to the spatial coordinates of the surface area corresponding to the three-dimensional undulating surface and the target space grid node planning model, the surface of the air layer area and the surface of the underground layer area are constructed, wherein the surface element points of the air layer area surface and the surface element points of the underground layer area surface are spatially symmetrical about the three-dimensional undulating surface of the target surface area;

[0008] Determine the underground layer acoustic wave field value corresponding to the underground layer area surface and the air layer pseudo acoustic wave field value corresponding to the air layer area surface according to the earthquake source information, the finite difference algorithm and the underground layer area spatial coordinates corresponding to the underground layer area surface;

[0009] According to the acoustic wave field value of the underground layer and the pseudo acoustic wave field value of the air layer, a finite difference simulation of the three-dimensional undulating surface seismic wave field is carried out and the surface free surface boundary condition is implicitly realized.

[0010] According to another aspect of the present invention, a three-dimensional undulating surface seismic wave field forward modeling device is provided. The device comprises:

[0011] A regional surface construction module is used to construct the surface of the air layer region and the surface of the underground layer region according to the surface region spatial coordinates corresponding to the three-dimensional undulating surface and the target space grid node planning model;

[0012] An acoustic wave field value determination module is used to determine the underground layer acoustic wave field value corresponding to the underground layer area surface and the air layer pseudo acoustic wave field value corresponding to the air layer area surface according to the earthquake source information, the finite difference algorithm and the underground layer area spatial coordinates corresponding to the underground layer area surface;

[0013] The surface acoustic wave field forward modeling module is used to carry out the finite difference simulation of the three-dimensional undulating surface seismic wave field and implicitly realize the three-dimensional undulating surface with free surface boundary conditions according to the underground layer acoustic wave field value and the air layer pseudo acoustic wave field value.

[0014] According to another aspect of the present invention, there is provided an electronic device, the electronic device comprising:

[0015] at least one processor; and

[0016] a memory communicatively connected to the at least one processor; wherein,

[0017] The memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor so that the at least one processor can perform the three-dimensional undulating surface seismic wave field forward modeling method described in any embodiment of the present invention.

[0018] According to another aspect of the present invention, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores computer instructions for enabling a processor to implement the three-dimensional undulating surface seismic wave field forward modeling method described in any embodiment of the present invention when the computer instructions are executed.

[0019] The technical solution of the embodiment of the present invention constructs the surface of the air layer area and the surface of the underground layer area according to the spatial coordinates of the surface area corresponding to the three-dimensional undulating surface and the target space grid node planning model; determines the underground layer acoustic wave field value corresponding to the underground layer area surface and the air layer pseudo acoustic wave field value corresponding to the air layer area surface according to the source information, the finite difference algorithm and the underground layer area spatial coordinates corresponding to the underground layer area surface; carries out finite difference simulation of the seismic wave field of the three-dimensional undulating surface and implicitly realizes the surface free surface boundary condition according to the underground layer acoustic wave field value and the air layer pseudo acoustic wave field value, solves the problem of high calculation cost and inability to be used in industry, can reduce data errors in the numerical simulation process of the seismic acoustic wave field of the three-dimensional undulating surface, improves the accuracy of determining the seismic acoustic wave field value, effectively reduces data calculation costs, and improves practicality.

[0020] It should be understood that the contents described in this section are not intended to identify the key or important features of the embodiments of the present invention, nor are they intended to limit the scope of the present invention. Other features of the present invention will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0022] Figure 1 is a flow chart of a forward modeling method for a three-dimensional undulating surface seismic wave field provided according to Embodiment 1 of the present invention;

[0023] Figure 2 is a schematic diagram of a regional surface structure provided according to Embodiment 1 of the present invention;

[0024] Figure 3 is a flow chart of a forward modeling method for a three-dimensional undulating surface seismic wave field provided according to a second embodiment of the present invention;

[0025] Figure 4 is a schematic diagram of a virtual three-dimensional space grid provided according to Embodiment 2 of the present invention;

[0026] Figure 5 is a diagram showing the relationship between the interpolation coefficient and the window function according to the second embodiment of the present invention;

[0027] Figure 6 is a schematic diagram of a three-dimensional undulating surface seismic wave field forward modeling device provided according to a third embodiment of the present invention;

[0028] Figure 7It is a schematic diagram of the structure of an electronic device for implementing the forward modeling method of a three-dimensional undulating surface seismic wave field according to an embodiment of the present invention. DETAILED DESCRIPTION

[0029] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0030] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0031] Embodiment 1

[0032] Figure 1 A flowchart of a three-dimensional undulating surface seismic wavefield forward modeling method is provided for the first embodiment of the present invention. This embodiment can be applied to the case of simulating the seismic acoustic wavefield of a real three-dimensional undulating surface on land. The method can be executed by a three-dimensional undulating surface seismic wavefield forward modeling device. The three-dimensional undulating surface seismic wavefield forward modeling device can be implemented in the form of hardware and / or software. The three-dimensional undulating surface seismic wavefield forward modeling device can be configured in an electronic device. Figure 1 As shown, the method includes:

[0033] S101, constructing the surface of the air layer area and the surface of the underground layer area according to the surface area spatial coordinates corresponding to the three-dimensional undulating surface and the target space grid node planning model.

[0034] The three-dimensional undulating surface may refer to the surface of the land area where the seismic acoustic wave field is to be determined. The surface area spatial coordinates may refer to the spatial coordinates corresponding to each surface element point constituting the three-dimensional undulating surface. It should be noted that the density of each surface element constituting the three-dimensional undulating surface may be determined according to actual conditions, and the present invention does not specifically limit this.

[0035] Figure 2 Schematic diagram of the surface structure of the region provided by the first embodiment of the present invention. Figure 2 As shown, the uppermost region surface is the air layer region surface, the middle region surface is the three-dimensional undulating surface, and the lowermost region surface is the underground region surface. It is worth noting that the air layer region surface may refer to the region surface of the air layer of the three-dimensional undulating surface, and the underground region surface may refer to the region surface of the underground layer of the three-dimensional undulating surface. Among them, the surface element points of the air layer region surface and the surface element points of the underground region surface are spatially symmetrical about the three-dimensional undulating surface.

[0036] Specifically, the spatial coordinates of each surface area can be input into the target space grid node planning model, so that the spatial coordinates corresponding to the air layer and the spatial coordinates corresponding to the underground layer can be obtained, and then the air layer area surface and the underground layer area surface can be constructed according to the spatial coordinates corresponding to the air layer and the spatial coordinates corresponding to the underground layer.

[0037] It should be noted that the air layer area surface determined by the target space grid node planning model is based on the real three-dimensional surface morphology, and the surface element points in the air layer area surface are all set on integer grid nodes to facilitate the subsequent spatial finite difference calculation. The shortest distance from the air layer area surface to the three-dimensional undulating surface can be calculated, and the point with the shortest distance between the three-dimensional undulating surface and the air layer area surface is the projection point of the air layer grid point, that is, the underground layer area surface.

[0038] Exemplarily, the method of constructing the air layer region surface and the underground layer region surface based on the surface region spatial coordinates corresponding to the three-dimensional undulating surface and the target space grid node planning model includes: for each of the surface region spatial coordinates in the three-dimensional undulating surface, inputting the surface region spatial coordinates into the target space grid node planning model to perform layer coordinate calculation, and determining the air layer region spatial coordinates corresponding to the surface region spatial coordinates; constructing the air layer region surface based on all the air layer region spatial coordinates; and constructing the underground layer region surface based on the air layer region surface and the three-dimensional undulating surface.

[0039] The underground region spatial coordinates may refer to the spatial coordinates corresponding to each surface element point constituting the underground region surface. The air region spatial coordinates may refer to the spatial coordinates corresponding to each surface element point constituting the air region surface.

[0040] Specifically, for each surface area spatial coordinate, the surface area spatial coordinate is input into the target space grid node planning model to calculate the air layer coordinate, and the calculation result is the air layer area spatial coordinate. All air layer area spatial coordinates are combined to construct the air layer area surface. According to the surface element points of the air layer area surface and the three-dimensional undulating surface, the surface element points of the underground layer area surface that are spatially symmetrical about the three-dimensional undulating surface are determined.

[0041] Exemplarily, the method of constructing the underground layer region surface that is symmetrical about the three-dimensional undulating surface based on the air layer region spatial coordinates and the surface region spatial coordinates includes: determining, based on the air layer region spatial coordinates and the surface region spatial coordinates, each underground layer region spatial coordinate that is symmetrical about the surface region spatial coordinates of the air layer region spatial coordinates; and constructing the underground layer region surface based on all the underground layer region spatial coordinates.

[0042] Specifically, according to the air layer region spatial coordinates, the underground layer region spatial coordinates that are symmetric to the surface region spatial coordinates are determined, and all the underground layer region spatial coordinates are combined to construct the underground layer region surface.

[0043] S102, determining the underground layer acoustic wave field value corresponding to the underground layer area surface and the air layer pseudo acoustic wave field value corresponding to the air layer area surface according to the earthquake source information, the finite difference algorithm and the underground layer area spatial coordinates corresponding to the underground layer area surface.

[0044] Among them, the earthquake source information may refer to the earthquake source information when the earthquake occurs. The underground acoustic wave field value may refer to the acoustic wave field value corresponding to each point on the surface of the underground layer area. The air layer pseudo acoustic wave field value may refer to the pseudo acoustic wave field value corresponding to each grid point on the surface of the air layer area introduced to drive the finite difference calculation.

[0045] Specifically, the earthquake source information and the spatial coordinates of the underground area corresponding to the underground area surface are input into the finite difference algorithm to calculate the underground acoustic wave field value corresponding to the underground area surface and the air layer pseudo acoustic wave field value corresponding to the air layer area surface.

[0046] S103, conducting a finite difference simulation of a three-dimensional undulating surface seismic wave field and implicitly realizing a free surface boundary condition of the surface according to the acoustic wave field value of the underground layer and the pseudo acoustic wave field value of the air layer.

[0047] Specifically, the pseudo-acoustic wave field value of the air layer is set to the opposite number of the acoustic wave field value of the underground layer. On the basis of determining the pseudo-acoustic wave field value of the air layer and the acoustic wave field value of the underground layer, the acoustic wave field value (pressure component) is converted into the particle vibration velocity component on the surface element point of the three-dimensional undulating surface according to the first-order acoustic wave equation, thereby realizing the finite difference simulation of the seismic wave field of the three-dimensional undulating surface, and the particle vibration velocity wave field value on the real surface can be obtained. At the same time, the acoustic wave field value on the corresponding surface area grid point is implicitly set to 0, and the surface free surface boundary condition is realized accordingly.

[0048] The technical solution of the embodiment of the present invention is to construct an air layer area surface and an underground layer area surface according to the surface area spatial coordinates corresponding to the three-dimensional undulating surface and the target space grid node planning model, wherein the air layer area surface and the underground layer area surface are spatially symmetric with respect to the three-dimensional undulating surface; determine the underground layer acoustic wave field value corresponding to the underground layer area surface and the air layer pseudo acoustic wave field value corresponding to the air layer area surface according to the source information, the finite difference algorithm and the underground layer area spatial coordinates corresponding to the underground layer area surface; carry out a finite difference simulation of the three-dimensional undulating surface seismic wave field according to the underground layer acoustic wave field value and the air layer pseudo acoustic wave field value and implicitly realize the surface free surface boundary condition, thereby solving the problem of high calculation cost and inability to be used in industry, reducing data errors in the numerical simulation process of the three-dimensional undulating surface seismic acoustic wave field, improving the accuracy of determining the seismic acoustic wave field value, effectively reducing data calculation costs, and improving practicality.

[0049] Embodiment 2

[0050] Figure 3 This is a flow chart of a forward modeling method for a three-dimensional undulating surface seismic wave field provided in the second embodiment of the present invention. Based on the above embodiments, this embodiment further refines the determination of the underground layer acoustic wave field value corresponding to the surface of the underground layer area and the air layer pseudo acoustic wave field value corresponding to the surface of the air layer area. Figure 3 As shown, the method includes:

[0051] S301, constructing the surface of the air layer area and the surface of the underground layer area according to the surface area spatial coordinates corresponding to the three-dimensional undulating surface and the target space grid node planning model.

[0052] S302: construct a virtual three-dimensional space grid according to the surface area spatial coordinates and the target space grid node planning model.

[0053] It should be noted that the virtual three-dimensional space grid can be simply understood as a three-dimensional grid divided by the real three-dimensional undulating surface on land. Figure 4 Schematic diagram of a virtual three-dimensional space grid provided in Embodiment 2 of the present invention. Figure 4 As shown, Figure 4 The light gray three-dimensional space grid is the constructed virtual three-dimensional space grid, the inclined dark gray plane is the three-dimensional undulating surface, the black hollow circles may refer to the surface element points in the air layer area surface, and the black solid circles may refer to the surface element points in the underground layer area surface.

[0054] It is worth noting that the virtual three-dimensional space grid at least includes the three-dimensional undulating surface, the surface of the air layer area and the surface of the underground layer area. The number of layers of the virtual three-dimensional space grid is generally set to be slightly larger than the difference order of the finite difference spatial derivative.

[0055] It is also important to note that Figure 4 As shown, in order to facilitate the participation in spatial finite difference calculations, based on the target space grid node planning model, the surface element points in the constructed air layer area surface are determined according to the real three-dimensional surface morphology, and all of them are set on the integer grid nodes of the virtual three-dimensional space grid to facilitate the participation in spatial finite difference calculations.

[0056] Specifically, for each surface area spatial coordinate, the surface area spatial coordinate is input into the target space grid node planning model, and the virtual three-dimensional space grid is obtained according to the output result of the target space grid node planning model.

[0057] S303: Determine the acoustic wave field value of the underground grid point corresponding to each underground grid point in the virtual three-dimensional space grid according to the earthquake source information and a finite difference algorithm.

[0058] The underground grid points are grid points in the virtual three-dimensional space grid that are located below the three-dimensional undulating surface. Figure 4 As shown, the underground grid point may refer to the light grey grid point under the three-dimensional undulating surface in the virtual three-dimensional space grid. The acoustic wave field value of the underground grid point may refer to the acoustic wave field value corresponding to the underground grid point.

[0059] Specifically, the finite difference algorithm uses the earthquake source information as input data, and then can calculate the underground grid point acoustic wave field value corresponding to each underground grid point.

[0060] Exemplarily, determining the underground grid point acoustic wave field value corresponding to each underground grid point in the virtual three-dimensional space grid based on the earthquake source information and the finite difference algorithm includes: determining the three-dimensional finite difference calculation formula corresponding to the finite difference algorithm when calculating the three-dimensional space acoustic wave field value; for each of the underground grid points, inputting the earthquake source space coordinates, the earthquake source signal and the grid point space coordinates corresponding to the underground grid point into the three-dimensional finite difference calculation formula to calculate the acoustic wave field value, and determining the underground grid point acoustic wave field value corresponding to the underground grid point based on the output of the three-dimensional finite difference calculation formula.

[0061] The earthquake source information includes the earthquake source spatial coordinates and the earthquake source signal; the acoustic wave equation of the classic second-order variable finite difference algorithm is shown in the following formula:

[0062]

[0063] Among them, p(x,t) represents the acoustic wave field value at time t at position x; s(t) represents the source signal; v(x) and ρ(x) represent the acoustic wave velocity and density distribution of the underground medium respectively; δ(x s ) represents the Delta function, which is used to calculate the source space coordinate x s Load the source signal at .

[0064] The acoustic wave equation of the second-order variable finite difference algorithm is converted into a three-dimensional finite difference calculation formula. The three-dimensional finite difference calculation formula is as follows:

[0065]

[0066] Among them, x s ,y s and z s represents the three-dimensional spatial coordinates of the earthquake source; p(x,y,z,t) represents the acoustic wave field value at the position x,y,z at time t, s(t) represents the earthquake source signal, v(x,y,z,t) and p(x,y,z,t) represent the acoustic wave velocity and density distribution of the underground medium respectively, δ(x s ,yy s ,zz s ) represents the Delta function, which is used to calculate the source space coordinate (x s ,y s ,z s ) is loaded with the source signal.

[0067] Specifically, for each underground grid point, the earthquake source spatial coordinates, earthquake source signal and the grid point spatial coordinates corresponding to the underground grid point can be used as input signals, and input into a three-dimensional finite difference calculation formula to calculate the acoustic wave field value. According to the output of the three-dimensional finite difference calculation formula, the acoustic wave field value of the underground grid point corresponding to each underground grid point can be obtained.

[0068] It should be noted that when the finite difference method is used to solve the seismic wave field, the accuracy of the numerical calculation is related to the size of the underground grid in the virtual three-dimensional space grid, the density of the grid division, and also depends on the accuracy of the time differential and space differential in the partial differential equation calculation.

[0069] S304, determining the acoustic wave field value of the underground layer corresponding to the surface of the underground layer area according to the acoustic wave field value of the underground grid point and an interpolation algorithm;

[0070] The acoustic wave field value of the underground layer may refer to the acoustic wave field value corresponding to the surface of the underground layer area, that is, Figure 2 , the acoustic wave field value corresponding to the surface of the lowest layer.

[0071] It should be noted that if Figure 4 As shown, regarding the three-dimensional undulating surface, most of the surface element points in the underground layer area surface that is spatially symmetrical with the air layer area surface are located on non-integer space grid points, and the underground layer acoustic wave field values ​​cannot be directly calculated in the finite difference implementation process. In order to calculate the acoustic wave field value corresponding to the underground layer area surface on the non-integer grid, consider using the wave field at the surrounding integer grid points in the three-dimensional region (i.e., the acoustic wave field value of the underground grid point corresponding to the underground grid point in S203), and obtain the acoustic wave field value corresponding to the underground layer area surface located on the non-integer grid point by interpolation. This method needs to be performed within each finite difference time step. After obtaining the wave field at that moment, the acoustic wave field value corresponding to the underground layer area surface is calculated by three-dimensional space interpolation.

[0072] Exemplarily, determining the underground layer sound wave field value corresponding to the underground layer area surface according to the underground grid point sound wave field value and the interpolation algorithm includes: for each underground layer area point in the underground layer area surface, determining a preset number of underground grid points around the underground layer area point; determining the three-dimensional space domain interpolation coefficient and the interpolation calculation window function term according to the underground layer area spatial coordinates corresponding to the underground layer area point and the underground grid point spatial coordinates corresponding to the underground grid point; determining the underground layer sound wave field value corresponding to the underground layer area surface according to the interpolation coefficient, the interpolation calculation window function term and the sound wave field value of a preset number of underground grid points around the underground layer area point.

[0073] The underground layer region point may refer to the surface element point constituting the surface of the underground layer region.

[0074] Specifically, the present invention needs to perform three-dimensional interpolation calculation on the wave field value in three-dimensional space. The present invention uses the SINC function under the action of the Kaiser window to perform high-precision three-dimensional space interpolation calculation. The present invention can use the SINC function to calculate the interpolation coefficient of the SINC according to the spatial coordinates of the underground layer area corresponding to the underground layer area point.

[0075] The interpolation coefficient calculation formula is as follows:

[0076]

[0077] Among them, x is the spatial coordinate of the underground area point.

[0078] Since the SINC function is a continuous function, it needs to be windowed in the actual calculation process to achieve high-precision sampling. The present invention uses a preset number of underground grid points around the underground layer area point to determine the interpolation calculation window function term. Preferably, the present invention uses the Kaiser function with 4 sampling points on each side and a total of 9 points as the interpolation calculation window function term. Among them, Figure 5 The relationship between the interpolation coefficient and the window function is shown in the figure below: Figure 5 shown.

[0079] Specifically, the interpolation calculation window function term is determined as follows:

[0080]

[0081] Where I0 is the first kind zero-order modified Bessel function.

[0082] In the actual calculation process, because the windowed SINC interpolation calculation is performed for 9×9×9 sample points in the three-dimensional space near each underground layer area point, in order to save the amount of calculation, the Kaiser windowed SINC function interpolation coefficient multidimensional array within a specific accuracy range can be calculated in advance and introduced into the interpolation calculation. Taking the example of 20 times encryption between each adjacent grid, such as a 10m spatial sampling interval, the interpolation accuracy after segmentation can be accurate to 0.5m, and the corresponding interpolation coefficient is a 6-dimensional array with a size of 9×9×9×20×20×20.

[0083] The underground layer area point is set as the center of the interpolation area, and the 9×9×9 integer grid sample points in the surrounding area are used as input. The wave field values ​​at each grid point in the underground layer are obtained by interpolating and weighted averaging the interpolation coefficients of the updated points in the area to be interpolated and the wave field values ​​at the three-dimensional grid points near the mirror symmetric points.

[0084] Specifically, the interpolation expression is as follows:

[0085]

[0086] Among them, ix, iy, iz are the integer grid point numbers of the three-dimensional area near the underground area point to be interpolated. P(ix, iy, iz) is the acoustic wave field value corresponding to the area point to be superimposed in the underground area point at the current moment, P 3d-intelp (x) is the point wave field value of the underground layer area after three-dimensional SINC interpolation.

[0087] Similarly, the acoustic wave field value corresponding to each underground layer area point in the underground layer area surface can be obtained.

[0088] It should be noted that since the three-dimensional interpolation process may involve the sound wave field value corresponding to the surface of the air layer area above the three-dimensional undulating surface, the sound wave field value corresponding to the surface of the air layer area is an unknown quantity at this time. The pseudo sound wave field value of the air layer involved in the interpolation is initially set to 0 in each finite difference time step, so that it participates in the spatial interpolation calculation, and the underground sound wave field value obtained that is symmetrical about the three-dimensional undulating surface is multiplied by -1 and assigned to the surface element point of the air layer area surface, so that it obtains the corresponding sound wave field value. This process is iterated in a loop to obtain the sound wave field value of the air layer grid point located above the three-dimensional undulating surface in the virtual three-dimensional space grid. Exemplarily, for the three-dimensional surface calculation test, iterations within 5 times can obtain relatively stable sound wave field values ​​of the air layer grid points, so that it can participate in the calculation of the next finite difference time step at the three-dimensional surface.

[0089] S305 . Determine, according to the underground layer acoustic wave field value, an air layer pseudo acoustic wave field value corresponding to the surface of the air layer region.

[0090] Specifically, according to the underground layer acoustic wave field value, the air layer pseudo acoustic wave field value corresponding to the air layer region surface is calculated by the principle that the air layer region surface and the underground layer region surface are spatially symmetric with respect to the three-dimensional undulating surface.

[0091] Exemplarily, determining the air layer pseudo sound wave field value corresponding to the surface of the air layer area based on the underground layer sound wave field value includes: determining the opposite sound wave field value corresponding to the underground layer sound wave field value, and determining the opposite sound wave field value as the air layer pseudo sound wave field value corresponding to the surface of the air layer area.

[0092] Specifically, since the grid pressure component of the air layer in the virtual three-dimensional space grid is always 0, the normal central difference operation at the boundary of the real land undulating surface can be realized by determining the opposite number based on the acoustic wave field value of the underground layer, and the free surface boundary condition is realized at the same time. The wave field value located on the surface of the air layer area is obtained by artificially setting the opposite number of the wave field at the underground symmetric point. This processing method expresses the free surface boundary condition of the undulating surface in the calculation at the undulating surface, and also ensures the stability of the wave field finite difference in the actual calculation domain.

[0093] S306. According to the acoustic wave field value of the underground layer and the pseudo acoustic wave field value of the air layer, a finite difference simulation of the seismic wave field of the three-dimensional undulating surface is performed and the three-dimensional undulating surface with the free surface boundary condition of the surface is implicitly realized.

[0094] The technical solution of the present invention constructs a virtual three-dimensional space grid according to the spatial coordinates of the surface area and the target space grid node planning model. According to the source information and the finite difference algorithm, the acoustic wave field values ​​of the underground grid points corresponding to each underground grid point in the virtual three-dimensional space grid are determined. According to the acoustic wave field values ​​of the underground grid points and the interpolation algorithm, the acoustic wave field values ​​of the underground layer corresponding to the surface of the underground layer area are determined. According to the acoustic wave field values ​​of the underground layer, the pseudo acoustic wave field values ​​of the air layer corresponding to the surface of the air layer area are determined. In the calculation process, the false diffraction waves generated by the "step-shaped" grid formed by the discretization of the model can be significantly reduced. These false signals will cover the effective reflection wave components in the area where the model is more complex. At the same time, the travel time of the reflection wave related to the free surface calculated by the present invention is more accurate than the conventional vacuum finite difference method, and the simulated reflection wave travel time is almost completely consistent with the theoretical result. On the other hand, by pre-setting the form of a specific precision three-dimensional space interpolation coefficient array table, on the basis of having a sufficiently high three-dimensional space wave field interpolation accuracy, the calculation amount of three-dimensional interpolation is significantly reduced, and it has great potential in practical applications.

[0095] Embodiment 3

[0096] Figure 6 The schematic diagram of the structure of a three-dimensional undulating surface seismic wave field forward modeling device provided in the third embodiment of the present invention. Figure 6 As shown, the device comprises:

[0097] The regional surface construction module 601 is used to construct an air layer regional surface and an underground layer regional surface according to the surface regional spatial coordinates corresponding to the three-dimensional undulating surface and the target space grid node planning model, wherein the air layer regional surface and the underground layer regional surface are spatially symmetrical about the three-dimensional undulating surface;

[0098] The acoustic wave field value determination module 602 is used to determine the underground layer acoustic wave field value corresponding to the underground layer area surface and the air layer pseudo acoustic wave field value corresponding to the air layer area surface according to the earthquake source information, the finite difference algorithm and the underground layer area spatial coordinates corresponding to the underground layer area surface;

[0099] The surface acoustic wave field forward modeling module 603 is used to carry out numerical simulation of three-dimensional undulating surface seismic wave fields and implicitly realize the surface free surface boundary conditions according to the underground layer acoustic wave field values ​​and the air layer pseudo acoustic wave field values.

[0100] The technical solution of the embodiment of the present invention is to construct an air layer area surface and an underground layer area surface according to the surface area spatial coordinates corresponding to the three-dimensional undulating surface and the target space grid node planning model, wherein the air layer area surface and the underground layer area surface are spatially symmetric with respect to the three-dimensional undulating surface; determine the underground layer acoustic wave field value corresponding to the underground layer area surface and the air layer pseudo acoustic wave field value corresponding to the air layer area surface according to the source information, the finite difference algorithm and the underground layer area spatial coordinates corresponding to the underground layer area surface; carry out numerical simulation of the seismic wave field of the three-dimensional undulating surface and implicitly realize the free surface boundary condition of the surface according to the underground layer acoustic wave field value and the air layer pseudo acoustic wave field value, thereby solving the problem of high calculation cost and inability to be used in industry, reducing data errors in the numerical simulation process of the seismic acoustic wave field of the three-dimensional undulating surface, improving the accuracy of determining the seismic acoustic wave field value, effectively reducing data calculation costs, and improving practicality.

[0101] Optionally, the regional surface construction module 601 includes:

[0102] A regional spatial coordinate determination unit is used for inputting the surface regional spatial coordinate into the target space grid node planning model for layer coordinate calculation for each surface regional spatial coordinate in the three-dimensional undulating surface, and determining the air layer regional spatial coordinate corresponding to the surface regional spatial coordinate;

[0103] An air layer region surface construction unit, used for constructing the air layer region surface according to all the air layer region space coordinates;

[0104] The underground layer area surface construction unit is used to construct the underground layer area surface according to the air layer area surface and the three-dimensional undulating surface.

[0105] Optionally, the underground layer area surface construction unit is specifically used to:

[0106] Determine, based on the air layer region spatial coordinates and the surface region spatial coordinates, the spatial coordinates of each underground layer region that is symmetrical about the surface region spatial coordinates of the air layer region;

[0107] The surface of the underground layer area is constructed according to all the spatial coordinates of the underground layer area.

[0108] Optionally, the acoustic wave field value determination module 602 includes:

[0109] A spatial grid construction unit, configured to construct a virtual three-dimensional spatial grid according to the spatial coordinates of the surface area and the target spatial grid node planning model, wherein the virtual three-dimensional spatial grid at least covers the three-dimensional undulating surface, the surface of the air layer area and the surface of the underground layer area;

[0110] A grid point acoustic wave field value determination unit is used to determine the underground grid point acoustic wave field value corresponding to each underground grid point in the virtual three-dimensional space grid according to the earthquake source information and the finite difference algorithm, wherein the underground grid point is a grid point in the virtual three-dimensional space grid located below the three-dimensional undulating surface;

[0111] An underground layer acoustic wave field value determination unit, used to determine the underground layer acoustic wave field value corresponding to the surface of the underground layer area according to the underground grid point acoustic wave field value and an interpolation algorithm;

[0112] The air layer pseudo acoustic wave field value determining unit is used to determine the air layer pseudo acoustic wave field value corresponding to the surface of the air layer area according to the underground layer acoustic wave field value.

[0113] Optionally, the grid point acoustic wave field value determination unit is specifically used to:

[0114] Determine a three-dimensional finite difference calculation formula corresponding to the finite difference algorithm when calculating a three-dimensional space acoustic wave field value;

[0115] For each of the underground grid points, the source spatial coordinates, the source signal and the grid point spatial coordinates corresponding to the underground grid point are input into the three-dimensional finite difference calculation formula to calculate the acoustic wave field value, and based on the output of the three-dimensional finite difference calculation formula, the underground grid point acoustic wave field value corresponding to the underground grid point is determined.

[0116] Optionally, the underground layer acoustic wave field value determination unit is specifically used to:

[0117] For each underground layer area point in the underground layer area surface, determining a preset number of underground grid points around the underground layer area point;

[0118] Determine three-dimensional space domain interpolation coefficients and interpolation calculation window function terms according to the underground layer area spatial coordinates corresponding to the underground layer area points and the underground grid point spatial coordinates corresponding to the underground grid points;

[0119] The underground acoustic wave field value corresponding to the underground area surface is determined according to the interpolation coefficient, the interpolation calculation window function term and the acoustic wave field values ​​of a preset number of underground grid points around the underground area point.

[0120] Optionally, the air layer pseudo-acoustic wave field value determination unit is specifically used to:

[0121] An opposite acoustic wave field value corresponding to the underground layer acoustic wave field value is determined, and the opposite acoustic wave field value is determined as an air layer pseudo acoustic wave field value corresponding to the surface of the air layer region.

[0122] The three-dimensional undulating surface seismic wavefield forward modeling device provided in the embodiment of the present invention can execute the three-dimensional undulating surface seismic wavefield forward modeling method provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the execution method.

[0123] Embodiment 4

[0124] Figure 7 A schematic diagram of the structure of an electronic device 10 that can be used to implement an embodiment of the present invention is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices (such as helmets, glasses, watches, etc.) and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present invention described and / or required herein.

[0125] like Figure 7 As shown, the electronic device 10 includes at least one processor 11, and a memory connected to the at least one processor 11, such as a read-only memory (ROM) 12, a random access memory (RAM) 13, etc., wherein the memory stores a computer program that can be executed by at least one processor, and the processor 11 can perform various appropriate actions and processes according to the computer program stored in the read-only memory (ROM) 12 or the computer program loaded from the storage unit 18 to the random access memory (RAM) 13. In the RAM 13, various programs and data required for the operation of the electronic device 10 can also be stored. The processor 11, the ROM 12, and the RAM 13 are connected to each other through a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.

[0126] A number of components in the electronic device 10 are connected to the I / O interface 15, including: an input unit 16, such as a keyboard, a mouse, etc.; an output unit 17, such as various types of displays, speakers, etc.; a storage unit 18, such as a disk, an optical disk, etc.; and a communication unit 19, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 19 allows the electronic device 10 to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks.

[0127] The processor 11 may be a variety of general and / or special processing components with processing and computing capabilities. Some examples of the processor 11 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, a digital signal processor (DSP), and any appropriate processor, controller, microcontroller, etc. The processor 11 executes the various methods and processes described above, such as the method for three-dimensional undulating surface seismic wave field forward modeling.

[0128] In some embodiments, the method of three-dimensional undulating surface seismic wavefield forward modeling can be implemented as a computer program, which is tangibly contained in a computer-readable storage medium, such as a storage unit 18. In some embodiments, part or all of the computer program can be loaded and / or installed on the electronic device 10 via the ROM 12 and / or the communication unit 19. When the computer program is loaded into the RAM 13 and executed by the processor 11, one or more steps of the method of three-dimensional undulating surface seismic wavefield forward modeling described above can be performed. Alternatively, in other embodiments, the processor 11 can be configured to perform the method of three-dimensional undulating surface seismic wavefield forward modeling in any other appropriate manner (for example, by means of firmware).

[0129] Various implementations of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chips (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0130] Computer programs for implementing the methods of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that when the computer program is executed by the processor, the functions / operations specified in the flow chart and / or block diagram are implemented. The computer program may be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a stand-alone software package, or entirely on a remote machine or server.

[0131] In the context of the present invention, a computer-readable storage medium may be a tangible medium that may contain or store a computer program for use by or in combination with an instruction execution system, device or equipment. A computer-readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices or equipment, or any suitable combination of the foregoing. Alternatively, a computer-readable storage medium may be a machine-readable signal medium. A more specific example of a machine-readable storage medium may include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0132] To provide interaction with a user, the systems and techniques described herein may be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and a pointing device (e.g., a mouse or trackball) through which the user can provide input to the electronic device. Other types of devices may also be used to provide interaction with the user; for example, the feedback provided to the user may be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any form (including acoustic input, voice input, or tactile input).

[0133] The systems and techniques described herein may be implemented in a computing system that includes backend components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes frontend components (e.g., a user computer with a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such backend components, middleware components, or frontend components. The components of the system may be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), a blockchain network, and the Internet.

[0134] A computing system may include a client and a server. The client and the server are generally remote from each other and usually interact through a communication network. The client and server relationship is generated by computer programs running on the corresponding computers and having a client-server relationship with each other. The server may be a cloud server, also known as a cloud computing server or cloud host, which is a host product in the cloud computing service system to solve the defects of difficult management and weak business scalability in traditional physical hosts and VPS services.

[0135] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the present invention can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solution of the present invention can be achieved, and this document does not limit this.

[0136] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A three-dimensional undulating surface seismic wave field forward modeling method, characterized in that: include: According to the spatial coordinates of the surface area corresponding to the three-dimensional undulating surface and the target space grid node planning model, the surface of the air layer area and the surface of the underground layer area are constructed, wherein the surface element points of the air layer area surface and the surface element points of the underground layer area surface are spatially symmetrical about the three-dimensional undulating surface; Determine the underground layer acoustic wave field value corresponding to the underground layer area surface and the air layer pseudo acoustic wave field value corresponding to the air layer area surface according to the earthquake source information, the finite difference algorithm and the underground layer area spatial coordinates corresponding to the underground layer area surface; According to the acoustic wave field value of the underground layer and the pseudo acoustic wave field value of the air layer, a finite difference simulation of the seismic wave field of the three-dimensional undulating surface is carried out and the three-dimensional undulating surface with the boundary condition of the surface free surface is implicitly realized.

2. The method according to claim 1, characterized in that The method of constructing the surface of the air layer region and the surface of the underground layer region according to the spatial coordinates of the surface region corresponding to the three-dimensional undulating surface and the target space grid node planning model includes: For each of the surface area spatial coordinates in the three-dimensional undulating surface, the surface area spatial coordinates are input into the target space grid node planning model to perform layer coordinate calculation, and the air layer area spatial coordinates corresponding to the surface area spatial coordinates are determined; Constructing the surface of the air layer region according to the spatial coordinates of all the air layer regions; The surface of the underground layer area is constructed based on the surface of the air layer area and the three-dimensional undulating surface.

3. The method according to claim 2, characterized in that The step of constructing the underground layer region surface that is symmetrical about the three-dimensional undulating surface according to the air layer region spatial coordinates and the surface region spatial coordinates comprises: Determine, based on the air layer region spatial coordinates and the surface region spatial coordinates, the spatial coordinates of each underground layer region that is symmetrical about the surface region spatial coordinates of the air layer region; The surface of the underground layer area is constructed according to all the spatial coordinates of the underground layer area.

4. The method according to claim 1, characterized in that: The method of determining the underground layer acoustic wave field value corresponding to the underground layer area surface and the air layer pseudo acoustic wave field value corresponding to the air layer area surface according to the earthquake source information, the finite difference algorithm and the underground layer area spatial coordinates corresponding to the underground layer area surface comprises: According to the surface area spatial coordinates and the target space grid node planning model, a virtual three-dimensional space grid is constructed, wherein the virtual three-dimensional space grid at least covers the three-dimensional undulating surface, the surface of the air layer area and the surface of the underground layer area; Determine the acoustic wave field value of the underground grid point corresponding to each underground grid point in the virtual three-dimensional space grid according to the earthquake source information and the finite difference algorithm, wherein the underground grid point is a grid point in the virtual three-dimensional space grid located below the three-dimensional undulating surface; Determining the acoustic wave field value of the underground layer corresponding to the surface of the underground layer area according to the acoustic wave field value of the underground grid point and an interpolation algorithm; According to the underground layer sound wave field value, the air layer pseudo sound wave field value corresponding to the surface of the air layer area is determined.

5. The method according to claim 4, characterized in that The earthquake source information includes earthquake source spatial coordinates and earthquake source signals; the method of determining the acoustic wave field values ​​of underground grid points corresponding to each underground grid point in the virtual three-dimensional space grid according to the earthquake source information and a finite difference algorithm includes: Determine a three-dimensional finite difference calculation formula corresponding to the finite difference algorithm when calculating a three-dimensional space acoustic wave field value; For each of the underground grid points, the source spatial coordinates, the source signal and the grid point spatial coordinates corresponding to the underground grid point are input into the three-dimensional finite difference calculation formula to calculate the acoustic wave field value, and based on the output of the three-dimensional finite difference calculation formula, the underground grid point acoustic wave field value corresponding to the underground grid point is determined.

6. The method according to claim 4, characterized in that The step of determining the underground layer acoustic wave field value corresponding to the surface of the underground layer area according to the underground grid point acoustic wave field value and an interpolation algorithm includes: For each underground layer area point in the underground layer area surface, determining a preset number of underground grid points around the underground layer area point; Determine three-dimensional space domain interpolation coefficients and interpolation calculation window function terms according to the underground layer area spatial coordinates corresponding to the underground layer area points and the underground grid point spatial coordinates corresponding to the underground grid points; The underground acoustic wave field value corresponding to the underground area surface is determined according to the interpolation coefficient, the interpolation calculation window function term and the acoustic wave field values ​​of a preset number of underground grid points around the underground area point.

7. The method according to claim 4, characterized in that The step of determining the air layer pseudo sound wave field value corresponding to the surface of the air layer region according to the underground layer sound wave field value comprises: An opposite acoustic wave field value corresponding to the underground layer acoustic wave field value is determined, and the opposite acoustic wave field value is determined as an air layer pseudo acoustic wave field value corresponding to the surface of the air layer region.

8. A three-dimensional undulating surface seismic wave field forward modeling device, characterized in that: include: A regional surface construction module is used to construct an air layer regional surface and an underground layer regional surface according to the surface regional spatial coordinates corresponding to the three-dimensional undulating surface and the target space grid node planning model, wherein the air layer regional surface and the underground layer regional surface are spatially symmetrical about the three-dimensional undulating surface; An acoustic wave field value determination module is used to determine the underground layer acoustic wave field value corresponding to the underground layer area surface and the air layer pseudo acoustic wave field value corresponding to the air layer area surface according to the earthquake source information, the finite difference algorithm and the underground layer area spatial coordinates corresponding to the underground layer area surface; The surface acoustic wave field forward modeling module is used to carry out the finite difference simulation of the three-dimensional undulating surface seismic wave field and implicitly realize the surface free surface boundary condition according to the underground layer acoustic wave field value and the air layer pseudo acoustic wave field value.

9. An electronic device, characterized in that: The electronic device comprises: at least one processor; and a memory communicatively connected to the at least one processor; wherein, The memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor so that the at least one processor can perform the three-dimensional rough surface seismic wavefield forward modeling method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to implement the three-dimensional undulating surface seismic wave field forward modeling method according to any one of claims 1 to 7 when executed.

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