Forward modeling method based on acoustic wave-viscoelastic wave coupling equation

Abstract

The invention relates to a forward modeling method based on an acoustic wave-viscoelastic wave coupling equation, and belongs to the field of seismic exploration. The method comprises the following steps: firstly, giving a seismic source wavelet, establishing a speed model, giving a conventional first-order speed-stress viscoelastic wave equation, and calculating a pressure component relational expression according to a known stress tensor, a pressure field, a deviatoric stress tensor and an average value of a negative normal positive stress component; substituting the equation into the pressure component relational expression and carrying out time derivative to obtain a pressure partial differential equation, substituting the equation into a stress tensor, pressure field and deviatoric stress relation, deducing a sound wave-viscoelastic wave coupling equation in combination with the pressure partial differential equation, and substituting seismic wavelets and a velocity model to obtain a seismic wave-viscoelastic wave coupling equation; and obtaining a forward modeling wave field and a seismic record of each component. Experiments show that compared with a conventional sound wave-elastic wave coupling equation, the method has an obvious amplitude attenuation effect on a seismic wave field, and better conforms to the real situation of underground propagation of seismic waves.

Description

Technical Field

[0001] The invention belongs to the field of numerical simulation in seismic exploration, and in particular relates to a forward simulation method based on an acoustic wave-viscoelastic wave coupling equation. Background Art

[0002] Seismic wave forward modeling is the process of simulating the propagation of waves in underground media using computers. Efficient and high-precision numerical simulation of seismic wave fields is the basis of full waveform inversion and least squares reverse time migration. In recent years, offshore exploration has gradually developed towards deep and complex areas. Ocean bottom node acquisition technology (OBN) has been increasingly used to obtain higher quality multi-component seismic data. Seismic exploration has entered the multi-component field, which has put forward higher requirements for seismic wave forward modeling. However, conventional elastic wave equations cannot fully simulate and utilize OBN data. The main reason is that there is still a lack of systematic and in-depth research on the propagation laws of seismic waves in marine environments containing fluid and solid media.

[0003] In the numerical simulation of offshore OBN data, some scholars use the partition method, that is, the acoustic wave equation is used in the water layer and the elastic wave equation is used in the solid. However, this equation requires strict fluid-solid boundary conditions, which is a great challenge for the simulation of irregular seabed interfaces. Some scholars also introduce the relationship between pressure and stress into conventional elastic waves to derive the acoustic-elastic wave coupling equation. Although it can simulate OBN data and does not require fluid-solid boundary conditions, in offshore exploration, the upper layer is a fluid medium and the lower layer is a solid medium. The acoustic-elastic wave equation does not consider the absorption and attenuation factors of the underground wave field, which does not conform to the actual seismic wave propagation situation. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a forward modeling method based on the acoustic-viscoelastic wave coupling equation. The model experiment of the method shows that compared with the conventional acoustic-elastic wave coupling equation, the seismic wave field of the acoustic-viscoelastic wave coupling equation has an obvious amplitude attenuation effect, and the amplitude spectrum analysis shows that the main frequency of the acoustic-viscoelastic wave coupling equation moves to a low frequency, showing the frequency dissipation characteristics of the viscoelastic medium, which is more in line with the actual situation of seismic wave propagation underground.

[0005] The present invention adopts the following technical solutions: The present invention provides a forward modeling method based on an acoustic wave-viscoelastic wave coupling equation, and the method is as follows: The first step is to give a source wavelet and establish a velocity model; The second step is to calculate the pressure component relationship from the known stress tensor, pressure field, deviatoric stress tensor and the average value of the negative normal stress component given the first-order velocity-stress viscoelastic wave equation; The third step is to substitute the first-order velocity stress-viscoelastic wave equation into the pressure component relationship and take the derivative with respect to time to obtain the pressure partial differential equation; The fourth step is to introduce the first-order velocity stress-viscoelastic wave equation into the stress tensor, pressure field and deviatoric stress relationship and derive the acoustic wave-viscoelastic wave coupling equation in combination with the pressure partial differential equation; Step 5: Based on the acoustic-viscoelastic wave coupling equation in step 4, the seismic wavelet and velocity model are introduced, and forward modeling is performed using the tenth-order space to obtain the forward wave field of each component and the seismic record.

[0006] The present invention also provides a specific forward modeling method based on the acoustic wave-viscoelastic wave coupling equation, and the method specifically comprises the following steps: Step 1: Use Ricker wavelet as the source wavelet W(t), where t represents time. Then, the P-wave velocity, density, and P-wave quality factor model M(x, z) are given. x and z represent the spatial position coordinates. x=1, 2, 3, …, Nx, z=1,2, 3, …, Nz. Nx and Nz represent the total number of horizontal and vertical grid points in the model, respectively. There is one source shot, which is located in the middle of the top of the model. There are Nz receivers in total. The receivers are evenly distributed on the top of the model to receive seismic records. The second step is to give a first-order velocity-stress viscoelastic wave equation; specifically, as shown in formula (1), where , represent the horizontal and vertical components of velocity respectively, , , represent the normal stress in the x-direction, the normal stress in the z-direction, and the shear stress component, respectively. , , The horizontal and vertical components of the normal stress memory variable and the shear stress component; represents density, and is the Lame coefficient, and is the strain relaxation time of P-wave and S-wave, represents stress; the formula (1) is: ; Slack variables and quality factors The relationship is as shown in formula (2), where and are the longitudinal wave quality factor and the transverse wave quality factor, respectively. , , represents the main frequency of the source wavelet; the formula (2) is: ; The third step is to give the relationship between the stress tensor, the pressure field and the deviatoric stress tensor; the relationship is shown in formula (3), where is the stress tensor , and They represent the pressure field, the deviatoric stress tensor and the unit tensor respectively; the formula (3) is ; The fourth step is to calculate the pressure component of the wave field from the average value of the negative normal stress component, as shown in formula (4). The formula (4) is: ; Step 5: Substitute the first-order velocity stress viscoelastic wave equation (1) in the second step into (4) to obtain the pressure relationship; The specific pressure relationship is as shown in formula (5): ; Step 6. Then, the partial differential equation of the pressure component can be obtained by taking the time derivative of the pressure relationship, as shown in formula (6). Formula (6) is: ; Step 7: Substitute equation (1) into equation (3) and combine with equation (6) to obtain the acoustic wave-viscoelastic wave coupling equation, as shown in equation (7); equation (7) is: ; Step 8. Based on the given source wavelet and model parameters, the derived acoustic-viscoelastic wave coupling equation is applied to load the source on the P component for forward modeling. The forward modeling of the acoustic-viscoelastic wave coupling equation requires repeating the above 8 steps. Based on the excited source, simultaneous reception is performed at each detection point to obtain the forward wave field of each component and the seismic record.

[0007] The beneficial effects of the present invention compared with the prior art are as follows: the method of the present invention introduces the relationship between the pressure component and the stress into the conventional first-order velocity stress-viscoelastic wave equation, and derives the first-order velocity stress-viscoelastic wave coupling equation. Model experiments show that the seismic wave field of the acoustic-viscoelastic wave coupling equation has an obvious amplitude attenuation effect compared with the acoustic-elastic wave coupling equation, and the amplitude spectrum analysis shows that the main frequency of the acoustic-viscoelastic wave coupling equation moves to a low frequency, showing the frequency dissipation characteristics of the viscoelastic medium, which is more in line with the actual situation of seismic wave propagation underground. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 It is a schematic diagram of the horizontal layered model; Figure 2 is the earthquake sub-wave map; Figure 3 is the wave field snapshot diagram of the acoustic-elastic wave coupling equation; where a is the wave field snapshot diagram of Vx, b is the wave field snapshot diagram of Vz, and c is the wave field snapshot diagram of the P component; Figure 4 is the wave field snapshot of the acoustic wave-viscoelastic wave coupling equation; where a is the wave field snapshot of Vx, b is the wave field snapshot of Vz, and c is the wave field snapshot of the P component; Figure 5 This is a comparison diagram of the P component wave field at 2.4 km in the horizontal direction; Figure 6 are P-component seismic records; a represents the P-component seismic record simulated by the acoustic-elastic wave coupling equation, and b represents the P-component seismic record simulated by the acoustic-viscoelastic wave coupling equation; Figure 7 This is the comparison result of P component seismic records at 2.4km in the horizontal direction; Figure 8 It is the amplitude spectrum of P component seismic record. DETAILED DESCRIPTION

[0009] The technical solution of the present invention will be further described below with reference to examples; however, the protection scope of the present invention is not limited to the specific forms of the embodiments.

[0010] The present invention is based on the conventional first-order velocity stress-viscoelastic wave equation and uses the relationship between pressure and normal stress to derive the acoustic-viscoelastic wave coupling equation. The model experimental results show that the seismic wave field of the acoustic-viscoelastic wave coupling equation has an obvious amplitude attenuation effect compared with the acoustic-elastic wave coupling equation, and the amplitude spectrum analysis shows that the main frequency of the acoustic-viscoelastic wave coupling equation moves to a low frequency, showing the frequency dissipation characteristics of the viscoelastic medium, which is more in line with the actual situation of seismic wave propagation underground.

[0011] Example 1 The present invention takes a double-layer model as an example to illustrate, which includes a longitudinal wave velocity model, a transverse wave velocity model, a density model, a longitudinal wave quality factor model, and a transverse wave quality factor model. The double-layer model has a lateral length of 4800m and a longitudinal depth of 3200m. The model is evenly divided into two layers in the longitudinal direction. In the upper layer, the longitudinal wave velocity is 2500m / s, the transverse wave velocity is 1450m / s, and the density is 1767kg / m 3 , longitudinal wave quality factor is 110, transverse wave quality factor is 95; in the lower layer: longitudinal wave velocity is 3000m / s, transverse wave velocity is 1734m / s, density is 1850kg / m 3 , the longitudinal wave quality factor is 130, and the shear wave quality factor is 115 (such as Figure 1 The grid step size of the model in the x and z directions is 8m.

[0012] Based on the model, the earthquake source is 2400m in the horizontal direction, and 600 detection points are set. The detection points are evenly distributed above the model with an interval of 8m. The shot point depth is 800m, and the detection points are evenly placed above the model.

[0013] The specific implementation mode of the present invention is described in detail below, and the specific steps are as follows: (1) Use a signal generator to obtain the Ricker wavelet with a source wavelet W(t) of 20 Hz (e.g. Figure 2 As shown in the figure, t represents time. The double-layer horizontal layered model with a horizontal length of 4800m and a vertical length of 3200m is meshed, and the mesh step size in the x and z directions of the model is 8m, resulting in a model with a mesh size of 600×400, where x and z represent the grid position coordinates (x=1, 2,3, …, 600, z=1, 2, 3, …, 400); (2) Given the first-order velocity-stress viscoelastic wave equation, as in equation (1), , represent the horizontal and vertical components of velocity respectively, , , represent the normal stress in the x-direction, the normal stress in the z-direction, and the shear stress component, respectively. , , Horizontal and vertical components of the normal stress memory variable and the shear stress component. represents density, and is the Lame coefficient, and is the strain relaxation time of P-wave and S-wave, represents stress. The formula (1) is: ; Slack variables and quality factors The relationship is as shown in formula (2), where and are the longitudinal wave quality factor and the transverse wave quality factor, respectively. , , represents the main frequency of the source wavelet. The formula (2) is: ; (3) The relationship between the given stress tensor, pressure field and deviatoric stress tensor is shown in equation (3), where is the stress tensor , and They represent the pressure field, the deviatoric stress tensor and the unit tensor respectively. The formula (3) is .

[0014] (4) The pressure component of the wave field can be calculated from the average value of the negative normal stress component, as shown in formula (4). The formula (4) is .

[0015] (5) Substituting the conventional first-order velocity stress viscoelastic wave equation (1) into equation (4), we can obtain the pressure relationship (5). The equation (5) is: ; (6) Then, by taking the time derivative of equation (5), the partial differential equation of the pressure component can be obtained as shown in equation (6). The equation (6) is: ; (7) Then, substituting equation (1) into equation (3) and combining it with equation (6), the acoustic wave-viscoelastic wave coupling equation can be obtained, as shown in equation (7). The equation (7) is: ; (8) Based on the given source wavelet and model parameters, the derived equation (7) is used for forward modeling.

[0016] The forward modeling method based on the acoustic-viscoelastic wave coupling equation needs to repeat the above 8 steps. In order to prove the beneficial effect of the method described in the present invention, it is compared with the acoustic-elastic wave coupling equation. The wave field snapshot of the acoustic-elastic wave coupling equation is shown in Figure 3 , the wave field snapshot of the acoustic-viscoelastic wave coupling equation is as follows Figure 4 . Figure 5 The comparison results of the P component wave field at the horizontal position of 2.4 km are shown in Figure 1, where the solid line represents the acoustic-elastic wave coupling equation and the dotted line represents the acoustic-viscoelastic wave coupling equation. Figure 3 , 4 , 5 It can be seen that the acoustic wave-viscoelastic wave coupling equation has an obvious amplitude attenuation effect. Figure 6 is the earthquake record of P component. Figure 7 The comparison results of the seismic records of the acoustic-elastic wave coupling equation and the acoustic-viscoelastic wave coupling equation at 2.4 km in the vertical direction are shown in Figure 2. The solid line represents the acoustic-elastic wave coupling equation, and the dotted line represents the acoustic-viscoelastic wave coupling equation. It can be seen that the seismic records simulated by the acoustic-viscoelastic wave coupling equation have phase shift and attenuation. Figure 8It is the amplitude spectrum of the vertical component of the acoustic-elastic wave coupling equation and the acoustic-viscoelastic wave coupling equation, where the solid line represents the acoustic-elastic wave coupling equation and the dotted line represents the amplitude spectrum of the acoustic-viscoelastic wave coupling equation. It can be seen that the main frequency of the amplitude spectrum of the acoustic-viscoelastic wave coupling equation moves toward low frequency. The model shows that this method takes into account the absorption and attenuation factors of the stratum, and the seismic wave shows obvious frequency dissipation characteristics during the propagation of the underground medium, which is more in line with the actual situation of seismic wave propagation underground.

Claims

1. A forward modeling method based on the acoustic wave-viscoelastic wave coupling equation, characterized in that: The first step is to give a source wavelet and establish a velocity model; Step 2: Given the first-order velocity-stress viscoelastic wave equation, the pressure component relationship is calculated from the known stress tensor, pressure field, deviatoric stress tensor and the average value of the negative normal stress component; The third step is to substitute the first-order velocity stress-viscoelastic wave equation into the pressure component relationship and take the derivative with respect to time to obtain the pressure partial differential equation; The fourth step is to introduce the first-order velocity stress-viscoelastic wave equation into the stress tensor, pressure field and deviatoric stress relationship and derive the acoustic wave-viscoelastic wave coupling equation in combination with the pressure partial differential equation; Step 5: Based on the acoustic-viscoelastic wave coupling equation in step 4, the seismic wavelet and velocity model are introduced, and forward modeling is performed using the tenth-order space to obtain the forward wave field of each component and the seismic record.

2. A forward modeling method based on the acoustic wave-viscoelastic wave coupling equation according to claim 1, characterized in that: The method specifically comprises the following steps: Step 1: Use Ricker wavelet as the source wavelet W(t), where t represents time. Then, the P-wave velocity, density, and P-wave quality factor model M(x, z) are given. x and z represent the spatial position coordinates. x=1, 2, 3, …, Nx, z=1, 2,3, …, Nz. Nx and Nz represent the total number of horizontal and vertical grid points in the model, respectively. There is one source shot, which is located in the middle of the top of the model. There are Nz receivers in total. The receivers are evenly distributed on the top of the model to receive seismic records. The second step is to give a first-order velocity-stress viscoelastic wave equation; as shown in formula (1), where , represent the horizontal and vertical components of velocity respectively, , , represent the normal stress in the x-direction, the normal stress in the z-direction, and the shear stress component, respectively. , , The horizontal and vertical components of the normal stress memory variable and the shear stress component; represents density, and is the Lame coefficient, and is the strain relaxation time of P-wave and S-wave, represents stress; the formula (1) is: ； Slack variables and quality factors The relationship is as shown in formula (2), where and are the longitudinal wave quality factor and the transverse wave quality factor, respectively. , , represents the main frequency of the source wavelet; the formula (2) is: ； Step 3: The relationship between the given stress tensor, pressure field and deviatoric stress tensor is shown in equation (3), where is the stress tensor , and They represent the pressure field, the deviatoric stress tensor and the unit tensor respectively; the formula (3) is ; The fourth step is to calculate the pressure component of the wave field from the average value of the negative normal stress component, as shown in formula (4). The formula (4) is: ; Step 5: Substituting the conventional first-order velocity stress viscoelastic wave equation (1) into equation (4), the pressure relationship equation (5) can be obtained; the equation (5) is: ； Step 6. Then, the partial differential equation of the pressure component can be obtained by taking the time derivative of equation (5) as shown in equation (6); the equation (6) is: ； Step 7: Substitute equation (1) into equation (3) and combine with equation (6) to obtain the acoustic wave-viscoelastic wave coupling equation, as shown in equation (7); equation (7) is: ； Step 8. Based on the given source wavelet and model parameters, the derived acoustic-viscoelastic wave coupling equation is applied to load the source on the P component for forward modeling. The forward modeling of the acoustic-viscoelastic wave coupling equation requires repeating the above 8 steps. Based on the excited source, simultaneous reception is performed at each detection point to obtain the forward wave field of each component and the seismic record.

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