Brief description of the drawings
Fig. 1 is the schematic flow sheet of elastic vector reverse-time migration imaging method;
Fig. 2-1 is the velocity of longitudinal wave field according to the Marmosi2 elastic fluid models built;
Fig. 2-2 is the shear wave velocity field according to the Marmosi2 elastic fluid models built;
Fig. 3-1 is that forward direction is extrapolated to the 1s moment using decoupling continuation side in 5.8 kms to 12.4 km regions in the x direction
The component of the vector compressional wave of source wavefield after the separation of journey method in the x-direction;
Fig. 3-2 is that forward direction is extrapolated to the 1s moment using decoupling continuation side in 5.8 kms to 12.4 km regions in the x direction
The component of the vector compressional wave of source wavefield after the separation of journey method in the z-direction;
Fig. 3-3 is that forward direction is extrapolated to the 1s moment using decoupling continuation side in 5.8 kms to 12.4 km regions in the x direction
The component of the vector shear wave of source wavefield after the separation of journey method in the x-direction;
Fig. 3-4 is that forward direction is extrapolated to the 1s moment using decoupling continuation side in 5.8 kms to 12.4 km regions in the x direction
The component of the vector shear wave of source wavefield after the separation of journey method in the z-direction;
Fig. 4-1 is that inverse time continuation to the 1s moment uses decoupling continuation side in 5.8 kms to 12.4 km regions in the x direction
The component of the vector compressional wave of detection wave field after the separation of journey method in the x-direction;
Fig. 4-2 is that inverse time continuation to the 1s moment uses decoupling continuation side in 5.8 kms to 12.4 km regions in the x direction
The component of the vector compressional wave of detection wave field after the separation of journey method in the z-direction;
Fig. 4-3 is that inverse time continuation to the 1s moment uses decoupling continuation side in 5.8 kms to 12.4 km regions in the x direction
The component of the vector shear wave of detection wave field after the separation of journey method in the x-direction;
Fig. 4-4 is that inverse time continuation to the 1s moment uses decoupling continuation side in 5.8 kms to 12.4 km regions in the x direction
The component of the vector shear wave of detection wave field after the separation of journey method in the z-direction;
Fig. 5-1 be using vector dot product structure elastic wave cross-correlation image-forming condition obtain 5.8 kms in the x direction extremely
PP imaging sections in 12.4 km regions;
Fig. 5-2 be using vector dot product structure elastic wave cross-correlation image-forming condition obtain 5.8 kms in the x direction extremely
PS imaging sections in 12.4 km regions;
Fig. 5-3 be using vector dot product structure elastic wave cross-correlation image-forming condition obtain 5.8 kms in the x direction extremely
SP imaging sections in 12.4 km regions;
Fig. 5-4 be using vector dot product structure elastic wave cross-correlation image-forming condition obtain 5.8 kms in the x direction extremely
SS imaging sections in 12.4 km regions;
Fig. 6-1 is after final superposition and carries out the PP imaging sections of Laplce's filtering;
Fig. 6-2 is after final superposition and carries out the PS imaging sections of Laplce's filtering;
Fig. 6-3 is after final superposition and carries out the SP imaging sections of Laplce's filtering;
Fig. 6-4 is after final superposition and carries out the SS imaging sections of Laplce's filtering.
Embodiment
As shown in figure 1, elastic vector reverse-time migration method, step are as follows:
Step 1:According to dielectric model, given source wavelet, realize that wave field just pushes out, using decoupling extension equation method
The longitudinal and transverse wave field of decoupling is obtained, specific method is as follows:
(1), according to dielectric model set in advance, source wavelet is loaded, using elastic wave propagation operator, realizes seismic wave
The positive time continuation of field, build source vector wave field:
Utilize following one-order velocity-stress equations for elastic waves
Structure source wavefield is just pushing out staggering mesh finite-difference operator, and wherein ρ is density, and C is elastic fluid rigidity
Matrix, v=(vx,vy,vz)TParticle Vibration Velocity vector field is represented, superscript notation " T " represents transposition, vxRepresent particle vibration speed
Spend the component of vector field in the x-direction, vyRepresent component of the Particle Vibration Velocity vector field along y, vzRepresent Particle Vibration Velocity vector
Component of the field along z, τ=(σxx,σyy,σzz,τyz,τxz,τxy)TIt is stress tensor, σxx、σyyAnd σzzIt is direct stress, τyz、τxzAnd τxy
It is shearing stress,Derivative of the Particle Vibration Velocity vector field on time orientation is represented,Represent stress tensor on time orientation
Derivative, L is differential matrix,
Wherein, lx, lyAnd lzRepresent respectively along the derivative in x, y and z directionss, the stiffness matrix C tables in isotropic medium
It is shown as
Wherein λ and μ is Lame Coefficient.Discretization is carried out to above-mentioned wave equation and obtains following elastic wave continuation operator:
Wherein, τSRepresent the discrete stress field of source wavefield, vSThe discrete Particle Vibration Velocity field of source wavefield is represented, η is border
Absorption coefficient, absorption coefficient η=0 in target area, the absorption coefficient η=200 (0.5-0.5cos (π in the absorption region of border
R/R)), r=1,2 ..., R, R be absorbed layer thickness, π represents pi, and Δ t be time sampling interval, when n Δs t expressions are whole
Between point, (n+1/2) Δ t is half timing node, n=1,2 ..., N, T0The earthquake record that=N Δs t represents total receives duration, DfWith
DbHigh-order staggering mesh finite-difference matrix operator is represented respectively, and expression is
With
WhereinWithForwardly and rearwardly Difference Schemes with Staggered in the x-direction is represented,WithRepresent in the y-direction
Forwardly and rearwardly Difference Schemes with Staggered, whereinWithRepresent forwardly and rearwardly staggered-mesh difference lattice in the z-direction
Formula, specific form are as follows:
Wherein, Δ x, Δ y and Δ z be respectively along the sampling interval in x, y and z directionss,It is 2M
Rank staggering mesh finite-difference coefficient, f (i, j, k) are space networks lattice point (i, j, k) smooth functions.
(2), during source wavefield forward direction time continuation, the source wavefield for decoupling the acquisition decoupling of extension equation method is utilized
P-wave And S data:
Using the P-wave And S field data for decoupling the acquisition decoupling of extension equation method during wave field extrapolation, pass through public affairs first
Formula (3) calculates source wavefield compressional wave stress wave field:
WhereinSource wavefield compressional wave stress field,Derivative of the compressional wave stress wave field on time orientation is represented,Represent
Divergence operator, then the Particle Vibration Velocity field by compressional wave stress field acquisition focus compressional wave:
WhereinSource wavefield longitudinal-wave particle vibration velocity field is represented,Represent source wavefield compressional wave
Derivative of the Particle Vibration Velocity field on time orientation,Represent gradient operator,Represent the particle vibration of source wavefield compressional wave
The component of velocity vector field in the x-direction,Component of the Particle Vibration Velocity vector field of source wavefield compressional wave along y is represented,Table
Show component of the Particle Vibration Velocity vector field of source wavefield compressional wave along z, finally from the total wave field v of focusSIn subtract source wavefield
Longitudinal wave fieldSource wavefield shear wave field is obtained, i.e.,
WhereinThe Particle Vibration Velocity field of source wavefield shear wave is represented,Represent that source wavefield is horizontal
The component of the Particle Vibration Velocity vector field of ripple in the x-direction,Represent the Particle Vibration Velocity vector field of source wavefield shear wave along y
Component,Represent component of the Particle Vibration Velocity vector field of source wavefield shear wave along z.Outside specification word description,
The present invention can also be intuitively embodied in Figure of description, accompanying drawing 3-1 is the speed given to 2-1 and Fig. 2-2 with reference to the accompanying drawings
The focus longitudinal wave field obtained after the separation of the model elastic wave field that 5.8 kms to 12.4 km regions calculate in the x direction is in the x-direction
Component;Accompanying drawing 3-2 is the rate pattern given to 2-1 and Fig. 2-2 with reference to the accompanying drawings 5.8 kms to 12.4 kms in the x direction
The component of the focus longitudinal wave field obtained after the elastic wave field separation that region calculates in the z-direction;Accompanying drawing 3-3 is to 2-1 with reference to the accompanying drawings
Obtained after being separated with the given rate pattern elastic wave fields that 5.8 kms calculate to 12.4 km regions in the x direction of Fig. 2-2
The component of focus shear wave field in the x-direction, accompanying drawing 3-4 be to 2-1 and Fig. 2-2 with reference to the accompanying drawings give rate pattern in the x direction
The component of the focus shear wave field obtained after the elastic wave field separation that 5.8 kms to 12.4 km regions calculate in the z-direction.From accompanying drawing
3-1 to accompanying drawing 3-4 can clearly be seen that wave field is separated and come.
Step 2:According to dielectric model, using multi-component seismic data as boundary value condition, realize outside the inverse time of seismic wave field
Push away, it is as follows using the longitudinal and transverse wave field for decoupling the acquisition decoupling of extension equation method, specific method:
(1), according to dielectric model set in advance, using the multi-component seismic data of surface seismic records as boundary value condition, profit
With elastic wave propagation operator, the inverse time continuation of seismic wave field is realized, builds detection vector wave field:
By multi-component earthquake data as boundary value condition, it is loaded into following inverse time extrapolation equation
Wherein, τRRepresent the discrete stress field of detection wave field, vRThe discrete Particle Vibration Velocity field of detection wave field is represented, η is border
Absorption coefficient, absorption coefficient η=0 in target area, the absorption coefficient η=200 (0.5-0.5cos (π in the absorption region of border
R/R)), r=1,2 ..., R, R be absorbed layer thickness, π represents pi, and Δ t be time sampling interval, when n Δs t expressions are whole
Between point, (n+1/2) Δ t is half timing node, n=1,2 ..., N, T0The earthquake record that=N Δs t represents total receives duration, DfWith
DbHigh-order staggering mesh finite-difference matrix operator is represented respectively, and expression is
With
WhereinWithForwardly and rearwardly Difference Schemes with Staggered in the x-direction is represented,WithRepresent along y side
To forwardly and rearwardly Difference Schemes with Staggered, whereinWithRepresent forwardly and rearwardly staggered-mesh difference in the z-direction
Form, specific form are as follows:
Wherein, Δ x, Δ y and Δ z be respectively along the sampling interval in x, y and z directionss,It is 2M
Rank staggering mesh finite-difference coefficient, f (i, j, k) are space networks lattice point (i, j, k) smooth functions.
(2), during detection wave field inverse time continuation, the detection wave field for decoupling the acquisition decoupling of extension equation method is utilized
P-wave And S data:
Using the P-wave And S field data for decoupling the acquisition decoupling of extension equation method during wave field extrapolation, pass through public affairs first
Formula (7) calculates detection wave field compressional wave stress field:
WhereinDetection wave field compressional wave stress field,Derivative of the detection wave field compressional wave stress field on time orientation is represented,Divergence operator is represented, then the Particle Vibration Velocity field of detection wave field compressional wave is obtained by detection wave field compressional wave stress field:
WhereinDetection wave field longitudinal-wave particle vibration velocity field is represented,Represent detection wave field compressional wave
Derivative of the Particle Vibration Velocity field on time orientation,Represent gradient operator,Represent the particle vibration of detection wave field compressional wave
The component of velocity vector field in the x-direction,Component of the Particle Vibration Velocity vector field of detection wave field compressional wave along y is represented,Table
Show component of the Particle Vibration Velocity vector field of detection wave field compressional wave along z, finally from the total wave field v of detection wave fieldRIn subtract detection
Wave field longitudinal wave fieldDetection wave field shear wave field is obtained, i.e.,
WhereinThe Particle Vibration Velocity field of detection wave field shear wave is represented,Represent that detection wave field is horizontal
The component of the Particle Vibration Velocity vector field of ripple in the x-direction,Represent the Particle Vibration Velocity vector field edge of detection wave field shear wave
Y component,Represent component of the Particle Vibration Velocity vector field of detection wave field shear wave along z.Accompanying drawing 4-1 is that detection wave field passes through
The component of the vector longitudinal wave field that solution decoupling extension equation method obtains in the x-direction;Accompanying drawing 4-2 is detection wave field by decoupling continuation side
The component of the vector longitudinal wave field that journey method obtains in the z-direction;Accompanying drawing 4-3 is the arrow that detection wave field is obtained by decoupling extension equation method
Measure the component of shear wave field in the x-direction, accompanying drawing 4-4 is detection wave field by decoupling vector shear wave field that extension equation method obtains along z
The component in direction.It can clearly be seen that wave field is separated from accompanying drawing 4-1 to accompanying drawing 4-4 to come.
Step 3:It is imaged, is marked using the vector wave site product cross-correlation image-forming condition of source wavefield illumination compensation
The imaging results of amount, specific method are as follows:
The detection wave field decoupling P-wave And S that the source wavefield decoupling P-wave And S obtained using step 1 is obtained with step 2 enters
Go as follows
Vector dot product cross-correlation is imaged, and carries out focus illumination compensation, obtains the multi-component seismic data elasticity vector inverse time
Offset scalar imaging results.Wherein IPPRepresent PP imaging results, IPSIt is PS imaging results, ISPIt is SP imaging results, ISSSS into
As result, t represents time, T0Represent that earthquake record receives duration,Represent that source wavefield longitudinal-wave particle is shaken
Dynamic velocity field,The component of the Particle Vibration Velocity vector field of source wavefield compressional wave in the x-direction is represented,Represent source wavefield
Component of the Particle Vibration Velocity vector field of compressional wave along y,Represent the Particle Vibration Velocity vector field of source wavefield compressional wave along z's
Component,Detection wave field longitudinal-wave particle vibration velocity field is represented,Represent that the particle of detection wave field compressional wave shakes
The component of dynamic velocity vector field in the x-direction,Component of the Particle Vibration Velocity vector field of detection wave field compressional wave along y is represented,
Component of the Particle Vibration Velocity vector field of detection wave field compressional wave along z is represented,Represent source wavefield shear wave
Particle Vibration Velocity field,The component of the Particle Vibration Velocity vector field of source wavefield shear wave in the x-direction is represented,Represent
Component of the Particle Vibration Velocity vector field of source wavefield shear wave along y,Represent the Particle Vibration Velocity arrow of source wavefield shear wave
Component of the field along z is measured,The Particle Vibration Velocity field of detection wave field shear wave is represented,Represent detection wave field
The component of the Particle Vibration Velocity vector field of shear wave in the x-direction,Represent the Particle Vibration Velocity vector field of detection wave field shear wave
Along y component,Component of the Particle Vibration Velocity vector field of detection wave field shear wave along z is represented, symbol represents vector dot product.
Outside specification word description, the present invention can also be intuitively embodied in Figure of description, Fig. 5-1 is utilized based on illumination
The PP imaging sections that the elastic wave cross-correlation image-forming condition of the vector dot product structure of compensation obtains;Fig. 5-2 is utilized based on illumination
The PS imaging sections that the elastic wave cross-correlation image-forming condition of the vector dot product structure of compensation obtains;Fig. 5-3 is utilized based on illumination
The SP imaging sections that the elastic wave cross-correlation image-forming condition of the vector dot product structure of compensation obtains;Fig. 5-4 is utilized based on illumination
The SS imaging sections that the elastic wave cross-correlation image-forming condition of the vector dot product structure of compensation obtains.
Step 4:Low frequency noise compacting is carried out to the imaging results of acquisition, specific implementation method is as follows:
Utilize following Laplce's filtering algorithm
Processing is filtered to imaging section, obtains final imaging results.WhereinRepresent Laplace operator,WithIt is to carry out filtered PP, PS, SP and SS imaging section of Laplce respectively.Fig. 6-1 is most
The superposition at end simultaneously carries out the PP imaging sections of Laplce's filtering.Fig. 6-2 is final superposition and carries out Laplce's filtering
PS imaging sections, Fig. 6-3 is final superposition and carries out the SP imaging sections of Laplce's filtering, and Fig. 6-4 is final superposition
And carry out the SS imaging sections of Laplce's filtering.