CN111694051B - Gaussian beam-based viscoacoustic medium seismic wave forward modeling method - Google Patents
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Abstract
The invention provides a Gaussian beam-based viscoacoustic medium seismic wave forward modeling method, and relates to the technical field of seismic wave numerical simulation. Firstly, reading a forward velocity model, a Q value model and parameter files of the two models, and determining a seismic source function; then tracking central rays from the shot point along different directions, and calculating a Gaussian beam corresponding to each ray; dividing a receiving channel by taking a window as a unit, tracking central rays along different directions from the center of the window, and calculating a Gaussian beam corresponding to each ray; selecting ray bundle pairs from shot points and window central points, and mapping the reflectivity of the forward velocity model into local plane waves; carrying out inverse oblique superposition on the Fourier transform of the local plane wave to obtain the seismic record of a receiving channel in the window; and finally, stacking the seismic records corresponding to all the receiving channels to obtain the final single-shot seismic record. The method improves the calculation efficiency of forward modeling of the primary scattered wave on the premise of ensuring the calculation accuracy.
Description
Technical Field
The invention relates to the technical field of seismic wave numerical simulation, in particular to a viscoelastic acoustic medium seismic wave forward modeling method based on Gaussian beams.
Background
Seismic wavefield numerical simulation is an important method throughout seismic data acquisition, processing, and interpretation. The fast and high-precision seismic wave forward modeling method has important significance in research. The method for simulating the seismic waves based on the acoustic medium ignores the influence of viscosity of the medium on the propagation of the seismic waves, but the dynamic characteristics of the seismic waves, including energy attenuation, frequency band narrowing, phase distortion and the like, can be obviously influenced by the property.
The Yue wave and other 'acoustic medium primary scattering wave field Gaussian beam Bom forward' published in 2019 by the scientific newspaper of geophysical, and a method for forward evolution of acoustic medium Gaussian beam Bon is introduced. The method is based on a linearized seismic inversion theory, uses a Green function based on Gaussian beam expression, converts local plane waves into a scattered wave field at a receiving point by utilizing inverse oblique superposition, and improves the calculation efficiency of an alignment algorithm in a way of establishing a wavelet base. The complex layered model and the Marmousi model (an open seismic acoustic wave model) are subjected to simulation calculation by a one-time scattering wave field Gaussian beam forward modeling method of the acoustic medium such as Yueyuebo, and the accuracy and the effectiveness of the method are well verified by a forward modeling result.
The geophysics article 2017, which discloses Wuyu and the like, "fractional Laplace operator decoupling-based viscoacoustic medium earthquake forward modeling and reverse time migration", introduces a seismic wave forward modeling method solved on the basis of a fractional Laplace operator viscoacoustic wave equation with decoupling of medium dispersion effect and attenuation effect. The method adopts a staggered grid finite difference to approximate a time derivative, calculates a spatial derivative by an improved pseudo-spectrum method, and removes boundary reflection by a PML absorption boundary. Tests aiming at the concave model show that the viscoelastic medium seismic wave simulation method has a good forward effect.
"finite difference forward modeling of variable mechanism number of viscous acoustic wave equation", zeitzeri and the like, is disclosed in 03 of 2019, and a finite difference seismic wave field forward modeling method of variable mechanism number of viscous acoustic wave equation, which is provided under a generalized standard linear body model, is introduced, namely different relaxation mechanism numbers and different simulation precisions are used in different areas of the model to achieve the purpose of unifying calculation efficiency and simulation precision. And seismic wave simulation calculation is carried out on the layered model and the SEAM model by a viscous acoustic wave equation variable mechanism finite difference forward modeling method, and an experimental result has a good effect.
As can be seen from the above examples, the conventional gaussian beam-based forward seismic wave forward modeling method is for acoustic media rather than for viscoelastic media, and the finite difference forward modeling method for viscoelastic media can obtain a good seismic wave simulation effect, but has low computational efficiency.
Disclosure of Invention
The technical problem to be solved by the present invention is to provide a method for forward modeling of a seismic wave of a viscoelastic medium based on a gaussian beam, aiming at the defects of the prior art, so as to forward model the seismic wave of the viscoelastic medium.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a viscoelastic acoustic medium seismic wave forward modeling method based on Gaussian beams comprises the following steps:
step 1: reading in a forward velocity model, a Q value model and parameter files of the two models, and determining a seismic source function; the parameter files of the two models comprise transverse and longitudinal grid numbers, grid intervals, shot positions, seismic source main frequencies, reference frequencies, maximum frequencies, initial beam widths, positions of receiving channels, the number of the receiving channels, the intervals of the receiving channels, sampling intervals and sampling numbers of each channel of seismic data of the forward velocity model and the Q value model;
step 2: tracking central rays from the shot point along different directions, and calculating a Gaussian beam corresponding to each ray;
for a viscoelastic medium, after central rays are traced from a shot point along different directions, a gaussian beam corresponding to each ray is shown as follows:
wherein u isGB(x，xs，pSω) represents a Gaussian beam corresponding to each ray after the shot points trace the central ray in different directions, x represents grid point coordinates in the forward velocity model, and x represents a grid point coordinate in the forward velocity modelsAs coordinates of the location of the shot point, pSAnd AGB(x，xs) Respectively, a Gaussian beam from shot point xsSlowness and amplitude propagated to grid point x, i is an imaginary unit, τR(x，xs)、τI(x，xs)、τO(x，xs) Respectively representing the Gaussian beam from shot point xsIntegral of real, imaginary and Q values propagated to grid point x, ω being angular frequency, ωrFor reference angular frequency, Q is used for representing the strength of the positive velocity model anisotropy, and t is the travel time of a central ray;
and step 3: dividing a receiving channel for receiving seismic waves by taking a window as a unit, tracking central rays from the center of the window along different directions, and calculating a Gaussian beam corresponding to each ray;
after tracing the central rays from the window center along different directions, the gaussian beam corresponding to each ray is as follows:
wherein u isGB(x，xL，pLω) is the Gaussian beam corresponding to each ray after tracing the central ray from the window center in different directions, xLAt the center of the window, τR(x，xL)、τI(x，xL)、τQ(x，xL) Respectively representing the Gaussian beam from the center x of the windowLIntegral of real, imaginary and Q-values propagated to grid point x；pLAnd AGB(x，xL) Respectively gaussian beam from window center xLSlowness and amplitude propagated to grid point x;
and 4, step 4: selecting ray bundle pairs from shot points and window central points, and mapping the reflectivity of the forward speed model into local plane waves by using a wavelet bank method considering a Q value;
the expression for mapping the reflectivity of the forward speed model into local plane waves by using the wavelet bank method considering the Q value is as follows:
wherein, U (L, x)s，psx，PLxT) local plane waves for reflectivity mapping, L denotes different window centers, psx、pLxHorizontal components of slowness of the Gaussian beam propagating from the shot and window center points to grid point x, c0(x)、c1(x) Background velocity and disturbance velocity, A, respectively, of the forward velocity modelRIs the real part of the product of the beam pair amplitude, AIThe imaginary part of the product of the beam pair amplitude,
for the set of scattering points in the forward velocity model, δ () is the Rake wavelet, which is the convolution sign, S (ω) represents the seismic wavelet, SH(t，τ′I，τ′Q) Is s (t, τ'I，τ′Q) Of Hilbert transform, τ'R、τ′I、τ′QRespectively the real travel time, the virtual travel time and the Q value integral of the Gaussian beam from the shot point to the central point of the window, w0Is the primary beamwidth of the radiation beam;
τ′Icorresponding maximum value
τ′QCorresponding maximum value
Is the maximum value recorded as a discrete point on the central ray for τ'IAnd τ'QA time sample sequence is established as shown in the following formula:
wherein N and K are respectively corresponding to tau'IAnd τ'QThe total number of sample points of (a),
are respectively for τ'IAnd τ'QThe sampling interval of (a);
then s (t, τ'I，τ′Q) At each time sample sequence point, the following equation is shown:
by sampling values at sequential points in time
Bilinear interpolation is performed to obtain s (t, τ'I，τ′Q) As shown in the following equation:
wherein the content of the first and second substances,
all are weight coefficients, and the specific expression is as follows:
and 5: and carrying out inverse oblique superposition on the Fourier transform of the local plane wave to obtain the seismic record of the receiving channel in the window, wherein the formula is as follows:
where u is the seismic record of the receiver channel in the window, xrFor the receive channel in the window, psz、pLzThe vertical component of slowness of the Gaussian beam propagating from the shot and window center points to grid point x, respectively,. DELTA.L is the distance between the centers of adjacent windows, U (L, x)s，psx，pLxω) is U (L, x)s，psx，pLxT) Fourier transform;
step 6: and stacking the seismic records corresponding to all the receiving channels to obtain the final single-shot seismic record.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: according to the Gaussian beam-based positive modeling method for the seismic waves of the viscoelastic medium, the Green function represented by the Gaussian beam is used, the wavelet bank method considering the Q value is adopted to synthesize the local plane waves, the positive modeling of the seismic waves of the viscoelastic medium is further realized, and the calculation efficiency of the positive modeling of the scattered waves at one time is improved on the premise of ensuring the calculation accuracy.
Drawings
Fig. 1 is a flowchart of a viscoelastic acoustic medium seismic wave forward modeling method based on a gaussian beam according to an embodiment of the present invention;
FIG. 2 is a velocity profile of a complex laminar viscoelastic model according to an embodiment of the present invention;
FIG. 3 is a graph illustrating Q-values of a complex layered model according to an embodiment of the present invention;
FIG. 4 is a diagram of a simulation result of a finite difference method of a complex laminar viscoelastic model according to an embodiment of the present invention;
fig. 5 is a diagram of a simulation result of a primary scattered field gaussian beam born forward modeling method for a complex layered acoustic model according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
In this embodiment, a complex layered viscoelastic model is used, and the viscoelastic medium seismic wave forward modeling method based on the gaussian beam is used to perform forward modeling simulation on the seismic wave in the viscoelastic medium.
In this embodiment, a viscoelastic acoustic medium seismic wave forward modeling method based on gaussian beams, as shown in fig. 1, includes the following steps:
step 1: reading in a forward velocity model, a Q value model and parameter files of the two models, and determining a seismic source function; the parameter files of the two models comprise transverse and longitudinal grid numbers, grid intervals, main frequencies of a seismic source at a shot position and reference frequencies omega of a forward velocity model and a Q value modelrMaximum frequency, initial beam width w of the beam0Receiving channel positions, receiving channel quantity, receiving channel intervals, sampling intervals and sampling numbers of each channel of seismic data;
in this embodiment, the velocity distribution and the Q value distribution of the complex layered viscoelastic model are shown in fig. 2 and 3, where x represents the lateral distance, z represents the depth, 1000 grid points are provided in the lateral direction of the model, and the grid distance is 10 meters; 550 grid points are arranged in the longitudinal direction, and the grid distance is 5 meters; the shot point is positioned in the middle of the top layer of the model; the number of the receiving tracks is 241, the track spacing is 20 meters, and the receiving tracks are uniformly arranged on two sides of a shot point respectively.
Step 2: tracking central rays from the shot point along different directions, and calculating a Gaussian beam corresponding to each ray;
for a viscoelastic medium, after central rays are traced from a shot point along different directions, a gaussian beam corresponding to each ray is shown as follows:
wherein u isGB(x，xs，pSω) represents a Gaussian beam corresponding to each ray after the shot points trace the central ray in different directions, x represents grid point coordinates in the forward velocity model, and x represents a grid point coordinate in the forward velocity modelsAs coordinates of the location of the shot point, pSAnd AGB(x，xs) Respectively, a Gaussian beam from shot point xsSlowness and amplitude propagated to grid point x, i is an imaginary unit, τR(x，xs)、τI(x，xs)、τQ(x，xs) Respectively representing the Gaussian beam from shot point xsIntegral of real, imaginary and Q values propagated to grid point x, ω being angular frequency, ωrFor reference angular frequency, Q is used for representing the strength of the positive velocity model anisotropy, and t is the travel time of a central ray;
and step 3: dividing a receiving channel for receiving seismic waves by taking a window as a unit, tracking central rays from the center of the window along different directions, and calculating a Gaussian beam corresponding to each ray;
after tracing the central rays from the window center along different directions, the gaussian beam corresponding to each ray is as follows:
wherein u isGB(x，xL，pLω) is the Gaussian beam corresponding to each ray after tracing the central ray from the window center in different directions, xLIs the window center position, pLAnd AGB(x，xL) Respectively gaussian beam from window center xLSlowness and amplitude, τ, propagating to grid point xR(x，xL)、τI(x，xL)、τQ(x，xL) Respectively representing the Gaussian beam from the center x of the windowLThe real travel time, the virtual travel time and the Q value integral propagated to the grid point x;
and 4, step 4: selecting ray bundle pairs from shot points and window central points, and mapping the reflectivity of the forward speed model into local plane waves by using a wavelet bank method considering a Q value;
the expression for mapping the reflectivity of the forward speed model into local plane waves by using the wavelet bank method considering the Q value is as follows:
wherein, U (L, x)s，psx，PLxT) local plane waves for reflectivity mapping, L denotes different window centers, psx、pLxHorizontal components of slowness of the Gaussian beam propagating from the shot and window center points to grid point x, c0(x)、c1(x) Background velocity and disturbance velocity, A, respectively, of the forward velocity modelRIs the real part of the product of the beam pair amplitude, AIThe imaginary part of the product of the beam pair amplitude,
for the set of scattering points in the forward velocity model, δ () is the Rake wavelet, which is the convolution sign, S (ω) represents the seismic wavelet, SH(t，τ′I，τ′Q) Is s (t, τ'I，τ′Q) Of Hilbert transform, τ'R、τ′I、τ′QRespectively the real travel time, the virtual travel time and the Q value integral of the Gaussian beam from the shot point to the central point of the window, w0Is the primary beamwidth of the radiation beam;
τ′Icorresponding maximum value
τ′QCorresponding maximum value
Is the maximum value recorded as a discrete point on the central ray for τ'IAnd τ'QA time sample sequence is established as shown in the following formula:
wherein N and K are respectively corresponding to tau'IAnd τ'QThe total number of sample points of (a),
are respectively for τ'IAnd τ'QThe sampling interval of (a);
then s (t, τ'I，τ′Q) At each time sample sequenceThe points are shown by the following formula:
by sampling values at sequential points in time
Bilinear interpolation is performed to obtain s (t, τ'I，τ′Q) As shown in the following equation:
wherein the content of the first and second substances,
all are weight coefficients, and the specific expression is as follows:
and 5: and carrying out inverse oblique superposition on the Fourier transform of the local plane wave to obtain the seismic record of the receiving channel in the window, wherein the formula is as follows:
wherein u (x)r，xsω) seismic record of the receiver trace in the window, xrFor the receive channel in the window, psz、pLzFrom the shot point and window centre point to the gaussian beam respectivelyThe vertical component of slowness of grid point x, Δ L distance to the center of the neighboring window, U (L, x)s，psx，pLxω) is U (L, x)s，psx，PLxT) Fourier transform;
step 6: and stacking the seismic records corresponding to all the receiving channels to obtain the final single-shot seismic record.
In this embodiment, a seismic wave simulation result based on a complex layered viscoelastic model and using a finite difference method is shown in fig. 4, while a seismic wave simulation result using a viscoelastic acoustic medium seismic wave forward modeling method based on a gaussian beam of the present invention is shown in fig. 5, where offset is an offset distance and is used to represent a distance between a receiving channel and a shot point, and T is a receiving time and represents a time taken by the receiving channel to receive a seismic wave. From the two forward results, the results obtained by the primary scattering seismic wave field obtained by the method and the finite difference method are almost the same, but under the same calculation condition, the calculation time used by the finite difference method is 321 seconds, while the method only uses 5.3 seconds, so that the calculation efficiency is improved by nearly 60 times.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.
Claims (2)
1. A viscoelastic medium seismic wave forward modeling method based on Gaussian beams is characterized by comprising the following steps: the method comprises the following steps:
step 1: reading in a forward velocity model, a Q value model and parameter files of the two models, and determining a seismic source function;
step 2: tracking central rays from the shot point along different directions, and calculating a Gaussian beam corresponding to each ray;
and step 3: dividing a receiving channel for receiving seismic waves by taking a window as a unit, tracking central rays from the center of the window along different directions, and calculating a Gaussian beam corresponding to each ray;
and 4, step 4: selecting ray bundle pairs from shot points and window central points, and mapping the reflectivity of the forward speed model into local plane waves by using a wavelet bank method considering a Q value;
and 5: carrying out inverse oblique superposition on the Fourier transform of the local plane wave to obtain the seismic record of a receiving channel in the window;
step 6: stacking the seismic records corresponding to all receiving channels to obtain a final single-shot seismic record;
for a viscoelastic medium, after central rays are traced from a shot point along different directions, a gaussian beam corresponding to each ray is shown as follows:
wherein u isGB(x,xs,pSω) represents a Gaussian beam corresponding to each ray after the shot points trace the central ray in different directions, x represents grid point coordinates in the forward velocity model, and x represents a grid point coordinate in the forward velocity modelsAs coordinates of the location of the shot point, pSAnd AGB(x,xs) Respectively, a Gaussian beam from shot point xsSlowness and amplitude propagated to grid point x, i is an imaginary unit, τR(x,xs)、τI(x,xs)、τQ(x,xs) Respectively representing the Gaussian beam from shot point xsIntegral of real, imaginary and Q values propagated to grid point x, ω being angular frequency, ωrFor reference to angular frequency, for QThe strength of the positive speed model anisotropy is represented, and t is the travel time of the central ray;
step 3, after tracking central rays from the center of the window along different directions, the gaussian beam corresponding to each ray is shown as the following formula:
wherein u isGB(x,xL,pLω) is the Gaussian beam corresponding to each ray after tracing the central ray from the window center in different directions, xLAt the center of the window, τR(x,xL)、τI(x,xL)、τQ(x,xL) Respectively representing the Gaussian beam from the center x of the windowLThe real travel time, the virtual travel time and the Q value integral propagated to the grid point x; p is a radical ofLAnd AGB(x,xL) Respectively gaussian beam from window center xLSlowness and amplitude propagated to grid point x;
step 4, the expression for mapping the reflectivity of the forward speed model into local plane waves by using the wavelet bank method considering the Q value is as follows:
wherein, U (L, x)s,psx,pLxT) local plane waves for reflectivity mapping, L denotes different window centers, psx、pLxHorizontal components of slowness of the Gaussian beam propagating from the shot and window center points to grid point x, c0(x)、c1(x) Background velocity and disturbance velocity, A, respectively, of the forward velocity modelRIs the real part of the product of the beam pair amplitude, AIThe imaginary part of the product of the beam pair amplitude,
for the set of scattering points in the forward velocity model, δ () is the Rake wavelet, which is the convolution sign, S (ω) represents the seismic wavelet, SH(t,τ′I,τ′Q) Is s (t, τ'I,τ′Q) Of Hilbert transform, τ'R、τ′I、τ′QRespectively the real travel time, the virtual travel time and the Q value integral of the Gaussian beam from the shot point to the central point of the window, w0Is the primary beamwidth of the radiation beam;
τ′Icorresponding maximum value
τ′QCorresponding maximum value
Is the maximum value recorded as a discrete point on the central ray for τ'IAnd τ'QA time sample sequence is established as shown in the following formula:
wherein N and K are respectively corresponding to tau'IAnd τ'QThe total number of sample points of (a),
are respectively for τ'IAnd τ'QThe sampling interval of (a);
then s (t, τ'I,τ′Q) At each time sample sequence point, the following equation is shown:
by sampling values at sequential points in time
Bilinear interpolation is performed to obtain s (t, τ'I,τ′Q) As shown in the following equation:
wherein the content of the first and second substances,
all are weight coefficients, and the specific expression is as follows:
and 5, performing inverse oblique stacking on the Fourier transform of the local plane wave to obtain the seismic record of the receiving channel in the window, wherein the formula is as follows:
where u is the seismic record of the receiver channel in the window, xrFor the receive channel in the window, psz、pLzThe vertical component of slowness of the Gaussian beam propagating from the shot and window center points to grid point x, respectively,. DELTA.L is the distance between the centers of adjacent windows, U (L, x)s,psx,pLxω) is U (L, x)s,psx,pLxT) Fourier transform.
2. The method for forward modeling of viscoelastic medium seismic waves based on gaussian beams as claimed in claim 1, wherein: the parameter files of the two models in the step 1 comprise the transverse and longitudinal grid number, the grid spacing, the shot point position, the seismic source main frequency, the reference frequency, the maximum frequency, the initial beam width, the position of a receiving channel, the number of the receiving channel, the receiving channel spacing, the sampling spacing of each channel of seismic data and the sampling number of a forward velocity model and a Q value model.
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