A stable and efficient method and device for determining seismic wave propagation vector

Abstract

The application discloses a kind of stable and efficient seismic wave propagation vector determination method and device, the method includes: first according to finite difference method, the acoustic wave equation is solved to obtain seismic wave field data;Then based on the seismic wave field data, the spatial domain gradient of seismic wave field at a time, the time domain integration of seismic wave field at a time and the spatial domain gradient of the time domain integration of seismic wave field at a time are calculated;Finally, according to the seismic wave field data, the spatial domain gradient of seismic wave field at a time, the time domain integration of seismic wave field at a time and the spatial domain gradient of the time domain integration of seismic wave field at a time, determine the seismic wave propagation vector.Compared with traditional Poynting vector, the oscillation phenomenon existing in traditional Poynting vector is eliminated, and the calculation complexity is relatively low.

Description

Technical Field

[0001] This invention belongs to the field of seismic exploration technology, specifically relating to a stable and efficient method and apparatus for determining seismic wave propagation vectors. Background Technology

[0002] The seismic wave propagation vector, also known as the Poynting vector, is an energy flux density vector. In existing technologies, the Poynting vector represents the propagation direction of the energy flux density in the entire seismic wave field. The propagation direction obtained is also the propagation direction of the entire wave field, which can be used to calculate the earthquake propagation direction. Because its computational efficiency is much higher than other methods, it is widely used in the field of seismic exploration.

[0003] Existing methods for determining the Poynting vector contain harmonic function terms, which cause oscillations in the determination of the Poynting vector, resulting in inaccurate wave propagation direction. Furthermore, the Poynting vector requires preprocessing before further calculations, consuming additional computational resources.

[0004] Therefore, how to reduce the computational complexity of stable Poynting vectors and avoid the oscillation phenomenon that exists in the determination of traditional Poynting vectors is a technical problem that needs to be solved by those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to solve the technical problems of complex calculation of stable Poynting vector in the prior art, or the existence of oscillation phenomenon when determining Poynting vector in the prior art.

[0006] To achieve the above technical objectives, on the one hand, the present invention provides a stable and efficient method for determining the propagation vector of seismic waves, the method comprising: Seismic wave field data are obtained by solving the acoustic wave equation using the finite difference method. Based on the seismic wavefield data, the spatial domain gradient of the seismic wavefield at a certain time, the time domain integral of the seismic wavefield at a certain time, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time are calculated. The seismic wave propagation vector is determined based on the seismic wavefield data, the spatial domain gradient of the seismic wavefield at a certain time, the time domain integral of the seismic wavefield at a certain time, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time.

[0007] Furthermore, the seismic wavefield data is specifically determined using the following formula: ; In the formula, For seismic wavefield data, This represents the amplitude of the plane wave. For angular frequency, Let be the vector representing the direction of wave propagation. Let be the propagation speed of the wave in the medium.

[0008] Furthermore, the spatial domain gradient of the seismic wavefield at a certain moment is specifically determined by the following formula: ; In the formula, The spatial domain gradient of the seismic wave field at a certain moment. The symbol is for partial differentials. For spatial location, This represents the amplitude of the plane wave. For angular frequency, Let be the speed of wave propagation in the medium. Position in the direction of time. This is the vector representing the direction of wave propagation.

[0009] Furthermore, the time-domain integral of the seismic wavefield at a certain moment is specifically determined by the following formula: ; In the formula, For the time-domain integral of the seismic wave field at a certain moment, For wave field data, For integration, Position in the direction of time. This represents the amplitude of the plane wave. For angular frequency, Let be the speed of wave propagation in the medium. Position in the direction of time. Let be the vector representing the direction of wave propagation. For spatial location, This is the constant term obtained from the integral calculation.

[0010] Furthermore, the spatial domain gradient of the seismic wavefield time-domain integral at a certain moment is specifically determined by the following formula: ; In the formula, The spatial domain gradient of the seismic wave field at a certain moment, which is the time-domain integral. For the time-domain integral of the seismic wave field at a certain moment, For spatial location, This represents the amplitude of the plane wave. For angular frequency, Let be the speed of wave propagation in the medium. Position in the direction of time. This is the vector representing the direction of wave propagation.

[0011] Furthermore, the determination of the seismic wave propagation vector based on the seismic wavefield data, the spatial domain gradient of the seismic wavefield at a certain time, the time domain integral of the seismic wavefield at a certain time, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time is specifically performed using the following formula: ; In the formula, The vector for seismic wave propagation. For the time-domain integral of the seismic wave field at a certain moment, The spatial domain gradient of the seismic wave field at a certain moment. For seismic wavefield data, The spatial domain gradient of the seismic wave field at a certain moment, which is the time-domain integral. Position in the direction of time. This represents the amplitude of the plane wave. For angular frequency, Let be the speed of wave propagation in the medium. Position in the direction of time. Let be the vector representing the direction of wave propagation. For spatial location.

[0012] On the other hand, the present invention also provides a stable and efficient device for determining the propagation vector of seismic waves, the device comprising: The solver module is used to solve the acoustic wave equation using the finite difference method to obtain seismic wavefield data. The first determining module is used to calculate the spatial domain gradient of the seismic wavefield at a certain time, the time domain integral of the seismic wavefield at a certain time, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time based on the seismic wavefield data. The second determining module is used to determine the seismic wave propagation vector based on the seismic wave field data, the spatial domain gradient of the seismic wave field at a certain time, the time domain integral of the seismic wave field at a certain time, and the spatial domain gradient of the time domain integral of the seismic wave field at a certain time.

[0013] This invention provides a stable and efficient method and apparatus for determining seismic wave propagation vectors. Compared with existing technologies, this method first solves the acoustic wave equation using the finite difference method to obtain seismic wavefield data. Then, based on the seismic wavefield data, it calculates the spatial domain gradient, time domain integral, and spatial domain gradient of the time domain integral of the seismic wavefield at a certain time. Finally, it determines the seismic wave propagation vector based on the seismic wavefield data, the spatial domain gradient, the time domain integral, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time. Compared with the traditional Poynting vector, this method eliminates the oscillation phenomenon present in the traditional Poynting vector and has lower computational complexity. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments or prior art of this specification, the drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 The diagram shown is a flowchart illustrating the stable and efficient method for determining seismic wave propagation vectors provided in the embodiments of this specification. Figure 2 The diagram shown is a structural schematic of the stable and efficient seismic wave propagation vector determination device provided in the embodiments of this specification. Figure 3 The diagram shown is a schematic of the seismic wave field. Figure 4 The diagram shown is a schematic representation of the horizontal component of the seismic wave propagation vector determined by this scheme. Figure 5 The diagram shown is a schematic representation of the vertical component of the seismic wave propagation vector determined by this scheme. Figure 6 The diagram shows the horizontal components of the Poynting vector determined by the conventional scheme. Figure 7 The diagram shows the vertical component of the Poynting vector determined by the conventional scheme. Figure 8 The diagram shows the direction of the Poynting vector determined by the conventional method. Figure 9 The diagram shows the direction of the seismic wave propagation vector determined by the scheme in this application. Detailed Implementation

[0016] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0017] like Figure 1The diagram illustrates a flow chart of a stable and efficient method for determining seismic wave propagation vectors provided in the embodiments of this specification. While this specification provides the method operation steps or device structures shown in the embodiments or figures below, based on conventional methods or without creative effort, the method or device may include more or fewer operation steps or module units after partial merging. In steps or structures where there is no logically necessary causal relationship, the execution order of these steps or the module structure of the device is not limited to the execution order or module structure shown in the embodiments or figures of this specification. When the method or module structure is applied in actual devices, servers, or terminal products, it can be executed sequentially or in parallel according to the method or module structure shown in the embodiments or figures (e.g., in a parallel processor or multi-threaded processing environment, or even in a distributed processing or server cluster implementation environment).

[0018] The stable and efficient method for determining seismic wave propagation vectors provided in the embodiments of this specification can be applied to various terminal devices, such as... Figure 1 As shown, the method specifically includes the following steps: Step S101: Solve the acoustic wave equation using the finite difference method to obtain the seismic wave field data.

[0019] Specifically, seismic data is acquired, and then forward modeling is used to determine the acoustic wave equation, which is shown below: ; In the formula, For the velocity field, For seismic wave field, For source functions, , , These refer to spatial horizontal, spatial vertical, and temporal positions, respectively. It is a spatial direction vector. The coordinates of the earthquake source are given. Wavefield data of the seismic wavefield are obtained by solving the acoustic wave equation.

[0020] In this embodiment, the above-mentioned acoustic wave equation is solved using the finite difference method, and the seismic wavefield data is specifically determined using the following formula: ; In the formula, For seismic wavefield data, This represents the amplitude of the plane wave. For angular frequency, Let be the vector representing the direction of wave propagation. Let be the propagation speed of the wave in the medium.

[0021] Step S102: Calculate the spatial domain gradient of the seismic wavefield at a certain time, the time domain integral of the seismic wavefield at a certain time, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time based on the seismic wavefield data.

[0022] Specifically, by solving using the finite difference method, a high-precision wavefield spatial domain gradient, i.e., the spatial domain gradient of the seismic wavefield, can be obtained. of The formula for calculating the components is: , of The formula for calculating the components is: In the formula It is the difference order. For finite difference coefficients, to balance computational accuracy and efficiency, this method uses 10th-order finite difference accuracy in testing. , The computational data for these two items has already been obtained during the forward simulation process. Reusing this data can save computational resources.

[0023] In this embodiment of the application, the spatial domain gradient of the seismic wavefield at a certain moment is specifically determined by the following formula: ; In the formula, The spatial gradient of the seismic wave field. This is the symbol for partial differentials.

[0024] Specifically, the time-domain integral of the wave field at a certain moment It can be calculated from the wave field before that moment. The calculation formula is: Then, the finite difference method is used to calculate... Spatial domain gradient ,in of The formula for calculating the components is: , of The formula for calculating the components is: The test also used 10th-order precision finite difference.

[0025] In this embodiment of the application, the time-domain integral of the seismic wavefield at a certain moment is specifically determined by the following formula: ; In the formula, For the time-domain integral of the seismic wave field at a certain moment, For integration, This is the constant term obtained from the integral calculation.

[0026] The spatial gradient of the time-domain integral of the seismic wavefield at a certain moment is determined by the following formula: ; In the formula, The spatial domain gradient of the seismic wave field at a certain moment, which is the time-domain integral. This is the time-domain integral of the seismic wave field at a certain moment.

[0027] Step S103: Determine the seismic wave propagation vector based on the seismic wave field data, the spatial domain gradient of the seismic wave field at a certain time, the time domain integral of the seismic wave field at a certain time, and the spatial domain gradient of the time domain integral of the seismic wave field at a certain time.

[0028] In this embodiment of the application, the determination of the seismic wave propagation vector based on the seismic wavefield data, the spatial domain gradient of the seismic wavefield at a certain time, the time domain integral of the seismic wavefield at a certain time, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time is specifically determined by the following formula: ; In the formula, The vector for seismic wave propagation. For the time-domain integral of the seismic wave field at a certain moment, The spatial gradient of the seismic wave field. For seismic wavefield data, The spatial domain gradient is the time-domain integral of the seismic wave field at a certain moment.

[0029] Specifically, the process of determining the seismic wave propagation vector in this application only needs to include a constant term at the end. and unit direction vector Since no trigonometric function terms are involved, this method has two advantages in calculating the wave field propagation direction: First, because no trigonometric function terms are involved, this method does not exhibit the oscillation phenomenon that occurs in the Poynting vector determined by conventional schemes, significantly improving the calculation stability of the seismic wave propagation vector; second, the scheme in this application only uses the unit direction vector. The coefficients of the calculated seismic wave propagation vectors are determined by the ratio between their magnitudes. The proportions of each component of the vector remain unchanged, which facilitates the direct calculation of the wave field propagation direction and improves the accuracy of seismic wave propagation vector calculation. Figure 3 The diagram shown is a schematic representation of the seismic wave field. Figure 4 The diagram shown is a schematic representation of the horizontal component of the seismic wave propagation vector determined by this scheme. Figure 5 The diagram shown is a schematic representation of the vertical component of the seismic wave propagation vector determined by this scheme. Figure 6 The diagram shown illustrates the horizontal components of the Poynting vector determined by the conventional method. Figure 7 The diagram shows the vertical component of the Poynting vector determined by the conventional method. The horizontal axis, Distance / km, represents distance in kilometers, and the vertical axis, Depth / km, represents depth in kilometers. Figures 4 to 7 It is known that conventional schemes exhibit wavefront oscillations in both the horizontal and vertical components after determining the Poynting vector, while the scheme in this application shows no oscillations in either the horizontal or vertical components of the seismic wave propagation vector. Figure 8 The diagram shown illustrates the direction of the Poynting vector determined by the conventional method. Figure 9 The diagram shown is a schematic representation of the direction of the seismic wave propagation vector determined by the scheme in this application. Figures 3 to 9 In the image, the crosshair at the center represents the earthquake source. Figure 8 and Figure 9 It can be seen that the proposed scheme determines the direction of the seismic wave propagation vector in more detail compared to the conventional scheme.

[0030] Based on the aforementioned stable and efficient method for determining seismic wave propagation vectors, one or more embodiments of this specification also provide a platform or terminal for stable and efficient seismic wave propagation vector determination. This platform or terminal may include devices, software, modules, plug-ins, servers, clients, etc., using the methods described in the embodiments of this specification, combined with necessary hardware implementation. Based on the same innovative concept, the systems in one or more embodiments provided in this specification are as described in the following embodiments. Since the implementation schemes and methods for solving the system problem are similar, the specific system implementation in the embodiments of this specification can refer to the implementation of the aforementioned methods. Repeated details will not be repeated. The terms "unit" or "module" used below can refer to a combination of software and / or hardware that achieves a predetermined function. Although the systems described in the following embodiments are preferably implemented in software, hardware implementation, and a combination of software and hardware, are also possible and contemplated.

[0031] Specifically, Figure 2 This is a schematic diagram of the module structure of one embodiment of the stable and efficient seismic wave propagation vector determination device provided in this specification, as shown below. Figure 2 As shown, the stable and efficient seismic wave propagation vector determination device provided in this specification includes: Solver module 201 is used to solve the acoustic wave equation using the finite difference method to obtain seismic wave field data; The first determining module 202 is used to calculate the spatial domain gradient of the seismic wave field at a certain time, the time domain integral of the seismic wave field at a certain time, and the spatial domain gradient of the time domain integral of the seismic wave field at a certain time based on the seismic wave field data. The second determining module 203 is used to determine the seismic wave propagation vector based on the seismic wave field data, the spatial domain gradient of the seismic wave field at a certain time, the time domain integral of the seismic wave field at a certain time, and the spatial domain gradient of the time domain integral of the seismic wave field at a certain time.

[0032] It should be noted that the system described above may include other implementation methods based on the description of the corresponding method embodiments. The specific implementation methods can be referred to the description of the corresponding method embodiments above, and will not be elaborated here.

[0033] This application also provides an electronic device, including: processor; Memory used to store the processor's executable instructions; The processor is configured to perform the methods provided in the embodiments described above.

[0034] The electronic device provided in this application stores executable instructions for a processor in a memory. When the processor executes these instructions, it first solves the acoustic wave equation using the finite difference method to obtain seismic wavefield data. Then, based on the seismic wavefield data, it calculates the spatial domain gradient, the time domain integral, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time. Finally, it determines the seismic wave propagation vector based on the seismic wavefield data, the spatial domain gradient, the time domain integral, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time. Compared with the traditional Poynting vector, this eliminates the oscillation phenomenon present in the traditional Poynting vector and has lower computational complexity.

[0035] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0036] The methods or apparatus described in the embodiments provided in this specification can implement business logic through a computer program and record it on a storage medium. The storage medium can be read and executed by a computer to achieve the effects of the solutions described in the embodiments of this specification, such as: Seismic wave field data are obtained by solving the acoustic wave equation using the finite difference method. Based on the seismic wavefield data, the spatial domain gradient of the seismic wavefield at a certain time, the time domain integral of the seismic wavefield at a certain time, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time are calculated. The seismic wave propagation vector is determined based on the seismic wavefield data, the spatial domain gradient of the seismic wavefield at a certain time, the time domain integral of the seismic wavefield at a certain time, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time.

[0037] The storage medium can include physical devices for storing information, typically digitizing the information and then storing it using electrical, magnetic, or optical methods. The storage medium can include: devices that store information using electrical energy, such as various types of memory, like RAM and ROM; devices that store information using magnetic energy, such as hard disks, floppy disks, magnetic tapes, magnetic core memory, bubble memory, and USB flash drives; and devices that store information using optical methods, such as CDs or DVDs. Of course, there are other readable storage media, such as quantum memories and graphene memories.

[0038] The embodiments in this specification are not limited to conforming to industry communication standards, standard computer resource data update and data storage rules, or the situations described in one or more embodiments of this specification. Slightly modified implementations based on certain industry standards or custom methods or embodiments can also achieve the same, equivalent, or similar, or predictable, implementation effects as described above. Embodiments that utilize these modified or modified methods for data acquisition, storage, judgment, and processing still fall within the scope of optional implementations of the embodiments in this specification.

[0039] The controller can be implemented in any suitable manner. For example, it can take the form of a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers. Examples of controllers include, but are not limited to, the following microcontrollers: ARC 625D, Atmel AT91SAM, Microchip PIC18F26K20, and Silicon Labs C8051F320. A memory controller can also be implemented as part of the control logic of the memory. Those skilled in the art will also recognize that, in addition to implementing the controller in purely computer-readable program code form, the same functionality can be achieved by logically programming the method steps to make the controller take the form of logic gates, switches, ASICs, programmable logic controllers, and embedded microcontrollers. Therefore, such a controller can be considered a hardware component, and the means included therein for implementing various functions can also be considered as structures within the hardware component. Alternatively, the means for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0040] The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or plug-ins may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, indirect coupling or communication connection between devices or units, and may be electrical, mechanical, or other forms.

[0041] These computer program instructions can also be loaded onto a computer or other programmable resource data updating device, causing a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable device for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0042] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, system embodiments are basically similar to method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. In the description of this specification, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this specification. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described can be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0043] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A stable and efficient method for determining the propagation vector of seismic waves, characterized in that, The method includes: Seismic wave field data are obtained by solving the acoustic wave equation using the finite difference method. Based on the seismic wavefield data, the spatial domain gradient of the seismic wavefield at a certain time, the time domain integral of the seismic wavefield at a certain time, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time are calculated. The seismic wave propagation vector is determined based on the seismic wave field data, the spatial domain gradient of the seismic wave field at a certain time, the time domain integral of the seismic wave field at a certain time, and the spatial domain gradient of the time domain integral of the seismic wave field at a certain time. Specifically, the determination of the seismic wave propagation vector based on the seismic wavefield data, the spatial domain gradient of the seismic wavefield at a certain time, the time domain integral of the seismic wavefield at a certain time, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time is achieved through the following formula: ； In the formula, The vector for seismic wave propagation. For the time-domain integral of the seismic wave field at a certain moment, The spatial domain gradient of the seismic wave field at a certain moment. For seismic wavefield data, The spatial domain gradient of the seismic wave field at a certain moment, which is the time-domain integral. Position in the direction of time. This represents the amplitude of the plane wave. For angular frequency, Let be the speed of wave propagation in the medium. Let be the vector representing the direction of wave propagation. For spatial location.

2. The stable and efficient method for determining seismic wave propagation vectors as described in claim 1, characterized in that, The seismic wavefield data is specifically determined using the following formula: ； In the formula, For seismic wavefield data, This represents the amplitude of the plane wave. For angular frequency, Let be the vector representing the direction of wave propagation. Let be the propagation speed of the wave in the medium.

3. The stable and efficient method for determining seismic wave propagation vectors as described in claim 1, characterized in that, The spatial domain gradient of the seismic wavefield at a certain moment is specifically determined by the following formula: ； In the formula, The spatial domain gradient of the seismic wave field at a certain moment. The symbol is for partial differentials. For spatial location, This represents the amplitude of the plane wave. For angular frequency, Let be the speed of wave propagation in the medium. Position in the direction of time. This is the vector representing the direction of wave propagation.

4. The stable and efficient method for determining seismic wave propagation vectors as described in claim 1, characterized in that, The time-domain integral of the seismic wavefield at a certain moment is specifically determined by the following formula: ； In the formula, For the time-domain integral of the seismic wave field at a certain moment, For seismic wavefield data, For integration, This represents the amplitude of the plane wave. For angular frequency, Let be the speed of wave propagation in the medium. Position in the direction of time. Let be the vector representing the direction of wave propagation. For spatial location, This is the constant term obtained from the integral calculation.

5. The stable and efficient method for determining seismic wave propagation vectors as described in claim 1, characterized in that, The spatial domain gradient of the seismic wavefield time-domain integral at a certain moment is specifically determined by the following formula: ； In the formula, The spatial domain gradient of the seismic wave field at a certain moment, which is the time-domain integral. For the time-domain integral of the seismic wave field at a certain moment, For spatial location, This represents the amplitude of the plane wave. For angular frequency, Let be the speed of wave propagation in the medium. Position in the direction of time. This is the vector representing the direction of wave propagation.

6. A stable and efficient device for determining the propagation vector of seismic waves, characterized in that, The device includes: The solver module is used to solve the acoustic wave equation using the finite difference method to obtain seismic wavefield data. The first determining module is used to calculate the spatial domain gradient of the seismic wavefield at a certain time, the time domain integral of the seismic wavefield at a certain time, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time based on the seismic wavefield data. The second determining module is used to determine the seismic wave propagation vector based on the seismic wave field data, the spatial domain gradient of the seismic wave field at a certain time, the time domain integral of the seismic wave field at a certain time, and the spatial domain gradient of the time domain integral of the seismic wave field at a certain time. Specifically, the determination of the seismic wave propagation vector based on the seismic wavefield data, the spatial domain gradient of the seismic wavefield at a certain time, the time domain integral of the seismic wavefield at a certain time, and the spatial domain gradient of the time domain integral of the seismic wavefield at a certain time is achieved through the following formula: ； In the formula, The vector for seismic wave propagation. For the time-domain integral of the seismic wave field at a certain moment, The spatial domain gradient of the seismic wave field at a certain moment. For seismic wavefield data, The spatial domain gradient of the seismic wave field at a certain moment, which is the time-domain integral. Position in the direction of time. This represents the amplitude of the plane wave. For angular frequency, Let be the speed of wave propagation in the medium. Let be the vector representing the direction of wave propagation. For spatial location.

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