CN101082676A - Earthquake post-stack forward method of undulating surface - Google Patents

Earthquake post-stack forward method of undulating surface Download PDF

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CN101082676A
CN101082676A CNA200710049482XA CN200710049482A CN101082676A CN 101082676 A CN101082676 A CN 101082676A CN A200710049482X A CNA200710049482X A CN A200710049482XA CN 200710049482 A CN200710049482 A CN 200710049482A CN 101082676 A CN101082676 A CN 101082676A
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wave field
relief surface
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熊晓军
贺振华
黄德济
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Chengdu Univeristy of Technology
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Abstract

The invention discloses a post-stack forward modeling method of fluctuating ground, which comprises the following steps: proceeding rectangular packing for geological mould of the fluctuating ground; filling the fluctuating ground at random speed value or density value; adopting Snail elementary to calculate the reflective factor model; eliminating the reflective influence of fluctuating ground to transform to frerquency area as original wave field; utilizing Fuliye limit differential continuation operator of single-pass fluctuating equation to continue the wave field along depth axle from upwards to downwards; keeping the wave field between input datum face (fluctuating ground) and output datum surface at zero; transforming the wave field of frequency area after continuing to the time domain to image; processing the imaging result into earthquake section image through normal display software; possessing good earthquake wave field analoging effect for geological model of the fluctuating ground.

Description

The earthquake poststack forward modeling method of relief surface
Technical field
The present invention relates to the positive artistic skills art of the earthquake poststack category in the reflection wave seismic wave field numerical simulation process, is a kind of poststack forward modeling method of relief surface seismic wave field numerical simulation.
Background technology
The numerical simulation of seismic wave field is exactly under the situation of the structural model of the known underground medium of supposition and respective physical parameter, the propagation law of simulated earthquake ripple in underground various media, and calculate on ground or underground each observation station a kind of earthquake simulation method of the numerical value seismologic record that should observe.It on the one hand can be for earthquake data acquisition, processing, explanation provide theoretical foundation, the science of appraisal procedure, feasibility and advance; Can be used for checking the credibility of various interpretation results on the other hand, and the correctness of various inversion algorithms and reliability.From the angle of seismic wave propagation, the positive artistic skills art of the earthquake poststack of routine can be divided into ray-tracing scheme and wave equation method.Ray-tracing scheme can be handled relief surface neatly, but it is based on the kinematics of seismic event, the seismic event wave theory is reduced to ray theory, the main kinematics character of considering seismic wave propagation, lack the dynamic information of seismic event, result of calculation is similar to a certain extent, and using has the certain limitation condition, low to the complex geological tectonic imaging precision, the blind area appears sometimes.The wave equation method is directly found the solution wave equation by numerical method, the dynamic characteristic that has comprised seismic wave propagation, wave field abundant information, analog result are comparatively accurate, but the situation that it can only the processing horizontal face of land, the reference field of wave field extrapolation is necessary for a horizontal interface.
Summary of the invention
The present invention will provide a kind of earthquake poststack forward modeling method that is applicable to relief surface based on one-way wave equation, it not only can adapt to the surface conditions of fluctuating, and adopt one-way wave equation to calculate, have the imaging precision of very fast computing velocity and very high complex structure.
The positive artistic skills art of earthquake poststack of the relief surface based on one-way wave equation of the present invention, concrete steps comprise:
(1) adopt rectangle frame that the target geologic model is carried out overall package, the end face of rectangle frame is the reference field of output, and the relief surface top adopts arbitrary speed value or density value to carry out filling, and adopts regular grid that rate pattern and density model are carried out gridding.
(2) adopt the Si Naier theorem to calculate reflection coefficient, and utilize Ricker wavelet to carry out convolution and handle, obtain reflectivity model.
(3) eliminate the reflections affect of relief surface, and transform to frequency field as initial continuation wave field.
(4) utilize the Fourier finite difference continuation operator of one-way wave equation to carry out wave field extrapolation from the bottom up, and the wave field between maintenance input reference face (relief surface) and the output reference face is zero along degree of depth axle.
(5) wave field transformation with the frequency field after the continuation carries out imaging to time domain.
(6) software for display by routine is treated to seismic section image with imaging results.
The earthquake poststack forward modeling method of the relief surface based on one-way wave equation of the present invention, to keep a numerical value between input reference face and output reference face be that zero wave field layer solves the relief surface problem of wave equation earthquake poststack in just drilling, and drawn the advantage that ray-tracing scheme is handled relief surface flexibly.
The earthquake poststack forward modeling method of the relief surface based on one-way wave equation of the present invention, utilizing Fourier finite difference continuation operator to carry out wave field extrapolation in frequency field calculates, ability with stronger processing lateral velocity variation, have very high imaging precision for complex structure, improved ray-tracing scheme for the low shortcoming of complex structure imaging precision.
Specific implementation principle of the present invention is as follows:
The end face of selected rectangle frame is the reference field of wave field extrapolation, and it is a horizontal interface, and is positioned on the peak of relief surface; The right margin of rectangle frame, left margin and bottom boundaries overlap fully with the geologic model of input.Geologic model after the encapsulation is carried out the mesh generation of rule, so the surface configuration that rises and falls becomes the part of regular grid after by discretize, the grid on the relief surface adopts arbitrarily that velocity amplitude and density value carry out filling.Utilize the Si Naier theorem to calculate reflection coefficient,
R ( x , y , z i , t ) = Den ( x , y , z i + 1 , t ) × Vel ( x , y , z i + 1 , t ) - Den ( x , y , z i , t ) × Vel ( x , y , z i , t ) Den ( x , y , z i + 1 , t ) × Vel ( x , y , z i + 1 , t ) + Den ( x , y , z i , t ) × Vel ( x , y , z i , t )
And adopt Ricker wavelet (dominant frequency is selected according to the stratum characteristic in target work area, generally between 10Hz～90Hz) to carry out convolution and handle.
Eliminate the reflections affect of relief surface, and adopt Fourier transform with it transform to frequency field R (x, y, z, ω), as the wave field of initial continuation.Given frequencies omega is extracted initial wave field W (x, y, the z at this frequency place, ω), adopt Fourier finite difference continuation operator to carry out wave field extrapolation from the bottom up with up-going wave equation along degree of depth axle, the wave field after the continuation is W ' (x, y, 0, ω), this process can be expressed as
W′(x，y，0，ω)＝FFD z[W(x，y，z，ω)]
X wherein, y is respectively the coordinate of two horizontal directions in the rectangular coordinate system in space, and z is the coordinate of depth direction, and ω is a circular frequency, and FFDz is a Fourier finite difference continuation operator, (z t) is the density value of gridding to Den for x, y, (z t) is the velocity amplitude of gridding to Vel for x, y.The input wave field of next depth z i is a last depth z in the continuation process I+1The continuation result, one zero wave field layer is set between output reference face and input reference face simultaneously participates in normal wave field and propagate and the continuation process.
All frequencies are carried out cycle calculations, obtain on the output reference face frequency field wave field U (x, y, 0, ω).To U (x, y, 0, ω) carry out inverse-Fourier transform and transform to the time domain imaging, (t), the software for display by routine is treated to the stratigraphic section image with imaging results to simulation wave field I that must be to the end then for x, y.
Above-mentioned continuation operator obtains according to the one-way wave equation close approximation, adopts the stable Fourier finite difference operator of frequency field to realize (Ristow, 1994).This continuation operator can be approximately,
ω 2 v 2 + ∂ 2 ∂ x 2 = A 1 + A 2 + A 3
In the formula,
A 1 = ω 2 c 2 + ∂ 2 ∂ x 2 ; A 2 = ( ω v - ω c ) ; A 3 = ω v [ 1 - c v ] a v 2 ω 2 ∂ 2 ∂ x 2 1 + b v 2 ω 2 ∂ 2 ∂ x 2
Wherein v is the actual speed field, and c is the reference velocity field, and ω is an angular frequency, parameter a, and the value of b has influence on the inclination maximum of wave field imaging:
Figure A20071004948200062
The present invention adopts the seismic wave field poststack method for numerical simulation that is adapted to relief surface based on one-way wave equation, has following characteristics, mainly shows as:
(1) can handle the relief surface condition of earthquake poststack in just drilling neatly.
(2) the Fourier finite difference continuation operator with relief surface, one-way wave equation and frequency field organically combines.
(3) has accurate wave field imaging effect for the complex structure under the relief surface condition.
Description of drawings
Fig. 1 is the two-dimentional relief surface model of an acline, and the maximum fluctuating discrepancy in elevation on the face of land is 380 meters.
Fig. 2 carries out result behind the earthquake poststack forward simulation with present technique to the rate pattern among Fig. 1, and the reflection line-ups of acline is no longer straight as can be seen, but opposite with surface configuration; In addition, simulation only comprises primary reflection, signal to noise ratio (S/N ratio) height.
Fig. 3 is the two-dimentional relief surface model of a complex geological structure, the low-velocity anomal body that it is 2000 meter per seconds that the near surface place comprises two speed.
Fig. 4 carries out result behind the earthquake poststack forward simulation with present technique to the rate pattern among Fig. 3, and basically identical reflection interval of two of near surface low-velocity anomal bodies is not subjected to the influence of rugged topography as can be seen; In addition, because the influence of rugged topography and low-velocity anomal body, serious distortion has taken place in the reflection line-ups that is positioned at the acline at model middle part.
Embodiment
Earthquake poststack forward modeling method based on the relief surface of one-way wave equation is specially following steps:
(1) adopt rectangle frame that the target geologic model is carried out overall package, the end face of rectangle frame is the reference field of output, and the relief surface top adopts arbitrary speed value or density value to carry out filling, and adopts regular grid that rate pattern and density model are carried out gridding.If have only rate pattern, then adopt the experimental formula bulk density model of density and speed.
(2) adopt the Si Naier theorem to calculate reflection coefficient, and utilize Ricker wavelet to carry out convolution and handle, obtain reflectivity model.The dominant frequency of Ricker wavelet is selected (generally between 10Hz～90Hz) according to the stratum characteristic in work area.
(3) eliminate the reflections affect of relief surface, and transform to frequency field as initial continuation wave field.
(4) utilize the Fourier finite difference continuation operator of one-way wave equation to carry out wave field extrapolation from the bottom up, and the wave field between maintenance input reference face (relief surface) and the output reference face is zero along degree of depth axle.
Specifically: the wave field extrapolation of carrying out in the frequency circulation is calculated, and, with reference to primary wave with stop time of ripple, determine the frequency range f1 and the f2 of wave field extrapolation according to the stratum characteristic in work area, generally between 1Hz～5Hz, f2 is generally between 50Hz～100Hz for f1; In the single frequency circulation, carry out wave field extrapolation from the bottom up along degree of depth axle and calculate, determine Fourier finite difference continuation operator ω 2 v 2 + ∂ 2 ∂ x 2 = A 1 + A 2 + A 3 Wherein:
A 1 = ω 2 c 2 + ∂ 2 ∂ x 2 ; A 2 = ( ω v - ω c ) ; A 3 = ω v [ 1 - c v ] a v 2 ω 2 ∂ 2 ∂ x 2 1 + b v 2 ω 2 ∂ 2 ∂ x 2
Wherein v is the actual speed field, and c is the reference velocity field, and ω is an angular frequency, and selects parameter a according to the inclined degree on stratum, the value of b, and parameter a, the corresponding relation of the value of b and the inclination maximum of migration imaging is:
Figure A20071004948200075
Figure A20071004948200076
Figure A20071004948200077
Next depth z in the continuation process iThe input wave field be a last depth z I+1The continuation result, one zero wave field layer is set between output reference face and input reference face simultaneously participates in normal wave field and propagate and the continuation process.Wave field value between intact f1 of cycle calculations and the f2 is to the processing that zeroizes of other wave field value.
(5) wave field transformation with the frequency field after the continuation carries out imaging to time domain.
(6) software for display by routine is treated to seismic section image with imaging results.
Fig. 1 and Fig. 2 are the test examples of the two-dimentional relief surface model of an acline.
(1) rate pattern to the rectangle encapsulation carries out gridding, and the velocity setting of relief surface top is 500 meter per seconds (selected arbitrarily values), and density model is a constant 1; Determine that according to track pitch the spacing of grid directions X is 20 meters, determine that according to the degree of depth spacing of grid Z direction is 5 meters.
(2) adopt the Si Naier theorem to calculate reflection coefficient, and utilize dominant frequency to handle, obtain reflectivity model for the Ricker wavelet of 50Hz carries out convolution.
(3) eliminate the reflections affect of relief surface, and transform to frequency field as initial continuation wave field.
(4) utilize the Fourier finite difference continuation operator of one-way wave equation to carry out wave field extrapolation from the bottom up, and the wave field between maintenance input reference face (relief surface) and the output reference face is zero along degree of depth axle.Specifically,, determine the frequency range f1 and the f2 of cycle calculations according to the stratum characteristic in work area with reference to primary wave with stop time of ripple, general it be set to the effective band of geological data, f1=1 here, f2=100.Because the stratum is an acline, parameter a, b, the value inclination angle is the situation of 45 degree, is a=0.5, b=0.25.The initial wave field of each frequency between f1 and the f2 is carried out wave field extrapolation from the bottom up along degree of depth axle calculate, its continuation operator is the Fourier finite difference operator of the stable frequency field narrated previously.Next depth z in the continuation process iThe input wave field be a last depth z I+1The continuation result, one zero wave field layer is set between output reference face and input reference face simultaneously participates in normal wave field and propagate and the continuation process.Wave field value between intact f1 of cycle calculations and the f2 is to the processing that zeroizes of other wave field value.
(5) wave field transformation with the frequency field after the continuation carries out imaging to time domain.
(6) software for display by routine is treated to seismic section image with imaging results.Fig. 2 is the seismic section of earthquake poststack simulation.
Fig. 3 and Fig. 4 are the test examples of the two-dimentional relief surface model of an acline.
(1) rate pattern to the rectangle encapsulation carries out gridding, and the velocity setting of relief surface top is 300 meter per seconds (selected arbitrarily values), and density model is a constant 1; Determine that according to track pitch the spacing of grid directions X is 20 meters, determine that according to the degree of depth spacing of grid Z direction is 5 meters.
(2) adopt the Si Naier theorem to calculate reflection coefficient, and utilize dominant frequency to handle, obtain reflectivity model for the Ricker wavelet of 50Hz carries out convolution.
(3) eliminate the reflections affect of relief surface, and transform to frequency field as initial continuation wave field.
(4) utilize the Fourier finite difference continuation operator of one-way wave equation to carry out wave field extrapolation from the bottom up, and the wave field between maintenance input reference face (relief surface) and the output reference face is zero along degree of depth axle.Specifically,, determine the frequency range f1 and the f2 of cycle calculations according to the stratum characteristic in work area with reference to primary wave with stop time of ripple, general it be set to the effective band of geological data, f1=1 here, f2=100.Because the stratum is an acline, parameter a, b, the value inclination angle is the situation of 45 degree, is a=0.5, b=0.25.The initial wave field of each frequency between f1 and the f2 is carried out wave field extrapolation from the bottom up along degree of depth axle calculate, its continuation operator is the Fourier finite difference operator of the stable frequency field narrated previously.The input wave field of next depth z i is a last depth z in the continuation process I+1The continuation result, one zero wave field layer is set between output reference face and input reference face simultaneously participates in normal wave field and propagate and the continuation process.Wave field value between intact f1 of cycle calculations and the f2 is to the processing that zeroizes of other wave field value.
(5) wave field transformation with the frequency field after the continuation carries out imaging to time domain.
(6) software for display by routine is treated to seismic section image with imaging results.Fig. 4 is the seismic section of earthquake poststack simulation.

Claims (4)

1, the earthquake poststack forward modeling method of relief surface is characterized in that adopting following steps:
(1) adopt rectangle frame that the target geologic model is carried out overall package, the end face of rectangle frame is the reference field of output, and the relief surface top adopts arbitrary speed value or density value to carry out filling, and adopts regular grid that rate pattern and density model are carried out gridding.
(2) adopt the Si Naier theorem to calculate reflection coefficient, and utilize Ricker wavelet to carry out convolution and handle, obtain reflectivity model.
(3) eliminate the reflections affect of relief surface, and transform to frequency field as initial continuation wave field.
(4) utilize the Fourier finite difference continuation operator of one-way wave equation to carry out wave field extrapolation from the bottom up, and the wave field between maintenance input reference face (relief surface) and the output reference face (rectangular top) is zero along degree of depth axle.
(5) wave field transformation with the frequency field after the continuation carries out imaging to time domain.
(6) software for display by routine is treated to seismic section image with imaging results.
2, the earthquake poststack forward modeling method of relief surface according to claim 1, it is characterized in that: object module is carried out the rectangle encapsulation, and participate in normal wave field propagation and continuation between input reference face (relief surface) and output reference face (rectangular top) by one zero wave field layer is set.
3, the earthquake poststack forward modeling method of relief surface according to claim 1, it is characterized in that: adopt the Si Naier theorem to calculate reflection coefficient, and utilize Ricker wavelet to carry out convolution and handle, obtain reflectivity model, the dominant frequency of Ricker wavelet is selected according to the stratum characteristic in target work area, generally between 10Hz～90Hz.
4, the earthquake poststack forward modeling method of relief surface according to claim 1 and 2 is characterized in that: adopt the Fourier finite difference method operator of frequency field to carry out wave field extrapolation calculating from the bottom up along degree of depth axle.
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