Method and device for calculating the direction of propagation of an earthquake

Abstract

The application discloses a method and device for calculating the propagation direction of seismic waves. The method comprises the following steps: obtaining the wave equation of the seismic space-time acoustic wave, and obtaining the wave field information according to the wave equation; calculating the wave field component according to the wave field information; and substituting the wave field component and the wave field information into the pre-constructed wave field propagation direction vector expression of the seismic wave. The technical scheme can effectively reduce the deviation in the analysis of the propagation direction of the seismic wave, and improve the calculation accuracy.

Description

Technical Field

[0001] This invention relates to the field of exploration geophysics, specifically to a method and apparatus for calculating the direction of earthquake propagation. Background Technology

[0002] Accurate analysis of the direction of seismic wave propagation is beneficial for seismic wave field separation, suppressing seismic imaging noise, and providing velocity analysis for seismic imaging angular domain gather data.

[0003] Currently, Poynting vectors are commonly used in the analysis of seismic wave propagation direction. However, when applying conventional Poynting vectors to seismic waves, the presence of a zero gradient point on the wavefront leads to instability in the calculated wave propagation direction, which can easily cause deviations in the analysis of seismic wave propagation direction. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method for calculating the direction of earthquake propagation, which can effectively reduce deviations in the analysis of the direction of earthquake wave propagation and improve calculation accuracy.

[0005] This application provides a method for calculating the direction of earthquake propagation. The calculation method includes:

[0006] The calculation method includes:

[0007] Obtain the wave equation of seismic spatial-temporal acoustic waves;

[0008] Wave field information is obtained based on the wave equation.

[0009] The wave field components are calculated based on the wave field information.

[0010] Substitute the wavefield components and the wavefield information into the pre-constructed expression for the propagation direction vector of the seismic wavefield.

[0011] In one aspect, the wavefield information includes a time component and wavefield data, wherein the time component is P. t (x,t), where the wavefield data is P(x,t);

[0012] The steps for obtaining wave field information based on the wave equation include:

[0013] Solving the time derivative term of the wave equation using the finite difference method yields P(x,t-Δt) and P(x,t), where P(x,t-Δt) = P t (x,t), where x is the spatial direction vector, t is the time direction position, and Δt is the time step term.

[0014] In one aspect, the expression summarizing the wavefield data satisfies:

[0015] The expressions for the time components in summary satisfy:

[0016] A is the amplitude, and ω is the angular frequency. Let v be a unit vector orthogonal to the plane wavefront, and v be the propagation velocity of the seismic wave in the medium.

[0017] In one aspect, the wave field components include spatial vector components and spatiotemporal vector components, wherein the spatial vector components are P x (x,t), where the spatiotemporal vector component is P xt (x,t);

[0018] The steps for calculating wavefield components based on the wavefield information include:

[0019] Based on the wavefield data P(x,t), P(x-Δx,z,t), P(x+Δx,z,t), P(x,z-Δz,t) and P(x,z+Δz,t) are obtained respectively;

[0020] The spatial vector component P is derived from P(x-Δx,z,t), P(x+Δx,z,t), P(x,z-Δz,t), and P(x,z+Δz,t). x (x,t), where the space vector P x The formula for calculating the x-component of (x,t) is: The space vector P x The formula for calculating the z-component of (x,t) is: x represents the horizontal position in space, z represents the vertical position in space, Δx represents the change in the horizontal position in space, and Δz represents the change in the vertical position in space.

[0021] In one aspect, the expression summarizing the wavefield data satisfies: Δx is the spatial step size vector term.

[0022] In one aspect, the step of calculating the wave field components based on the wave field information further includes:

[0023] Based on P(x,t-Δt), we obtain P(x-Δx,z,t-Δt), P(x+Δx,z,t-Δt), (x,z-Δz,t-Δt) and P(x,z+Δz,t-Δt) respectively;

[0024] From P(x-Δx,z,t-Δt), P(x+Δx,z,t-Δt), (x,z-Δz,t-Δt), and P(x,z+Δz,t-Δt), the spatiotemporal vector component is obtained as P. xt(x,t), wherein the spatiotemporal vector component P xt The formula for calculating the x-component of (x,t) is: The spatiotemporal vector component P xt The formula for calculating the z-component of (x,t) is:

[0025] In one aspect, the spatiotemporal vector components are summarized to satisfy:

[0026] In one aspect, the expression for the direction vector of the seismic wave field propagation is s(x,t)=P t (x,t)·P x (x,t)-P(x,t)·P xt (x,t);

[0027] Substituting the wavefield components and the wavefield information into the pre-constructed expression for the seismic wavefield propagation direction vector, the expression for the seismic wavefield propagation direction vector satisfies:

[0028]

[0029] Furthermore, to address the aforementioned problems, this application also provides a calculation device for the direction of earthquake propagation, the calculation device comprising:

[0030] The acquisition module is used to acquire the wave equation of the spatial-temporal acoustic wave of the earthquake;

[0031] The calculation module is used to obtain wave field information based on the wave equation and calculate wave field components based on the wave field information.

[0032] The substitution module is used to substitute the wavefield components and the wavefield information into a pre-constructed expression for the propagation direction vector of the seismic wavefield.

[0033] The beneficial effects of this invention are as follows: after substituting the wavefield components and wavefield information into the pre-constructed seismic wavefield propagation direction vector expression, the corresponding values ​​of the trigonometric functions in the seismic wavefield propagation direction vector expression are very small, with virtually no oscillations. Therefore, the propagation direction calculated through the seismic wavefield propagation direction vector expression is more stable, thereby reducing the possibility of deviations in the analysis of seismic wave propagation direction. Attached Figure Description

[0034] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0035] Figure 1 This is a schematic diagram illustrating the steps of the method for calculating the earthquake propagation direction in this application;

[0036] Figure 2 A schematic diagram illustrating the wavefront oscillation phenomenon of the horizontal vector component in related technologies;

[0037] Figure 3 A schematic diagram illustrating the wavefront oscillation phenomenon of the vertical component of a vector in related technologies;

[0038] Figure 4 A schematic diagram of the vector horizontal components calculated by the earthquake propagation direction calculation method of this application;

[0039] Figure 5 A schematic diagram of the vertical component of the vector calculated by the method for calculating the earthquake propagation direction in this application;

[0040] Figure 6 A schematic diagram comparing the direction vectors in the calculation method and related technologies of this application;

[0041] Figure 7 This application Figure 6 Enlarged diagram of part A in the diagram;

[0042] Figure 8 This is a schematic diagram of the structure of the calculation device for the direction of earthquake propagation in this application.

[0043] Figure descriptions: 10, computing device; 100, acquisition module; 200, computing module; 300, substitution module. Detailed Implementation

[0044] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are merely illustrative of the technical solution of the present invention and are therefore intended to limit the scope of protection of the present invention.

[0045] It should be noted that, unless otherwise stated, the technical or scientific terms used in this application should have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0046] like Figure 2 and Figure 3As shown, it can be seen that the horizontal component of the vector exhibits wavefront oscillation, and the vertical component of the vector also exhibits wavefront oscillation, which will seriously affect the accuracy of the calculation of the earthquake propagation direction.

[0047] Therefore, such as Figure 1 As shown, this application provides a method for calculating the direction of earthquake propagation. The method for calculating the direction of earthquake propagation includes:

[0048] Step S10: Obtain the wave equation for the spatial-temporal acoustic wave during an earthquake. Seismic waves, generated during an earthquake, are vibrations propagating from the earthquake source in all directions; they are elastic waves radiating outwards from the epicenter. Based on propagation mode, they can be classified into three types: P-waves (longitudinal waves), S-waves (both P-waves and S-waves are body waves), and L-waves (surface waves). Seismic waves represent the propagation of mechanical motion, originating from the elasticity of the Earth's medium. Their properties are very similar to sound waves; both seismic waves and sound waves are mechanical waves.

[0049] Step S20: Obtain wave field information based on the wave equation. The wave field information can be calculated using the wave equation, and the propagation direction of the earthquake can be analyzed using the wave field information.

[0050] Step S30: Calculate the wave field components based on the wave field information; these wave field components can be used to analyze the seismic waves and further determine the propagation direction of the seismic waves.

[0051] Step S40: Substitute the wavefield components and wavefield information into the pre-constructed seismic wavefield propagation direction vector expression. In order to improve the accuracy of the analysis and calculation of the seismic wave propagation direction, a pre-constructed seismic wavefield propagation direction vector expression is used. By superimposing the wavefield components and wavefield information, the propagation direction can be analyzed according to the seismic wavefield propagation direction vector expression.

[0052] In this embodiment, after substituting the wavefield components and wavefield information into the pre-constructed seismic wavefield propagation direction vector expression, the corresponding values ​​of the trigonometric functions in the expression are very small, with virtually no oscillations. Therefore, the propagation direction calculated through the seismic wavefield propagation direction vector expression is more stable, thereby reducing the possibility of deviations in the analysis of seismic wave propagation direction.

[0053] See Figure 4 and Figure 5 As shown, it can be seen that there is basically no oscillation phenomenon in the wavefront of the vector horizontal component and the vector vertical component.

[0054] In this application, the wavefield information includes a time component and wavefield data, where the time component is P. t (x,t), and the wave field data is P(x,t).

[0055] The steps for obtaining wave field information based on the wave equation include:

[0056] Solving the time derivative term of the wave equation using the finite difference method yields P(X,t-Δt) and P(x,t), where P(x,t-Δt) = P t (x,t), where x is the spatial direction vector, t is the time direction position, and Δt is the time step term.

[0057] The expression for summarizing wavefield data satisfies: It is understandable that for seismic waves, their wavefield data can be summarized into the above expression.

[0058] The expressions for the time components satisfy the following: Similarly, for seismic waves, their time components can be summarized into the above expression.

[0059] A is the amplitude, and ω is the angular frequency. A unit vector orthogonal to the plane wavefront. This can also be understood as the direction of seismic wave propagation. v is the propagation speed of seismic waves in the medium.

[0060] In this application, the wave field components include spatial vector components and spatiotemporal vector components, where the spatial vector component is P. x (x,t), the spacetime vector component is P xt (x,t); This yields at least four pieces of information: wavefield data, time component, spatial vector component, and spatiotemporal vector component. These four pieces of information can be used to further express the expression of the propagation direction vector of the seismic wavefield, facilitating the analysis and calculation of the expression of the propagation direction vector of the seismic wavefield.

[0061] The steps for calculating wavefield components based on wavefield information include:

[0062] Based on the wave field data P(x,t), P(x-Δx,z,t), P(x+Δx,z,t), P(x,z-Δz,t) and P(x,z+Δz,t) are obtained respectively;

[0063] The spatial vector components P are derived from P(x-Δx,z,t), P(x+Δx,z,t), P(x,z-Δz,t), and P(x,z+Δz,t). x (x,t), where the space vector P x The formula for calculating the x-component of (x,t) is: Space vector P x The formula for calculating the z-component of (x,t) is: x represents the horizontal position in space, z represents the vertical position in space, Δx represents the change in the horizontal position in space, and Δz represents the change in the vertical position in space. For the spatial vector P... x (x,t) can be obtained by superimposing its x-components and z-components.

[0064] In this application, the expression summarizing the wave field data satisfies: Δx is the spatial step size vector term.

[0065] In this application, the step of calculating the wave field components based on the wave field information further includes:

[0066] Based on P(x,t-Δt), we obtain P(x-Δx,z,t-Δt), P(x+Δx,z,t-Δt), (x,z-Δz,t-Δt) and P(x,z+Δz,t-Δt) respectively;

[0067] From P(x-Δx,z,t-Δt), P(x+Δx,z,t-Δt), (x,z-Δz,t-Δt), and P(x,z+Δz,t-Δt), the spatiotemporal vector components are obtained as P. xt (x,t), where the spacetime vector component P xt The formula for calculating the x-component of (x,t) is: Spacetime vector component P xt The formula for calculating the z-component of (x,t) is: For the spacetime vector component P xt (x,t) can be obtained by superimposing its x-components and z-components.

[0068] In this application, the spatiotemporal vector components are summarized to satisfy: For seismic waves, their spatiotemporal vector components can be summarized into the above expression.

[0069] In this application, the expression for the direction vector of seismic wave field propagation is s(x,t)=P t (x,t)·P x (x,t)-P(x,t)·P xt (x,t); Substituting the wavefield components and wavefield information into the pre-constructed expression for the seismic wavefield propagation direction vector, the expression for the seismic wavefield propagation direction vector satisfies:

[0070]

[0071] Furthermore, to demonstrate that the calculation direction of the seismic wave field propagation direction vector expression is more accurate, this application further analyzes the seismic wave field propagation direction vector expression, such as the seismic wave simulation process, ωΔt, The values ​​of the terms are usually very small, and according to the first-order Taylor expansion, the above equation can be approximated as:

[0072]

[0073] The expanded approximate formula does not contain trigonometric function terms, only constant terms. and unit vector direction Therefore, the direction vector calculated using this method, since it does not contain trigonometric function terms, reduces oscillations and results in more stable calculations. Secondly, when calculating vectors using this method, the constant terms in each component have the same value. The proportional relationships of the directional components of a vector are equivalent to those of the unit vector direction. The proportional relationships of the components are independent of the constant term, and the calculation accuracy of the technical solution in this application is higher.

[0074] Furthermore, to further illustrate the wave field information P(x,t) and the time component P t (x,t), spatial vector component P x (x,t) and spatiotemporal vector component P xt The calculation process of substituting (x,t) into the expression for the propagation direction vector of the seismic wave field is explained below:

[0075]

[0076] Using the sum and difference formulas of trigonometric functions:

[0077] cos(α-β)=cos(α)cos(β)+sin(α)sin(β) (A2)

[0078] sin(α-β)=sin(α)cos(β)-cos(α)sin(β) (A3)

[0079]

[0080] In formula (A1) The term, according to formula (A2), can be transformed as follows:

[0081]

[0082] In formula (A1) The term, according to formula (A4), can be transformed as follows:

[0083]

[0084] In formula (A1) The terms can be simplified according to formulas (A3) and (A4) as follows:

[0085]

[0086] Substituting (A5), (A6), and (A7) into (A1) and simplifying, we get:

[0087]

[0088] This simplifies to obtain the expression for the direction vector of seismic wave field propagation.

[0089] See Figure 6 As shown, Figure 6 The outward direction of the black arrow is derived from the calculation method of this application, while the outward direction of the white arrow is derived from related technologies. Further reference... Figure 7 As shown, the white arrows point in partially incorrect directions, failing to point away from the epicenter. In contrast, the black arrows obtained using the calculation method described in this application point clearly and uniformly away from the epicenter. This demonstrates that the calculation method in this application yields a more accurate prediction of seismic wave propagation direction, thus reducing the possibility of deviations.

[0090] Furthermore, related technologies employ a novel Poynting vector constructed jointly from conventional seismic wavefields and Hilbert transform wavefields in the time direction, similar to constructing an envelope signal for a Poynting vector. However, this method requires the simultaneous construction of both conventional and Hilbert transform wavefields, necessitating a workflow involving two seismic wavefield simulations. This results in nearly twice the computational cost of conventional methods and lower algorithm execution efficiency. In contrast, the seismic propagation direction calculation method proposed in this application constructs a stable expression for the seismic wavefield propagation direction vector with less computational cost, effectively improving computational efficiency.

[0091] In this application, the wave equation is the spatiotemporal domain acoustic wave equation, which satisfies:

[0092]

[0093] Where v(x) is the velocity field, f(x) s (t) is the source function, and x is the spatial direction vector. s Here are the spatial coordinates of the earthquake source. The propagation characteristics of sound waves are similar to those of seismic waves; both are mechanical waves. The wave field data P(x,t) and the time component P can be obtained using the spatiotemporal domain sound wave equation. t (x,t). It should be noted that this application assumes a single, homogeneous propagation medium for calculating the direction of earthquake propagation.

[0094] See Figure 8As shown, this application also provides a calculation device 10 for earthquake propagation direction. The calculation device 10 includes: an acquisition module 100, a calculation module 200, and a substitution module 300. The acquisition module 100 is used to acquire the wave equation of the seismic spatiotemporal acoustic wave; the calculation module 200 is used to obtain wavefield information based on the wave equation and calculate the wavefield components based on the wavefield information; the substitution module 300 is used to substitute the wavefield components and wavefield information into a pre-constructed expression for the earthquake wavefield propagation direction vector.

[0095] This application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the computation method described above.

[0096] Specific embodiments and beneficial effects of the computer-readable storage medium in this application are described in the above-described method for calculating the direction of earthquake propagation, and will not be repeated here.

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the claims and specification of the present invention.

Claims

1. A method for calculating the direction of earthquake propagation, characterized in that, The calculation method includes: Obtain the wave equation of seismic spatial-temporal acoustic waves; Wave field information is obtained based on the wave equation; The wave field components are calculated based on the wave field information. Substitute the wavefield components and the wavefield information into the pre-constructed expression for the seismic wavefield propagation direction vector; The wavefield information includes a time component and wavefield data, wherein the time component is... The wave field data is ; The steps for obtaining wave field information based on the wave equation include: The time derivative term of the wave equation is solved using the finite difference method to obtain... and ,in, = , It is a spatial direction vector. Position in the direction of time. For time step; The expression for the wavefield data in summary satisfies: ; The expressions for the time components in summary satisfy: ; For amplitude, Angular frequency, A unit vector orthogonal to the plane wavefront. The velocity of seismic waves in the medium; The wave field components include spatial vector components and spatiotemporal vector components, wherein the spatial vector components are: The spatiotemporal vector components are ; The steps for calculating wavefield components based on the wavefield information include: Based on the wave field data Obtained respectively , , and ; Depend on , , and The spatial vector components are obtained. The space vector of The formula for calculating the components is: The space vector of The formula for calculating the components is: , For spatial horizontal position, For spatial vertical position, This represents the change in horizontal position in space. This refers to the change in vertical position in space. The expression for the wavefield data in summary satisfies: = , This is the spatial step size vector term; The step of calculating the wave field components based on the wave field information further includes: in accordance with Obtained respectively , , and ; Depend on , , and The spatiotemporal vector components are then obtained as follows: The spatiotemporal vector components mentioned above of The formula for calculating the components is: The spatiotemporal vector components of The formula for calculating the components is: ； In summary, the spatiotemporal vector components satisfy the following: 。 2. The calculation method according to claim 1, characterized in that, The expression for the direction vector of seismic wave field propagation is: ; Substituting the wavefield components and the wavefield information into the pre-constructed expression for the seismic wavefield propagation direction vector, the expression for the seismic wavefield propagation direction vector satisfies: 。 3. A device for calculating the direction of earthquake propagation, characterized in that, For executing the method for calculating the direction of earthquake propagation as described in claim 1, the computing device comprises: The acquisition module is used to acquire the wave equation of the spatial-temporal acoustic wave of the earthquake; The calculation module is used to obtain wave field information based on the wave equation and calculate wave field components based on the wave field information. The substitution module is used to substitute the wavefield components and the wavefield information into a pre-constructed expression for the propagation direction vector of the seismic wavefield.

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