Method and device for calculating seismic propagation direction

Abstract

The invention discloses a calculation method and a calculation device of an earthquake propagation direction. The calculation method comprises the steps that a wave equation of seismic time-space domain sound waves is acquired, and wave field information is acquired according to the wave equation; calculating a wave field component according to the wave field information; and substituting the wave field component and the wave field information into a pre-constructed seismic wave field propagation direction vector expression. According to the technical scheme, the situation that deviation occurs in the seismic wave propagation direction analysis can be effectively reduced, and the calculation precision is improved.

Description

Technical Field

[0001] The present invention relates to the field of exploration geophysics, and particularly relates to a method and device for calculating the seismic propagation direction. Background Art

[0002] Correctly analyzing the seismic wave propagation direction is beneficial for seismic wave field separation, suppressing seismic imaging noise, and providing velocity analysis for seismic imaging angle domain gather data, etc.

[0003] Currently, when analyzing the seismic wave propagation direction, the Poynting vector is usually introduced into the calculation application. However, when applying the conventional Poynting vector to seismic waves, there are gradient zero value points on the wave front, resulting in unstable phenomena in the calculated wave propagation direction and prone to deviations in analyzing the seismic wave propagation direction. Summary of the Invention

[0004] Aiming at the defects in the prior art, the present invention provides a method for calculating the seismic propagation direction, which can effectively reduce the deviation in analyzing the seismic wave propagation direction and improve the calculation accuracy.

[0005] A method for calculating the seismic propagation direction provided by this application includes:

[0006] The calculation method includes:

[0007] Obtain the wave equation of the seismic spatio-temporal domain acoustic wave;

[0008] Obtain the wave field information according to the wave equation;

[0009] Calculate the wave field components according to the wave field information;

[0010] Substitute the wave field components and the wave field information into the pre-constructed seismic wave field propagation direction vector expression.

[0011] In one aspect, the wave field information includes a time component and wave field data, the time component is P t (x, t), and the wave field data is P(x, t);

[0012] The step of obtaining the wave field information according to the wave equation includes:

[0013] Apply the difference method to solve the time derivative term of the wave equation to obtain P(x, t - Δt) and P(x, t), where P(x, t - Δt) = P t (x, t), 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 for summarizing the wave field data satisfies:

[0015] The expression summarizing the time component satisfies:

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

[0017] In one aspect, the wave field component includes a spatial vector component and a spatio-temporal vector component. The spatial vector component is P x (x, t), and the spatio-temporal vector component is P xt (x, t);

[0018] The steps for calculating the wave field component based on the wave field information include:

[0019] Obtaining P(x - Δx, z, t), P(x + Δx, z, t), P(x, z - Δz, t), and P(x, z + Δz, t) respectively from the wave field data P(x, t);

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

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

[0022] In one aspect, the steps for calculating the wave field component based on the wave field information further include:

[0023] Obtaining 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 from P(x, t - Δt);

[0024] Deriving the spatio-temporal vector component as P xt(x, t), where the spatio-temporal vector component P xt The formula for calculating the x-component of the spatio-temporal vector component P The spatio-temporal vector component P xt The formula for calculating the z-component of the spatio-temporal vector component P

[0025] In one aspect, it is summarized that the spatio-temporal vector component satisfies:

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

[0027] Substitute the wave field component and the wave field information into the pre-constructed expression of the propagation direction vector of the seismic wave field, then the expression of the propagation direction vector of the seismic wave field satisfies:

[0028]

[0029] In addition, to solve the above problems, the present application also provides a calculation device for the seismic propagation direction, and the calculation device includes:

[0030] An acquisition module, which is used to acquire the wave equation of the acoustic wave in the seismic spatio-temporal domain;

[0031] A calculation module, which is used to obtain wave field information according to the wave equation and calculate wave field components according to the wave field information;

[0032] A substitution module, which is used to substitute the wave field component and the wave field information into the pre-constructed expression of the propagation direction vector of the seismic wave field.

[0033] The beneficial effects of the present invention are reflected in that after substituting the wave field component and the wave field information into the pre-constructed expression of the propagation direction vector of the seismic wave field, the corresponding values of the trigonometric functions in the expression of the propagation direction vector of the seismic wave field are very small and there is basically no oscillation phenomenon. Thus, the propagation direction calculated and analyzed through the expression of the propagation direction vector of the seismic wave field is more stable, and further reduces the deviation in analyzing the propagation direction of seismic waves. Description of the Drawings

[0034] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the accompanying drawings required for the description of the specific embodiments or the prior art. 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 Schematic diagram of the flow steps of the calculation method for the earthquake propagation direction of the present application;

[0036] Figure 2 Schematic diagram showing the wavefront oscillation phenomenon of the vector horizontal component in the related art;

[0037] Figure 3 Schematic diagram showing the wavefront oscillation phenomenon of the vector vertical component in the related art;

[0038] Figure 4 Schematic diagram of the vector horizontal component calculated by the calculation method for the earthquake propagation direction of the present application;

[0039] Figure 5 Schematic diagram of the vector vertical component calculated by the calculation method for the earthquake propagation direction of the present application;

[0040] Figure 6 Schematic diagram for comparing the direction vectors between the calculation method of the present application and the related art;

[0041] Figure 7 The present application Figure 6 Enlarged schematic diagram of part A;

[0042] Figure 8 Schematic diagram of the structure of the calculation device for the earthquake propagation direction of the present application.

[0043] Explanation of the drawings: 10. Calculation device; 100. Acquisition module; 200. Calculation module; 300. Substitution module. Specific embodiments

[0044] The following will describe in detail the embodiments of the technical solutions of the present invention in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, so they are only examples and cannot be used to limit the protection scope of the present invention.

[0045] It should be noted that unless otherwise specified, the technical terms or scientific terms used in the present application should have the ordinary meanings understood by those skilled in the art to which the present invention belongs.

[0046] Such as Figure 2 And Figure 3As shown, it can be seen that in the related art, there are wavefront oscillation phenomena in the vector horizontal component and the vector vertical component, which will seriously affect the accuracy of calculating the seismic propagation direction.

[0047] For this reason, as Figure 1 shown, the present application provides a method for calculating the seismic propagation direction, and the method for calculating the seismic propagation direction includes:

[0048] Step S10, obtaining the wave equation of the seismic wave in the space-time domain; the seismic wave generated during an earthquake is a vibration that propagates in all directions from the seismic source, referring to the elastic wave that radiates from the seismic source in all directions. It can be divided into three types according to the propagation mode: longitudinal wave (P wave), transverse wave (S wave) (both longitudinal wave and transverse wave belong to body waves) and surface wave (L wave). The seismic wave is a propagation of mechanical motion and is generated by the elasticity of the earth's medium. Its properties are very similar to those of sound waves, and both seismic waves and sound waves are mechanical waves.

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

[0050] Step S30, calculating the wave field components based on the wave field information; through these wave field components, the seismic wave can be analyzed to further determine the propagation direction of the seismic wave.

[0051] Step S40, substituting the wave field components and the wave field information into the pre-constructed seismic wave field propagation direction vector expression; in the present application, in order to improve the accuracy of the analysis and calculation of the seismic wave propagation direction, a seismic wave field propagation direction vector expression is pre-constructed. Through the superposition of the wave field components and the wave field information, the propagation direction can be analyzed according to the seismic wave field propagation direction vector expression.

[0052] In this embodiment, after substituting the wave field components and the wave field information into the pre-constructed seismic wave field propagation direction vector expression, the corresponding values of the trigonometric functions in the seismic wave field propagation direction vector expression are very small and there is basically no oscillation phenomenon. Thus, the propagation direction analyzed and calculated through the seismic wave field propagation direction vector expression is more stable, and further reduces the situation of deviation in analyzing the seismic wave propagation direction.

[0053] Referring to Figure 4 and Figure 5 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 the present application, the wave field information includes a time component and wave field data, the time component is P t (x, t), and the wave field data is P(x, t).

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

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

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

[0058] The expression for summarizing the time component satisfies: Similarly, for seismic waves, their time component can be summarized into the above - mentioned expression form.

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

[0060] In this application, the wavefield component includes a spatial vector component and a spatio - temporal vector component. The spatial vector component is P x (x,t), and the spatio - temporal vector component is P xt (x,t); thus, at least four information data are obtained, namely wavefield data, time component, spatial vector component, and spatio - temporal vector component. Through these four information data, the expression of the propagation direction vector of the seismic wavefield can be further expressed, facilitating the analysis and calculation of the expression of the propagation direction vector of the seismic wavefield.

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

[0062] Obtain P(x - Δx,z,t), P(x + Δx,z,t), P(x,z - Δz,t), and P(x,z + Δz,t) respectively according to the wavefield data P(x,t);

[0063] Derive the spatial vector component P x (x,t) from P(x - Δx,z,t), P(x + Δx,z,t), P(x,z - Δz,t), and P(x,z + Δz,t), where the x - component calculation formula of the spatial vector P x (x,t) is: The z - component calculation formula of the spatial vector P x (x,t) is: x is the spatial horizontal position, z is the spatial vertical position, Δx is the change in the spatial horizontal position, and Δz is the change in the spatial vertical position. For the spatial vector P x (x,t), its x-component and z-component can be superimposed and obtained.

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

[0065] In this application, the steps for calculating the wave field components based on the wave field information further include:[[]]

[0066] 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 based on P(x, t - Δt);[[]]

[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 spatio-temporal vector component is obtained as P xt (x,t), where the x-component calculation formula of the spatio-temporal vector component P xt (x,t) is:[[]] The z-component calculation formula of the spatio-temporal vector component P xt (x,t) is:[[]] For the spatio-temporal vector component being P xt (x,t), its x-component and z-component can be superimposed and obtained.

[0068] In this application, the summarized spatio-temporal vector component satisfies:[[]] For seismic waves, their spatio-temporal vector components can be summarized into the above expression form.

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

[0070]

[0071] Furthermore, in order to show that the calculation direction of the expression for the seismic wave field propagation direction vector is more accurate, this application further analyzes the expression for the seismic wave field propagation direction vector, such as the simulation process of seismic waves, ωΔt, The value of the term is usually very small. According to the first-order Taylor expansion, the above formula can be approximated as:

[0072]

[0073] The expanded approximate formula does not contain trigonometric function terms and only contains constant terms and the unit vector direction Therefore, for the direction vector calculated by this method, since it does not contain trigonometric function terms, the oscillation phenomenon is reduced, and the calculation result of the method is more stable. Secondly, when calculating the vector by this method, since the numerical values of the constant terms included in each component are the same, all being the proportional relationship of each direction component of the vector is the same as that of the unit vector direction in each component ratio relationship, independent of the constant term, the calculation accuracy of the technical solution of this application is higher.

[0074] In addition, to further illustrate the calculation process of substituting the wave field information P(x,t), time component P t (x,t), spatial vector component P x (x,t) and spatio-temporal vector component P xt (x,t) into the expression of the seismic wave field propagation direction vector, the following is an explanation:

[0075]

[0076] Using the sum and difference angle formula 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] For the term in formula (A1), it can be transformed as follows according to formula (A2):

[0081]

[0082] For the term in formula (A1), it can be transformed as follows according to formula (A4):

[0083]

[0084] For the term in formula (A1), it can be simplified according to formulas (A3) and (A4) as:

[0085]

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

[0087]

[0088] From this simplification, the expression for the propagation direction vector of the seismic wave field is obtained.

[0089] Refer to Figure 6 as shown Figure 6 in which the outward extension direction of the black arrow is obtained by the calculation method of the present application, and the outward extension direction of the white arrow is obtained in the related art. Further refer to Figure 7 as shown. There are some disorders in the direction pointed by the white arrow and it does not point in the direction away from the central seismic source. However, the black arrow obtained by the calculation method of the present application has a clear and uniform direction, all pointing in the direction away from the central seismic source. It can be seen that the seismic wave propagation direction obtained by the calculation method of the present application is more accurate, thus reducing the deviation situation.

[0090] In addition, in the related art, a new Poynting vector is jointly constructed by using the conventional seismic wave field and the Hilbert transform wave field in the time direction, which is similar to constructing an envelope signal of a Poynting vector. However, this method requires constructing both the conventional wave field and the Hilbert transform wave field, that is, two workflows for seismic wave field simulation, and the computational amount is nearly twice that of the conventional method, and the algorithm execution efficiency is low. While the calculation method of the seismic propagation direction proposed in the present application constructs a stable expression for the propagation direction vector of the seismic wave field, with less computational amount, and can effectively improve the calculation efficiency.

[0091] In the present application, the wave equation is the acoustic wave equation in the space-time domain, and it satisfies:

[0092]

[0093] where v(x) is the velocity field, f(x s , t) is the source function, x is the spatial direction vector, and x s is the source spatial coordinate. The propagation characteristics of acoustic waves are similar to those of seismic waves, both being mechanical waves. Through the acoustic wave equation in the space-time domain, the wave field data P(x, t) and the time component P t (x, t) can be obtained. It should be noted that the present application assumes a single and uniform propagation medium for calculating the seismic propagation direction.

[0094] Refer to Figure 8As shown in the figure, the present application also provides a calculation device 10 for the 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 wave in the space-time domain; the calculation module 200 is used to obtain the wave field information based on the wave equation and calculate the wave field components based on the wave field information; the substitution module 300 is used to substitute the wave field components and the wave field information into the pre-constructed expression of the seismic wave field propagation direction vector.

[0095] The present application also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the above-mentioned calculation method is implemented.

[0096] For the specific embodiments and beneficial effects of the computer-readable storage medium in the present application, refer to the above-mentioned calculation method for the earthquake propagation direction, which will not be elaborated here.

[0097] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements 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 by the scope of the claims and the specification of the present invention.

Claims

1. A method for calculating the direction of earthquake propagation, characterized in that, The described calculation method includes: Obtaining the wave equation of seismic acoustic waves in the spatio-temporal domain; Obtaining wave field information based on the wave equation; Calculating wave field components based on the wave field information; Substituting the wave field components and the wave field information into the pre-constructed expression of the seismic wave field propagation direction vector.

2. The calculation method according to claim 1, wherein The wave field information includes a time component and wave field data, and the time component is P t (x, t), and the wave field data is P(x, t); The step of obtaining wave field information based on the wave equation includes: The differential method is applied to solve the time derivative term of the wave equation to obtain P(x, t - Δt) and P(x, t), where P(x, t - Δt) = P t (x, t), x is the spatial direction vector, t is the time direction position, and Δt is the time step term.

3. The calculation method according to claim 2, wherein The expression summarizing the above wave field data satisfies: The expression summarizing the time component satisfies: A is the amplitude, ω is the angular frequency, is the unit vector orthogonal to the plane wavefront, and v is the propagation velocity of the seismic wave in the medium.

4. The calculation method according to claim 3, characterized in that, The wave field components include a spatial vector component and a spatio-temporal vector component. The spatial vector component is P x (x, t), and the spatio-temporal vector component is P xt (x, t); The step of calculating wave field components based on the wave field information includes: Respectively obtaining P(x - Δx, z, t), P(x + Δx, z, t), P(x, z - Δz, t) and P(x, z + Δz, t) from the wave field data P(x, t); The spatial vector component P is obtained 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 spatial vector P x (x,t) has its x-component calculation formula as follows: The spatial vector P x (x,t) has its z-component calculation formula as follows: x is the spatial horizontal position, z is the spatial vertical position, Δx is the change in the spatial horizontal position, and Δz is the change in the spatial vertical position.

5. The calculation method according to claim 4, wherein The expression summarizing the wave field data satisfies: Δx is the spatial step vector term.

6. The calculation method according to claim 5, characterized in that The step of calculating wave field components based on the wave field information further includes: Respectively obtaining P(x - Δx, z, t - Δt), P(x + Δx, z, t - Δt), (x, z - Δz, t - Δt) and P(x, z + Δz, t - Δt) from P(x, t - Δt); 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 spatio-temporal vector component is obtained as P xt (x, t), where the spatio-temporal vector component P xt (x, t) has the x-component calculation formula as: The spatio-temporal vector component P xt (x, t) has the z-component calculation formula as:

7. The calculation method according to claim 6, characterized in that The summarized spatio-temporal vector components satisfy:

8. The calculation method according to claim 7, characterized in that The expression for the propagation direction vector of the seismic wave field is s(x,t) = P t (x,t)·P x (x,t) - P(x,t)·P xt (x,t); Substituting the wave field components and the wave field information into the pre-constructed expression of the seismic wave field propagation direction vector, then the expression of the seismic wave field propagation direction vector satisfies:

9. A calculating device for the direction of earthquake propagation, characterized in that, The described calculation device includes: An acquisition module, which is used to acquire the wave equation of seismic acoustic waves in the spatio-temporal domain; A calculation module, which is used to obtain wave field information based on the wave equation and calculate wave field components based on the wave field information; A substitution module, which is used to substitute the wave field components and the wave field information into the pre-constructed expression of the seismic wave field propagation direction vector.

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