CN112505775B - Seismic wave forward modeling method and device, storage medium and processor - Google Patents
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Abstract
The embodiment of the invention provides a seismic wave forward modeling method, a device, a storage medium and a processor, belonging to the technical field of geophysical exploration, wherein the method comprises the following steps: acquiring a three-dimensional frequency domain wave equation; performing finite difference processing on the wave equation based on a 125-point finite difference format to obtain a discrete equation; and performing seismic wave forward modeling by using the discrete equation.
Description
Technical Field
The invention relates to the technical field of geophysical exploration, in particular to a seismic wave forward modeling method, a seismic wave forward modeling device, a storage medium and a processor.
Background
The seismic wave forward modeling mainly aims to obtain the propagation rule of seismic waves in a known underground geological model, including propagation time, paths, energy and the like. Through forward modeling, the kinematics and dynamics characteristics of seismic wave propagation in a complex medium can be correctly known, and the characteristics of a reflection seismic wave field generated by a subsurface geological structure can be accurately analyzed.
In the related art, wave equations are often used to perform forward modeling on seismic waves, and numerical methods for forward modeling of seismic waves based on wave equations mainly include a pseudo-spectrum method, a finite element method, a finite difference method, and the like. Among them, the finite difference method is a commonly used method.
However, in the related art, the process of forward modeling the seismic waves based on the wave equation by using the finite difference method needs to be optimized.
Disclosure of Invention
The embodiment of the invention aims to provide a seismic wave forward modeling method, a seismic wave forward modeling device, a storage medium and a processor.
In order to achieve the above object, a first aspect of the present invention provides a seismic wave forward modeling method, including:
acquiring a three-dimensional frequency domain wave equation;
performing finite difference processing on the wave equation based on a 125-point finite difference format to obtain a discrete equation;
and performing seismic wave forward modeling by using the discrete equation.
Optionally, the obtaining the three-dimensional frequency domain wave equation includes:
and acquiring a three-dimensional frequency domain scalar wave equation.
Optionally, the obtaining of the three-dimensional frequency domain scalar wave equation includes:
acquiring a first-order displacement-stress scalar wave equation based on a Cauchy equation, a geometric equation and a Navier equation;
acquiring a second-order time domain scalar wave equation according to the first-order displacement-stress scalar wave equation;
and performing Fourier transform on the second-order time domain equation to obtain a three-dimensional frequency domain scalar wave equation.
Optionally, the first-order displacement-stress scalar wave equation includes:
wherein u (x, t) ═ u x ,u y ,u z ] T Represents the displacement, P (x, t) represents the liquid pressure, f (x, t) represents the seismic source term, x ═ x, y, z]Representing spatial position, t representing time, p representing a density parameter, L representing a partial differential operator, K representing a stiffness tensor matrix,
denotes the partial derivative, L T A transposed matrix, u, representing L x A displacement amount, u, in the x-coordinate direction representing a spatial position x y Displacement in the y coordinate direction, u, representing the spatial position x z Indicating the amount of displacement in the z-coordinate direction of the spatial position x.
Optionally, the second-order time domain scalar wave equation includes:
wherein,
denotes the Laplace operator, u (x, t) ═ u x ,u y ,u z ] T Represents the displacement, f (x, t) represents the seismic source term, and x is [ x, y, z ]]Representing the spatial position, t representing the time,
denotes partial derivative, u x A displacement amount, u, in the x-coordinate direction representing a spatial position x y A displacement amount, u, in the y-coordinate direction representing the spatial position x z Indicating the amount of displacement in the z-coordinate direction of the spatial position x.
Optionally, the three-dimensional frequency domain scalar wave equation includes:
wherein,
denotes a laplacian operator, U (x, ω) denotes a displacement amount corresponding to a frequency domain, ω denotes an angular frequency, v denotes a velocity, and x ═ x, y, z]Representing the spatial position, and f (x, t) representing the seismic source term.
Optionally, the 125-point finite difference format includes:
wherein, a i ，b i And c i Point pair representing different distance positions i
And
i ∈ (0, 26), dx represents the grid interval; u represents the corresponding shift amount in the frequency domain,
denotes the partial derivative, ax denotes the spatial sampling interval in the x-direction, ay denotes the spatial sampling interval in the y-direction, az denotes the spatial sampling interval in the z-direction,
representing the spatial partial derivative taken in the x-direction,
meaning taking the spatial partial derivative for the y-direction,
representing the taking of the spatial partial derivative, u, in the z direction i,j,k U (i Δ x, j Δ y, k Δ z) represents the frequency domain displacement amount at the grid point (i, j, k).
The invention provides a seismic wave forward modeling device in a second aspect, comprising:
the acquisition module is used for acquiring a three-dimensional frequency domain wave equation;
the finite difference module is used for carrying out finite difference processing on the wave equation based on a 125-point finite difference format to obtain a discrete equation;
and the forward modeling module is used for performing seismic wave forward modeling by using the discrete equation.
A third aspect of the present invention provides a machine-readable storage medium having stored thereon instructions for causing a machine to perform the seismic wave forward modeling method of any of the above-described embodiments of the present application.
A fourth aspect of the invention provides a processor, wherein the program is configured to execute the seismic wave forward modeling method according to any one of the above-mentioned embodiments.
Through the technical scheme, when the wave equation is numerically simulated by using the finite difference method, the difference of 125 grid points is adopted to replace the partial derivative of the central point of the wave equation, and compared with the prior art in which the difference of 27 grid points is adopted to replace the partial derivative of the central point of the wave equation, the precision is higher and the numerical dispersion is less.
Additional features and advantages of embodiments of the invention will be set forth in the detailed description which follows.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the embodiments of the invention and not to limit the embodiments of the invention. In the drawings:
FIG. 1 is a schematic flow chart of a seismic wave forward modeling method according to an embodiment of the invention;
FIG. 2 is a schematic process diagram of a finite difference method according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a 125-point finite difference grid distribution according to an embodiment of the present invention;
FIG. 4a is a 30Hz frequency domain wave field snapshot of a 27-point finite difference homogeneous medium according to an embodiment of the present invention;
FIG. 4b is a diagram of a snapshot of a frequency domain wave field of a 125-point finite difference homogeneous medium at 30Hz in accordance with an embodiment of the present invention;
FIG. 5a is a schematic time slice of 30Hz frequency domain of 27-point finite difference homogeneous medium according to the embodiment of the present invention;
FIG. 5b is a time slice diagram of a 30Hz frequency domain of a 125-point finite difference homogeneous medium according to an embodiment of the present invention;
FIG. 6 is a block diagram of the seismic forward modeling apparatus according to the embodiment of the present invention;
fig. 7 is an internal structural diagram of a computer device according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating embodiments of the invention, are given by way of illustration and explanation only, not limitation.
With the continuous development of seismic exploration technology and the continuous progress of the technology, reservoir seismic exploration develops towards a complex direction. With the reservoir exploration target scale becoming smaller and smaller, how to improve the inversion accuracy of the reservoir elastic parameters is a necessary requirement for geological inversion technology. Since the true formation information in the subsurface is three-dimensional, the waveform inversion gradually goes from two dimensions to three dimensions in order to provide a more accurate velocity model (which can be understood as a wavefield model).
Forward simulation is the basis of waveform inversion and reverse time migration, and the calculation precision and efficiency of forward calculation directly determine the precision of reverse time migration and waveform inversion, so that the improvement of the accuracy and effectiveness of forward operators is very important. Forward modeling often uses wave equations to model the wave process of seismic source waves in different media.
The numerical simulation method of the wave equation includes a finite difference method, a finite element method, a pseudo-spectrum method, and the like. The finite difference method is an important method for carrying out wave equation numerical simulation, has the advantages of high calculation speed, small occupied memory and the like, but the finite difference method adopted in the related technology has the problems of large numerical dispersion and low precision and resolution of wave field simulation when carrying out numerical simulation on the wave direction.
Based on this, in various embodiments of the present invention, a three-dimensional frequency domain wave equation is obtained, and a 125-point finite difference format is adopted to perform discrete difference processing on the wave equation, so as to realize forward modeling of the three-dimensional frequency domain wave equation. According to the scheme of the embodiment of the invention, the 125-point finite difference format is adopted to carry out difference processing on the wave equation, so that the numerical value dispersion phenomenon in the forward simulation process of the wave equation is reduced, and the precision in the forward simulation process of the wave equation is improved.
The embodiment of the invention provides a seismic wave forward modeling method, which comprises the following steps of:
step 101: acquiring a three-dimensional frequency domain wave equation;
step 102: performing finite difference processing on the wave equation based on a 125-point finite difference format to obtain a discrete equation;
step 103: and performing seismic wave forward modeling by using the discrete equation.
In practical application, because the calculation process of the time domain can be calculated recursively according to time slices, the rounding error of each time slice can be accumulated in the next time slice, and when the number of the calculated time slices is large, the accumulated error is large, the value of the simulated wave field is small, and the signal-to-noise ratio of the simulated result is low, the wave equation of the frequency domain is adopted in the invention. In the calculation process of the frequency domain, an equation set is integrally solved for the spatial grid according to the frequency slices, calculation errors are distributed to each grid point, and the frequency slices are independently calculated without accumulative errors, so that the method provided by the invention adopts the wave equation of the frequency domain, is beneficial to reducing the errors of seismic wave forward modeling and improving the accuracy of the seismic wave forward modeling.
In practical application, the wave equation can be used for representing wave characteristics of seismic waves propagating in various geological media.
In practical application, the wave equation can be wave equations of various types of seismic waves, such as wave equations of elastic waves and wave equations of scalar waves.
In an embodiment, taking a wave equation of a scalar wave as an example, the obtaining of the three-dimensional frequency domain scalar wave equation is described, including:
acquiring a first-order displacement-stress scalar wave equation based on a Cauchy equation, a geometric equation and a Navier equation;
acquiring a second-order time domain scale wave equation according to the first-order displacement-stress scale wave equation;
and performing Fourier transform on the second-order time domain equation to obtain a three-dimensional frequency domain scalar wave equation.
In practical application, the first-order displacement-stress scalar wave equation comprises:
wherein u (x, t) ═ u x ,u y ,u z ] T Represents the displacement, P (x, t) represents the liquid pressure, f (x, t) represents the seismic source term, x ═ x, y, z]Representing the spatial position, t time, p density parameter, L partial differential operator, K stiffness tensor matrix,
denotes the partial derivative, L T A transposed matrix, u, representing L x Displacement in the x coordinate direction, u, representing spatial position x y Displacement in the y coordinate direction, u, representing the spatial position x z Indicating the amount of displacement in the z-coordinate direction of the spatial position x.
In practical application, in the above formula (1),
wherein, λ represents the Lame coefficient,
meaning taking the spatial partial derivative for the x-direction,
meaning taking the spatial partial derivative for the y-direction,
representing taking the spatial partial derivative for the z direction.
In practical application, the stress equation in the first-order displacement-stress scalar wave equation can be substituted into the displacement equation in the first-order displacement-stress scalar wave equation to obtain a second-order time domain scalar wave equation.
In practical application, the second-order time domain scalar wave equation includes:
wherein,
denotes the Laplace operator, u (x, t) ═ u x ,u y ,u z ] T Represents the displacement, f (x, t) represents the seismic source term, and x is [ x, y, z ]]Representing the spatial position, t representing the time,
denotes partial derivative, u x Displacement in the x coordinate direction, u, representing spatial position x y Displacement in the y coordinate direction, u, representing the spatial position x z Indicating the amount of displacement in the z-coordinate direction of the spatial position x.
In practical application, the three-dimensional frequency domain scalar wave equation comprises:
wherein,
denotes a laplacian operator, U (x, ω) denotes a displacement amount corresponding to a frequency domain, ω denotes an angular frequency, v denotes a velocity, and x ═ x, y, z denotes [ x, y, z ]]Representing spatial position, and f (x, t) representing the seismic source term.
In practical applications, the above formula (4) can be expressed as:
wherein u (x, t) ═ u x ,u y ,u z ] T Represents the displacement, f (x, t) represents the seismic source term, x ═ x, y, z]Representing spatial position, t representing time,
denotes partial derivative, u x A displacement amount, u, in the x-coordinate direction representing a spatial position x y Displacement in the y coordinate direction, u, representing the spatial position x z Indicating the amount of displacement in the z-coordinate direction of the spatial position x.
According to the formula (5), since
Therefore, when the forward modeling of the seismic waves is carried out by using the obtained equation (5), the wave field condition of the seismic waves cannot be modeled, and therefore, a 125-point finite difference method pair is adopted
Processing, i.e. differential proxy of partial derivatives at the centre point with 125 points around the centre point
The continuous equation (5) is converted into a discrete equation, so that the propagation condition of seismic waves in different geological media is simulated.
In practical application, the 125-point finite difference format in the 125-point finite difference method includes:
wherein, a i ，b i And c i Point pairs representing different distance positions i
And
i ∈ (0, 26), dx represents the grid interval; u represents the corresponding shift amount in the frequency domain,
representing the partial derivative, ax representing the spatial sampling interval in the x-direction, ay representing the spatial sampling interval in the y-direction, az representing the spatial sampling interval in the z-direction,
representing the spatial partial derivative taken in the x-direction,
meaning taking the spatial partial derivative for the y-direction,
representing the taking of the spatial partial derivative, u, in the z direction i,j,k U (i Δ x, j Δ y, k Δ z) represents the amount of frequency domain displacement at the grid points (i, j, k).
In the above formulas (6), (7) and (8), a i ，b i And c i The following relationship is satisfied:
the above equations (6), (7), and (8) are substituted into the above equation (5), and a discrete equation is obtained.
In practical application, the obtained discrete equations include:
wherein u is i,j,k ＝u(iΔx,jΔy,kΔz)，a i ，b i And c i Point pair representing different distance positions i
And
i ∈ (0, 26), dx represents the grid interval; u represents the corresponding shift amount in the frequency domain,
representing partial derivatives, Δ x representing the spatial sampling interval in the x-direction, Δ y representing the spatial sampling interval in the y-direction, and Δ z representing the spatial sampling in the z-directionThe sample interval is measured at intervals of a sample,
representing the spatial partial derivative taken in the x-direction,
meaning taking the spatial partial derivative for the y-direction,
denotes taking the spatial partial derivative, u, of the z direction i,j,k U (i Δ x, j Δ y, k Δ z) represents the amount of frequency domain displacement at the grid points (i, j, k), ω represents angular frequency, v represents velocity, d represents i Points representing different distances to the mass acceleration term
Approximate weights.
In the above formula (12), d i The following relationship is satisfied:
after the discrete equation is obtained, the discrete equation can be used for simulating the propagation process of the seismic waves in the stratum with different media and structures, the forward modeling process of the seismic waves is completed, and a foundation is provided for subsequent waveform inversion and migration imaging.
When the finite difference method is used for carrying out numerical simulation on the wave equation, the differential quotient is used for replacing the differential quotient, so that when the space grid distance is too large, invalid wave fluctuation (the reason of numerical dispersion) can be generated, and the simulation precision is low. Therefore, the seismic wave forward modeling method provided by the embodiment of the invention obtains a three-dimensional frequency domain wave equation; performing finite difference processing on the wave equation based on a 125-point finite difference format to obtain a discrete equation; and performing seismic wave forward modeling by using the discrete equation.
According to the scheme of the embodiment of the invention, when the wave equation is numerically simulated by using the finite difference method, the difference of 125 grid points is adopted to replace the partial derivative of the central point of the wave equation, and compared with the method that the difference of 27 grid points is adopted to replace the partial derivative of the central point of the wave equation in the correlation technology, the precision is higher and the numerical dispersion is less.
The present invention will be described in further detail with reference to the following application examples.
The application embodiment takes the case that the finite difference method is applied to the scale wave as an example for explanation, and provides a frequency domain three-dimensional scale wave finite difference method. As shown in fig. 2, the frequency domain three-dimensional scalar wave finite difference method includes:
Specifically, the process of obtaining the three-dimensional frequency domain scale wave equation may be:
firstly, deriving a first-order displacement-stress scalar wave equation according to a Cauchy equation, a geometric equation and a Navigneaux equation; wherein, the first order displacement-stress scalar wave equation can be expressed by the above formula (1).
Secondly, substituting a stress equation in a scalar wave equation into a displacement equation and combining the equations into a second-order time domain scalar wave equation; the second-order time domain scalar wave equation can be expressed by the above formula (3).
Thirdly, converting the second-order time domain scalar wave equation into a three-dimensional frequency domain scalar wave equation through Fourier transform, wherein the three-dimensional frequency domain scalar wave equation can be expressed by the formula (4).
After the wave equation of the three-dimensional frequency domain scalar wave is obtained, the wave equation can be subjected to difference processing by using a 125-point finite difference method. Specifically, the grid distribution of the 125-point finite difference is shown in fig. 3, wherein the left side of fig. 3 is the distribution of the 125-point grid difference, and the right side of fig. 3 represents the weight coefficient values of points at different positions in the left side graph with respect to the center point. In the 125 finite difference method, there are 27 weight coefficients (i.e., 0-26 in FIG. 3) for the center point.
When the 125-point finite difference method is used for carrying out difference processing on the standard wave equation, points with the same surrounding distance have the same influence on the second derivative of the central point. The differential format of the second derivative can be expressed by the above equations (6), (7), (8).
In the embodiment, a frequency domain scalar wave equation problem is constructed through Fourier transformation based on a first-order displacement-stress scalar wave equation derived according to a Cauchy equation, a geometric equation and a Naville equation; the method comprises the steps of firstly obtaining a first-order displacement-stress scalar wave equation, giving a frequency domain three-dimensional scalar wave equation, dispersing the scalar wave equation by adopting a 125-point finite difference format, describing a specific difference form of the scalar wave equation, and carrying out difference research on the scalar wave equation by utilizing the constructed 125-point scalar wave finite difference format of the frequency domain, so that the accuracy of the scalar wave forward modeling is improved, and the numerical dispersion in the forward modeling process is inhibited.
Meanwhile, the forward modeling of the scalar wave is performed on the uniform medium model by using the 27-point finite difference method in the related art and the 125-point finite difference method in the invention, and the propagation process of the scalar wave in the uniform medium model is simulated, so that the 125-point finite difference method in the invention has higher precision in the forward modeling. The grid size of the forward modeling process is 1000m 500m, the space interval is 10m, the seismic source generates seismic waves with the frequency of 30Hz at the center (500m,500m,0m), and the geological model is a uniform medium model (in an isotropic medium, the propagation speed in each direction is the same).
The forward modeling results are shown in fig. 4a, fig. 4b, fig. 5a and fig. 5b, and fig. 4a and fig. 4b are wave field snapshot diagrams of the 27-point finite difference method and the 125-point finite difference method in the homogeneous medium model, respectively; fig. 5a and 5b are schematic time slices in the xoy plane at the same time y of 500m in the homogeneous medium model for the 27-point finite difference method and the 125-point finite difference method, respectively. With reference to fig. 5a and 5b, it can be seen that both difference methods have numerical dispersion, but the finite difference method of the 27-point format has larger numerical dispersion than the finite difference method of the 125-point format, and therefore, it is verified that the 125-point difference format has higher precision and better suppression of dispersion than the conventional 27-point format.
In order to implement the method according to the embodiment of the present invention, an embodiment of the present invention further provides a seismic wave forward modeling apparatus, which is disposed on an electronic device, and as shown in fig. 6, the seismic wave forward modeling apparatus 600 includes: an acquisition module 601, a finite difference module 602 and a forward modeling module 603; wherein,
the obtaining module 601 is configured to obtain a three-dimensional frequency domain wave equation;
the finite difference module 602 is configured to perform finite difference processing on the wave equation based on a 125-point finite difference format to obtain a discrete equation;
the forward modeling module 603 is configured to perform seismic wave forward modeling by using the discrete equation.
In an embodiment, the obtaining module 601 is further configured to:
and acquiring a three-dimensional frequency domain scalar wave equation.
In an embodiment, the obtaining module 601 is further configured to:
acquiring a first-order displacement-stress scalar wave equation based on a Cauchy equation, a geometric equation and a Navier equation;
acquiring a second-order time domain scalar wave equation according to the first-order displacement-stress scalar wave equation;
and carrying out Fourier transform on the second-order time domain equation to obtain a three-dimensional frequency domain scalar wave equation.
In an embodiment, the obtaining module 601 is further configured to:
the first order displacement-stress scalar wave equation comprises:
wherein u (x, t) ═ u x ,u y ,u z ] T Represents the displacement, P (x, t) represents the liquid pressure, f (x, t) represents the seismic source term, x ═ x, y, z]Representing spatial position, t representing time, p representing a density parameter, L representing a partial differential operator, K representing a stiffness tensor matrix,
denotes the partial derivative, L T A transposed matrix, u, representing L x A displacement amount, u, in the x-coordinate direction representing a spatial position x y A displacement amount, u, in the y-coordinate direction representing the spatial position x z Indicating the amount of displacement in the z-coordinate direction of the spatial position x.
In an embodiment, the obtaining module 601 is further configured to:
the second-order time domain scalar wave equation comprises:
wherein,
denotes the Laplace operator, u (x, t) ═ u x ,u y ,u z ] T Represents the displacement, f (x, t) represents the seismic source term, x ═ x, y, z]Representing spatial position, t representing time,
denotes the partial derivative, u x A displacement amount, u, in the x-coordinate direction representing a spatial position x y Displacement in the y coordinate direction, u, representing the spatial position x z Indicating the amount of displacement in the z-coordinate direction of the spatial position x.
In an embodiment, the obtaining module 601 is further configured to:
the three-dimensional frequency domain scalar wave equation comprises:
wherein,
denotes a Laplace operator, U (x, ω) denotes a displacement amount corresponding to a frequency domain, and ω denotes an angleFrequency, v denotes velocity, x ═ x, y, z]Representing spatial position, and f (x, t) representing the seismic source term.
In an embodiment, the finite difference module 602 is further configured to:
the 125-point finite difference format includes:
wherein, a i ，b i And c i Point pairs representing different distance positions i
And
i ∈ (0, 26), dx represents the grid interval; u represents the amount of shift corresponding to the frequency domain,
denotes the partial derivative, ax denotes the spatial sampling interval in the x-direction, ay denotes the spatial sampling interval in the y-direction, az denotes the spatial sampling interval in the z-direction,
meaning taking the spatial partial derivative for the x-direction,
meaning taking the spatial partial derivative for the y-direction,
representing the taking of the spatial partial derivative, u, in the z direction i,j,k U (i Δ x, j Δ y, k Δ z) represents the frequency domain displacement amount at the grid point (i, j, k).
In practical applications, the obtaining module 601, the finite difference module 602 and the forward simulation module 603 may be implemented by a processor in a seismic wave forward simulation apparatus.
It should be noted that: in the seismic wave forward modeling apparatus provided in the above embodiment, when performing forward modeling on seismic waves, only the division of each program module is illustrated, and in practical application, the processing distribution may be completed by different program modules according to needs, that is, the internal structure of the apparatus is divided into different program modules, so as to complete all or part of the processing described above. In addition, the seismic wave forward modeling device and the seismic wave forward modeling method provided by the embodiment belong to the same concept, and the specific implementation process is described in the method embodiment in detail and is not described herein again.
An embodiment of the present invention provides a storage medium, on which a program is stored, and when the program is executed by a processor, the method for seismic wave forward modeling is implemented.
The embodiment of the invention provides a processor, which is used for running a program, wherein the program executes the seismic wave forward modeling method during running.
In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as shown in fig. 7. The computer apparatus includes a processor a01, a network interface a02, a display screen a04, an input device a05, and a memory (not shown in the figure) connected through a system bus. Wherein processor a01 of the computer device is used to provide computing and control capabilities. The memory of the computer device comprises an internal memory a03 and a non-volatile storage medium a 06. The nonvolatile storage medium a06 stores an operating system B01 and a computer program B02. The internal memory a03 provides an environment for the operation of the operating system B01 and the computer programs B02 in the non-volatile storage medium a 06. The network interface a02 of the computer apparatus is used for communication with an external terminal through a network connection. The computer program is executed by the processor a01 to implement a seismic forward modeling method. The display screen a04 of the computer device may be a liquid crystal display screen or an electronic ink display screen, and the input device a05 of the computer device may be a touch layer covered on the display screen, a button, a trackball or a touch pad arranged on a casing of the computer device, or an external keyboard, a touch pad or a mouse.
Those skilled in the art will appreciate that the architecture shown in fig. 7 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
The embodiment of the invention provides equipment, which comprises a processor, a memory and a program which is stored on the memory and can run on the processor, wherein the processor executes the program to realize the seismic wave forward modeling method:
as will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.
The memory may include forms of volatile memory in a computer readable medium, Random Access Memory (RAM) and/or non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). The memory is an example of a computer-readable medium.
Computer-readable media, including both permanent and non-permanent, removable and non-removable media, may implement the information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include transitory computer readable media (transmyedia) such as modulated data signals and carrier waves.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in the process, method, article, or apparatus that comprises the element.
The above are merely examples of the present application and are not intended to limit the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement or the like made within the spirit and principle of the present application shall be included in the scope of the claims of the present application.
Claims (8)
1. A seismic wave forward modeling method, comprising:
acquiring a three-dimensional frequency domain scalar wave equation;
carrying out finite difference processing on the wave equation by adopting the difference of 125 grid points to replace the partial derivative of the central point of the wave equation, and obtaining a discrete equation;
performing seismic wave forward modeling by using the discrete equation;
wherein the finite difference format of the 125 grid points comprises:
wherein, a i ，b i And c i Point pairs respectively representing different distance positions i
And
i ∈ (0, 26), dx represents the grid interval; u represents the amount of shift corresponding to the frequency domain,
denotes the partial derivative, ax denotes the spatial sampling interval in the x-direction, ay denotes the spatial sampling interval in the y-direction, az denotes the spatial sampling interval in the z-direction,
representing the spatial partial derivative taken in the x-direction,
meaning taking the spatial partial derivative for the y-direction,
representing the taking of the spatial partial derivative, u, in the z direction i,j,k U (i Δ x, j Δ y, k Δ z) represents the amount of frequency domain displacement at the grid points (i, j, k), and u i-1,j,k Indicating the amount of frequency domain shift at (i-1, j, k).
2. The seismic wave forward modeling method according to claim 1, wherein said obtaining a three-dimensional frequency domain scalar wave equation comprises:
acquiring a first-order displacement-stress scalar wave equation based on a Cauchy equation, a geometric equation and a Navier equation;
acquiring a second-order time domain scalar wave equation according to the first-order displacement-stress scalar wave equation;
and carrying out Fourier transform on the second-order time domain equation to obtain a three-dimensional frequency domain scalar wave equation.
3. The seismic wave forward modeling method of claim 2, wherein said first order displacement-stress scalar wave equation comprises:
wherein u (x, t) ═ u x ,u y ,u z ] T Represents the displacement, P (x, t) represents the liquid pressure, f (x, t) represents the seismic source term, x ═ x, y, z]Representing the spatial position, t time, p density parameter, L partial differential operator, K stiffness tensor matrix,
denotes the partial derivative, L T A transposed matrix, u, representing L x A displacement amount, u, in the x-coordinate direction representing a spatial position x y A displacement amount, u, in the y-coordinate direction representing the spatial position x z Indicating the amount of displacement in the z-coordinate direction of the spatial position x.
4. The seismic wave forward modeling method of claim 2, wherein said second order time domain scalar wave equation comprises:
wherein,
denotes the Laplace operator, u (x, t) ═ u x ,u y ,u z ] T Represents the displacement, f (x, t) represents the seismic source term, x ═ x, y, z]Representing spatial position, t representing time,
denotes the partial derivative, u x A displacement amount, u, in the x-coordinate direction representing a spatial position x y A displacement amount, u, in the y-coordinate direction representing the spatial position x z Indicating the amount of displacement in the z-coordinate direction of the spatial position x.
5. The seismic wave forward modeling method of claim 2, wherein said three-dimensional frequency domain scalar wave equation comprises:
wherein,
denotes a laplacian operator, U (x, ω) denotes a displacement amount corresponding to a frequency domain, ω denotes an angular frequency, v denotes a velocity, and x ═ x, y, z]Representing the spatial position, and f (x, ω) representing the seismic source term in the frequency domain.
6. A seismic forward modeling apparatus, comprising:
the acquisition module is used for acquiring a three-dimensional frequency domain scalar wave equation;
the finite difference module is used for carrying out finite difference processing on the wave equation by adopting the difference of 125 grid points to replace the partial derivative of the central point of the wave equation, so as to obtain a discrete equation;
the forward modeling module is used for performing forward modeling on the seismic waves by using the discrete equation;
wherein the finite difference format of the 125 grid points comprises:
wherein, a i ，b i And c i Point pairs respectively representing different distance positions i
And
i ∈ (0, 26), dx represents the grid interval; u represents the amount of shift corresponding to the frequency domain,
representing the partial derivative, ax representing the spatial sampling interval in the x-direction, ay representing the spatial sampling interval in the y-direction, az representing the spatial sampling interval in the z-direction,
representing the spatial partial derivative taken in the x-direction,
meaning taking the spatial partial derivative for the y-direction,
denotes taking the spatial partial derivative, u, of the z direction i,j,k U (i Δ x, j Δ y, k Δ z) represents the frequency domain displacement at the grid points (i, j, k)Amount u i-1,j,k Indicating the amount of frequency domain shift at (i-1, j, k).
7. A storage medium having stored thereon instructions for causing a machine to perform the seismic wave forward modeling method of any of claims 1 to 5.
8. A processor configured to execute a program, wherein the program when executed by the processor is configured to perform the seismic wave forward modeling method according to any of claims 1-5.
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