CN112782761A - Single-pass wave forward modeling method and device, storage medium and processor - Google Patents
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Abstract
The embodiment of the invention provides a method, a device, a storage medium and a processor for single-pass wave forward modeling, belonging to the technical field of geophysical exploration, wherein the method comprises the following steps: determining a step-by-step Fourier wave field continuation operator; determining a HTI medium single-pass wave splitting step operator based on the step Fourier wave field continuation operator; and performing HTI medium single-pass wave cracking step method post-stack forward simulation by using the HTI medium single-pass wave cracking step method operator.
Description
Technical Field
The invention relates to the technical field of geophysical exploration, in particular to a method and a device for single-pass wave forward modeling, a storage medium and a processor.
Background
The seismic wave forward modeling mainly solves the propagation rule of the seismic waves in a known underground geological model, including propagation time, path, energy and the like. Through forward modeling, the kinematic and dynamic characteristics of seismic waves propagating 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 technology, wave equation is often used to perform forward modeling on seismic waves, and the wave equation method is the most important method for dealing with increasingly complex geological structure seismic wave propagation numerical simulation.
In reality, because the underground medium has cracks, sand-shale thin interbed and the like, which are non-uniform and anisotropic, the isotropic wave equation is adopted to carry out forward simulation, and the simulated wave has larger error when being transmitted underground, so the anisotropic wave equation is usually adopted to simulate the transmission process of the wave under the ground.
In addition, due to the action of a stress field, cracks, fissures and pores with preferred orientation are formed in the rock, the cracks, fissures or pores can be filled with fillings such as gas or fluid, the propagation of seismic waves in the cracked rock is equivalent to the propagation in a uniform elastic anisotropic solid, so that the cracked rock has equivalent anisotropy, and the cracks with preferred orientation and fillings such as gas or fluid can also be called wide-expansion anisotropy. Forward modeling of such fractured rocks is typically performed using a transversely isotropic (HTI) medium with a Horizontal axis of symmetry to equate such fractured rocks.
However, in the related art, the seismic wave forward modeling process based on the HTI medium needs to be optimized.
Disclosure of Invention
The invention aims to provide a method and a device for simulating single-pass wave forward modeling, a storage medium and a processor.
In order to achieve the above object, a first aspect of the present invention provides a method for single-pass forward modeling, including:
determining a step-by-step Fourier wave field continuation operator;
determining a HTI medium one-way wave-splitting step operator based on the step-by-step Fourier wave field continuation operator;
and performing HTI medium single-pass wave cracking step method post-stack forward simulation by using an HTI medium single-pass wave cracking step method operator.
In an embodiment of the present invention, determining a step-wise fourier wavefield prolongation operator comprises:
determining an acoustic wave equation and a speed reciprocal slowness; wherein the inverse velocity slowness comprises a reference slowness and a disturbance slowness;
performing a first phase shift continuation on the reference slowness; carrying out second phase shift continuation on the disturbance slowness; and obtaining a step-by-step Fourier wave field continuation operator.
In an embodiment of the present invention, the acoustic wave equation is defined as:
wherein v (x, z) is the longitudinal wave velocity, t is the time, P is the pressure, x is the horizontal direction, z is the direction perpendicular to the ground,
representing the spatial partial derivative taken in the x-direction,
representing taking the spatial partial derivative for the z direction,
representing the partial derivative over time.
In an embodiment of the invention, the step-wise fourier-wave-field prolongation operator is defined as:
wherein k isxIs a horizontal wave number, P1Is a frequency-space domain wavefield, P is a time-space domain wavefield, Δ z is a z-direction space step, F is a Fourier transform, F-1For inverse Fourier transformation, i is an imaginary number, w is the frequency, s0Is the background slowness,. DELTA.s is the disturbance slowness, ziIs the z-direction ith layer depth.
In the embodiment of the invention, the step-by-step Fourier wave field continuation operator is based on to determine the HTI medium single-pass wave fracture step method operator, and the method comprises the following steps:
determining a quasi-longitudinal wave frequency dispersion equation of the HTI medium;
decoupling a quasi-longitudinal wave frequency dispersion equation of the HTI medium to obtain the quasi-longitudinal wave frequency dispersion equation of the HTI medium;
dividing an HTI medium quasi-longitudinal wave frequency dispersion equation into a background vertical wave number and a disturbance vertical wave number;
and processing the background vertical wave number and the disturbance vertical wave number based on the step-by-step Fourier wave field continuation operator to obtain the HTI medium one-way wave splitting step operator.
In an embodiment of the present invention, the HTI media single-pass wave-fracturing step operator is defined as:
wherein epsilon and delta are anisotropic parameters, kz0Background vertical wavenumber, k, for HTI mediazΔPerturbation vertical wave number, k, for HTI mediaxThe HIT medium horizontal wave number.
In the embodiment of the invention, the HTI medium single-pass wave cracking step method post-stack forward simulation is carried out by utilizing an HTI medium single-pass wave cracking step method operator, and the method comprises the following steps:
based on the theory of an explosion reflecting surface, an HTI medium single-pass wave cracking step method operator is utilized to carry out HTI medium single-pass wave cracking step method post-stack forward simulation.
The second aspect of the present invention provides a single-pass forward modeling apparatus, comprising:
the first determination module is used for determining a step-by-step Fourier wave field continuation operator;
the second determination module is used for determining a HTI medium one-way wave splitting step operator based on the step-by-step Fourier wave field continuation operator;
and the forward modeling module is used for performing HTI medium single-pass wave cracking step method post-stack forward modeling by utilizing an HTI medium single-pass wave cracking step method operator.
A third aspect of the invention provides a machine-readable storage medium having stored thereon instructions for causing a machine to perform the single-pass forward modeling method of any of the above-described embodiments of the present application.
A fourth aspect of the invention provides a processor, a program being executed by the processor for performing the single-pass forward modeling method of any of the above-mentioned applications.
Determining a step-by-step Fourier wave field continuation operator by the technical scheme; determining a HTI medium one-way wave-splitting step operator based on the step-by-step Fourier wave field continuation operator; performing HTI medium single-pass wave cracking step method post-stack forward simulation by using an HTI medium single-pass wave cracking step method operator; in the forward modeling process, only the upgoing wave or the downgoing wave in the seismic wave propagation process is considered, the algorithm is simple, the calculation speed is high, no reflected wave interference exists, and the forward modeling effect is good.
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 without limiting the embodiments of the invention. In the drawings:
FIG. 1 is a schematic flow chart of a single-pass forward modeling method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a numerical simulation process according to an embodiment of the present invention;
FIG. 3a is a schematic diagram of a laminar velocity model according to an embodiment of the present invention;
FIG. 3b is a diagram illustrating the forward results of the layered velocity model after stacking according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a complex velocity model according to an embodiment of the present invention;
FIG. 5 is a diagram illustrating the post-stack forward results of a complex velocity model according to an embodiment of the present invention;
FIG. 6 is a block diagram of a single-pass forward modeling apparatus according to an embodiment of the present invention;
fig. 7 is an internal structural view 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.
In the related art, for forward simulation of the wave equation of the anisotropic medium, forward simulation of a quasi-longitudinal wave (also called as a qP wave) equation has the advantages of small occupied resources and high calculation speed.
From the analysis of the seismic wave propagation angle, the two-way wave equation usually adopts a whole-way acoustic wave equation or a whole-way elastic wave equation to simulate, and contains up-going wave and down-going wave information in wave field continuation, the simulated seismic wave field is closer to the seismic wave field actually observed in the field, the wave field information is rich, and the simulated seismic wave field not only contains meaningful primary reflected waves, but also contains various interference waves such as direct waves, multiple waves, evanescent waves and the like. However, the method based on the two-way wave equation has low calculation efficiency, and the signal-to-noise ratio of the simulated seismic wave field is low, so that the method is not beneficial to rapidly and intuitively analyzing the seismic reflection characteristics of the target geologic body.
Based on this, in the embodiment of the invention, a step-by-step Fourier wave field continuation operator is determined; determining a HTI medium one-way wave-splitting step operator based on the step-by-step Fourier wave field continuation operator; and performing HTI medium single-pass wave cracking step method post-stack forward simulation by using an HTI medium single-pass wave cracking step method operator. In the forward modeling process, only the upgoing wave or the downgoing wave in the seismic wave propagation process is considered, the algorithm is simple, the calculation speed is high, and the forward modeling effect is good.
The embodiment of the invention provides a single-pass wave forward modeling method, as shown in fig. 1, the method comprises the following steps:
step 101: determining a step-by-step Fourier wave field continuation operator;
step 102: determining a HTI medium one-way wave-splitting step operator based on the step-by-step Fourier wave field continuation operator;
step 103: and performing HTI medium single-pass wave cracking step method post-stack forward simulation by using an HTI medium single-pass wave cracking step method operator.
In practical application, according to the seismic wave scattering theory, the medium is divided into a uniform background medium and a disturbance medium which changes along with the space position, so that the seismic wave field can be divided into two parts, wherein one part is the wave field generated by the background medium, and the other part is the wave field generated by the disturbance medium. Based on the two parts of seismic wave fields, equivalent processing can be carried out by utilizing a distributed Fourier wave field continuation method.
First, the lateral velocity variation of the medium during seismic wave propagation is processed by defining a laterally invariant reference slowness and a laterally variable disturbance slowness. The step-by-step Fourier wave field continuation method carries out continuation on a wave field in two steps, wherein the first step carries out continuation on a reference slowness advancing wave field in a frequency-wave number domain, and the second step carries out continuation on a disturbance slowness advancing wave field in a frequency-space domain.
And secondly, solving a HTI medium one-way wave continuation operator, and decoupling an elastic wave frequency dispersion equation of the HTI medium on the basis of an Alkhalifah acoustic approximation theory to obtain a qP wave frequency dispersion equation of the HTI medium. And decomposing the dispersion equation into a background vertical wave number and a disturbance vertical wave number, and then extending the background vertical wave number and the disturbance vertical wave number by a step-by-step Fourier wave field extension method to obtain a HTI medium one-way wave extension operator.
Specifically, in one embodiment, determining a step-wise fourier wavefield prolongation operator comprises:
determining an acoustic wave equation and a speed reciprocal slowness; wherein the inverse velocity slowness comprises a reference slowness and a disturbance slowness;
performing a first phase shift continuation on the reference slowness; carrying out second phase shift continuation on the disturbance slowness; and obtaining a step-by-step Fourier wave field continuation operator.
In practice, the acoustic wave equation (or first order displacement-stress scalar wave equation) is defined as:
in practical applications, the inverse of the speed is defined as slowness, which can be defined as:
s(x,z)＝s0(z)+Δs(x,z) (2)
wherein s is0(z) is the background slowness and Δ s (x, z) is the perturbation slowness.
In practical application, the formula (2) is substituted into the formula (1), the wave equation is converted into a frequency domain, and Δ s is omitted2Obtaining:
wherein,
representing the laplacian operator, P is pressure.
Order to
For the Fourier transform of P to x, a reference slowness s is used0(z) performing a first phase shift extension on the horizontal wave number k after the first phase shift extensionxInverse Fourier transform to obtain P1. And then, in a frequency space domain, performing second phase shift continuation on the disturbance delta s (x, z) of the slowness, and finally performing inverse Fourier transform to obtain a step-by-step Fourier wave field continuation operator.
In practical application, the step-by-step Fourier wave field prolongation operator is defined as:
in one embodiment, determining the HTI medium single-pass wave-splitting step operator based on the step-by-step Fourier wave field continuation operator comprises:
determining a quasi-longitudinal wave frequency dispersion equation of the HTI medium;
decoupling a quasi-longitudinal wave frequency dispersion equation of the HTI medium to obtain the quasi-longitudinal wave frequency dispersion equation of the HTI medium;
dividing an HTI medium quasi-longitudinal wave frequency dispersion equation into a background vertical wave number and a disturbance vertical wave number;
and processing the background vertical wave number and the disturbance vertical wave number based on the step-by-step Fourier wave field continuation operator to obtain the HTI medium one-way wave splitting step operator.
In practical application, solving an equation with a Christoffel determinant of zero can obtain a frequency dispersion relation of HTI medium elastic wave coupling, decoupling the elastic waves, and assuming that the transverse wave speed is zero by using an acoustic approximation theory to obtain a qP wave frequency dispersion relation equation under HTI medium acoustic approximation.
In practical application, the qP wave dispersion relation equation is defined as:
where v is the longitudinal wave velocity.
In practical application, the stepped Fourier method is used for performing single-pass forward modeling on the HTI medium, and the vertical wave number of the HTI medium needs to be decomposed into a parameter transverse invariant part k according to the thought of the stepped Fourier methodz0And a laterally varying portion kzΔAnd then using k in the wavenumber-frequency domainz0Continuation of wave field, and final use of k in frequency-space domainzΔContinuation of the wave field.
In practical application, substituting the background coefficient medium parameters into equation (5) to obtain a background vertical wave number, which is defined as:
where v0 is the background velocity.
In practical application, computing the perturbation wave number by using a Tayor expansion, and taking a low-order approximation to obtain the perturbation wave number form of the HTI medium, wherein the perturbation wave number form is defined as:
in practical application, the background wave number and the disturbance wave number are substituted into the formula (4) to obtain the HTI medium one-way wave splitting step operator.
In practical application, the HTI medium single-pass wave-splitting step operator is defined as:
in one embodiment, the HTI medium single-pass wave-fracturing step-method post-stack forward simulation is performed by using an HTI medium single-pass wave-fracturing step-method operator, and includes:
based on the theory of an explosion reflecting surface, an HTI medium single-pass wave cracking step method operator is utilized to carry out HTI medium single-pass wave cracking step method post-stack forward simulation.
In practical application, the theory of the explosion reflecting surface is as follows: the reflected wave observed on the ground can be regarded as the observation result of simultaneously exciting seismic waves on the reflecting interface, namely, the self-exciting and self-receiving seismic section and the seismic waves generated by simultaneous explosion on the reflecting interface are propagated outwards at half speed, and the equivalent is that the upward waves are received on the ground.
According to the scheme of the embodiment of the invention, a step-by-step Fourier wave field continuation operator is determined; determining a HTI medium one-way wave-splitting step operator based on the step-by-step Fourier wave field continuation operator; performing HTI medium single-pass wave cracking step method post-stack forward simulation by using an HTI medium single-pass wave cracking step method operator; in the forward modeling process, only the upgoing wave or the downgoing wave in the seismic wave propagation process is considered, the algorithm is simple, the calculation speed is high, no reflected wave interference exists, and the forward modeling effect is good.
The present invention will be described in further detail with reference to the following application examples.
The application embodiment provides a forward modeling method based on an HTI medium single-pass wave-splitting step method, and with reference to FIG. 2, the method comprises the following steps:
step 201: establishing a step-by-step Fourier wave field continuation operator;
step 202: establishing an HTI medium one-way wave crack step operator;
step 203: HTI medium one-way wave splitting step method post-stack forward simulation.
Specifically, the implementation process of step 201 is as follows:
the stepwise Fourier wave field continuation method is based on the idea of velocity field splitting, the whole velocity field is regarded as superposition of a constant-speed background and variable-speed disturbance, phase shift processing is adopted for the constant-speed background during layer-by-layer wave field continuation, and time shift correction is adopted in a frequency-space domain for the variable-speed disturbance in a layer. This method inherits the advantages of phase shift methods while also accommodating moderate lateral variations in the velocity field and is far more computationally economical than phase shift plus interpolation.
Taking a two-dimensional acoustic wave equation as an example, the two-dimensional acoustic wave equation can be expressed by the above formula (1);
if the inverse of the velocity is defined as slowness, let the slowness of each point of the subsurface medium be s (x, z), where x, z are the coordinates of the point, and decompose the slowness into laterally variable and laterally invariant parts, where the slowness can be represented using equation (2) above.
Substituting the above equation (2) into the above equation (1), and transforming the wave equation into the frequency domain, omitting Δ s2Obtaining the formula (3);
order to
Is Fourier transform of P to xAlternatively, a reference slowness s is used0(z) performing a first phase shift extension on the horizontal wave number k after the first phase shift extensionxInverse Fourier transform to obtain P1. And then, in a frequency space domain, performing second phase shift continuation on the disturbance delta s (x, z) of the slowness, and finally performing inverse Fourier transform to obtain a final continuation formula, wherein the final continuation formula can be represented by the formula (4).
Specifically, the implementation process of step 202 is as follows:
solving an equation with a Christoffel determinant of zero to obtain a dispersion relation of qP wave coupling of the HTI medium, decoupling longitudinal waves and transverse waves, and assuming that the velocity of the transverse waves is zero by using an acoustic approximation theory to obtain a qP wave dispersion relation equation under the HTI medium acoustic approximation, wherein the qP wave dispersion relation equation can be expressed by the formula (5);
the method is characterized in that a step Fourier method is used for carrying out one-way wave forward modeling on the HTI medium, and the vertical wave number of the HTI medium needs to be decomposed into a parameter transverse invariant part k according to the thought of the step Fourier methodz0And a laterally varying portion kzΔAnd then using k in the wavenumber-frequency domainz0Continuation of wave field, and final use of k in frequency-space domainzΔContinuation of the wave field.
And (3) substituting the background coefficient medium parameters into equation (5) to obtain a background vertical wave number, wherein the background vertical wave number can be expressed by the formula (6).
Calculating the disturbance wave number by using a Tayor expansion, and taking a low-order approximation to obtain the disturbance wave number form of the HTI medium, wherein the disturbance wave number form of the HTI medium can be represented by the formula (7);
and (3) substituting the background wave number and the disturbance wave number into the wave propagation equation (4) to obtain an HTI medium wave field continuation equation, wherein the HTI medium wave field continuation equation can be expressed by the formula (8).
Specifically, the implementation process of step 203 is as follows:
the post-stack forward modeling is based on the explosion reflecting surface theory. Explosion reflecting surface theory: the reflected wave observed on the ground can be regarded as the observation result of simultaneously exciting seismic waves on the reflecting interface, namely, the self-exciting and self-receiving seismic section and the seismic waves generated by simultaneous explosion on the reflecting interface are propagated outwards at half speed, and the equivalent is that the upward waves are received on the ground.
The method comprises the following implementation steps:
firstly, calculating a reflection coefficient according to the speed and density data;
secondly, performing Fourier transform on the seismic source wave field to convert the seismic source wave field into a frequency domain;
third, from z to zmaxInitially, the source wavefield is calculated: performing seismic source wave field superposition;
s(x,zi,ω,ε,δ)＝s1(x,zi,ω,ε,δ)+ricker(ω)r(x,zi) (10)
where r is the reflection coefficient and ricker (w) is the Rake wavelet.
Fourthly, further proceeding the prolongation of the wave field
Wherein, the first step of continuation is carried out:
and (3) performing continuation of a wave field in the second step:
wherein, c (z)i) Is the ith layer velocity.
Fifthly, the process of the third to fourth is circulated until z is 0;
and sixthly, recording wave field information when z is 0, namely the obtained forward seismic record.
It should be noted here that normally the directly obtained rake wavelet is the minimum phase, which is the position with the takeoff point as the interface, but actually, this time is difficult to accurately locate on the seismic record, and we use the time of some obvious maximum (phase) on the vibration diagram as the arrival time of the wave, i.e. the concept of zero phase. From the fourier transform point of view, the wavelets can be synthesized from a series of sinusoids of different frequencies, different amplitudes, and different initial phases. The zero-phase wavelet can be regarded as a composite of a plurality of sine waves with one peak or trough time-aligned, at the main peak of the wavelet, all frequency components are peak positions, and the addition result is necessarily maximum, if the peaks or troughs of the frequency components are mutually staggered, the addition result is necessarily not up to the main extreme value of the zero-phase wavelet, so that the main peak (trough) value of the zero-phase wavelet is maximum in each wavelet with the same amplitude spectrum. It can be demonstrated that wavelets with the same amplitude spectrum have the same energy, so the resolution of the zero-phase wavelet is highest. Thus, the Rake wavelet is converted to a zero-phase wavelet.
According to the scheme of the embodiment of the invention, a step-by-step Fourier wave field continuation operator is determined; determining a HTI medium one-way wave-splitting step operator based on the step-by-step Fourier wave field continuation operator; performing HTI medium single-pass wave cracking step method post-stack forward simulation by using an HTI medium single-pass wave cracking step method operator; in the forward modeling process, only the upgoing wave or the downgoing wave in the seismic wave propagation process is considered, the algorithm is simple, the calculation speed is high, and the forward modeling effect is good.
Meanwhile, the present application embodiment also adopts a laminar velocity model for forward modeling, where fig. 3a is the laminar velocity model, the size of the model is 500 × 500 (grid points), and the grid distances in the x direction and the z direction are both 10 m. In forward modeling, Rake wavelets are adopted, the main frequency is 40HZ, the time sampling interval is 1ms, and the total sampling point is 2000. Fig. 3b shows the forward result of the velocity model of fig. 3a after the stack, from which it can be seen that the in-phase axis corresponds approximately to the laminar velocity model, but there is a diffracted wave. In order to verify the stability and the applicability of the HTI medium single-pass wave-splitting step method operator, forward simulation is carried out on a complex velocity model figure 4, a forward simulation result is shown in figure 5, and the same-phase axis of the figure 5 is consistent with that of the figure 4, so that the operator has good suitability.
In order to implement the method according to the embodiment of the present invention, an embodiment of the present invention further provides a single-pass wave forward modeling apparatus, which is disposed on an electronic device, and as shown in fig. 6, the single-pass wave forward modeling apparatus 600 includes: a first determining module 601, a second determining module 602 and a forward modeling module 603; wherein,
a first determining module 601, configured to determine a step-by-step fourier wave field prolongation operator;
a second determining module 602, configured to determine a single-pass wave-splitting step operator of the HTI medium based on the step-by-step fourier wave field continuation operator;
and the forward modeling module 603 is configured to perform HTI medium single-pass wave-splitting step method post-stack forward modeling by using an HTI medium single-pass wave-splitting step operator.
In an embodiment, the first determining module 601 is further configured to:
determining an acoustic wave equation and a speed reciprocal slowness; wherein the inverse velocity slowness comprises a reference slowness and a disturbance slowness;
performing a first phase shift continuation on the reference slowness; carrying out second phase shift continuation on the disturbance slowness; and obtaining a step-by-step Fourier wave field continuation operator.
In an embodiment, the first determining module 601 is further configured to:
the acoustic wave equation is defined as:
in an embodiment, the first determining module 601 is further configured to:
the step-wise fourier wavefield prolongation operator is defined as:
in an embodiment, the first determining module 602 is further configured to:
determining a quasi-longitudinal wave frequency dispersion equation of the HTI medium;
decoupling a quasi-longitudinal wave frequency dispersion equation of the HTI medium to obtain the quasi-longitudinal wave frequency dispersion equation of the HTI medium;
dividing an HTI medium quasi-longitudinal wave frequency dispersion equation into a background vertical wave number and a disturbance vertical wave number;
and processing the background vertical wave number and the disturbance vertical wave number based on the step-by-step Fourier wave field continuation operator to obtain the HTI medium one-way wave splitting step operator.
In an embodiment, the first determining module 602 is further configured to:
the HTI medium one-way wave-fracturing step operator is defined as:
in an embodiment, the forward modeling module 603 is further configured to:
based on the theory of an explosion reflecting surface, an HTI medium single-pass wave cracking step method operator is utilized to carry out HTI medium single-pass wave cracking step method post-stack forward simulation.
In practical applications, the first determining module 601, the second determining module 602, and the forward modeling module 603 may be implemented by a processor in a single-pass forward modeling apparatus.
It should be noted that: the single-pass wave forward simulation apparatus provided in the foregoing embodiment is only illustrated by dividing the program modules when performing forward simulation on a single-pass wave, and in practical applications, the processing may be distributed to different program modules according to needs, that is, the internal structure of the apparatus may be divided into different program modules to complete all or part of the processing described above. In addition, the single-pass wave forward modeling apparatus provided in the above embodiment and the single-pass wave forward modeling method embodiment belong to the same concept, and the specific implementation process thereof is described in the method embodiment, and is not described herein again.
An embodiment of the present invention provides a storage medium on which a program is stored, which when executed by a processor implements the above-described single-pass forward modeling method.
The embodiment of the invention provides a processor, wherein the processor is used for running a program, and the one-way wave forward modeling method is executed when the program runs.
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 program B02 in the nonvolatile storage medium a 06. The network interface a02 of the computer device is used for communication with an external terminal through a network connection. The computer program is executed by the processor a01 to implement a single-pass 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 when the processor executes the program, the one-way wave forward modeling method is realized as follows:
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 non-transitory and non-transitory, removable and non-removable media, may implement 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, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.
Claims (10)
1. A single-pass forward modeling method is characterized by comprising the following steps:
determining a step-by-step Fourier wave field continuation operator;
determining a HTI medium single-pass wave splitting step operator based on the step Fourier wave field continuation operator;
and performing HTI medium single-pass wave cracking step method post-stack forward simulation by using the HTI medium single-pass wave cracking step method operator.
2. The single-pass wave forward modeling method of claim 1, wherein said determining a step-wise fourier-wave-field prolongation operator comprises:
determining an acoustic wave equation and a speed reciprocal slowness; wherein the inverse speed slowness comprises a reference slowness and a disturbance slowness;
performing a first phase shift continuation on the reference slowness; carrying out second phase shift continuation on the disturbance slowness; and obtaining a step-by-step Fourier wave field continuation operator.
3. The single pass forward modeling method of claim 2, wherein the acoustic wave equation is defined as:
wherein v (x, z) is the longitudinal wave velocity, t is the time, P is the pressure, x is the horizontal direction, z is the direction perpendicular to the ground,
representing the spatial partial derivative taken in the x-direction,
representing taking the spatial partial derivative for the z direction,
representing partial derivatives with respect to time。
4. The single-pass wave forward modeling method of claim 2, wherein the step-wise fourier-wave-field prolongation operator is defined as:
wherein k isxIs a horizontal wave number, P1Is a frequency-space domain wavefield, P is a time-space domain wavefield, Δ z is a z-direction space step, F is a Fourier transform, F-1For inverse Fourier transformation, i is an imaginary number, w is the frequency, s0Is the background slowness,. DELTA.s is the disturbance slowness, ziIs the z-direction ith layer depth.
5. The method for single-pass wave forward modeling according to claim 1, wherein said determining an HTI medium single-pass wave fracturing step operator based on said step-by-step Fourier wave field continuation operator comprises:
determining a quasi-longitudinal wave frequency dispersion equation of the HTI medium;
decoupling the quasi-longitudinal wave frequency dispersion equation of the HTI medium to obtain the quasi-longitudinal wave frequency dispersion equation of the HTI medium;
dividing the HTI medium quasi-longitudinal wave frequency dispersion equation into a background vertical wave number and a disturbance vertical wave number;
and processing the background vertical wave number and the disturbance vertical wave number based on the step Fourier wave field continuation operator to obtain the HTI medium one-way wave splitting step operator.
6. The single pass forward modeling method of claim 1, wherein the HTI media single pass wave fracking operator is defined as:
wherein, ε and δAs the anisotropy parameter, kz0Background vertical wavenumber, k, for HTI mediazΔPerturbation vertical wave number, k, for HTI mediaxThe HIT medium horizontal wave number.
7. The method for single-pass wave forward modeling according to claim 1, wherein said performing HTI media single-pass wave-splitting step-stacked forward modeling using said HTI media single-pass wave-splitting step operator comprises:
based on the theory of an explosion reflecting surface, the HTI medium single-pass wave cracking step method operator is utilized to carry out HTI medium single-pass wave cracking step method post-stack forward modeling.
8. A single-pass forward modeling apparatus, comprising:
the first determination module is used for determining a step-by-step Fourier wave field continuation operator;
the second determination module is used for determining a HTI medium one-way wave splitting step operator based on the step-by-step Fourier wave field continuation operator;
and the forward modeling module is used for performing HTI medium single-pass wave cracking step method post-stack forward modeling by using the HTI medium single-pass wave cracking step method operator.
9. A storage medium having stored thereon instructions for causing a machine to perform the single pass forward modeling method of any of claims 1 to 7.
10. A processor configured to execute a program, wherein the program when executed by the processor is configured to perform the single-pass forward modeling method according to any of claims 1-7.
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