kernels for finitefrequency signals Applications in migration velocity updating and tomography XiaoBi Xie University of California at Santa Cruz Sanya China July 2428 2011 A brief introduction ID: 326084
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Slide1
Sensitivity kernels for finite-frequency signals: Applications in migration velocity updating and tomography
Xiao-Bi
Xie
University of California at Santa Cruz
Sanya
, China July 24-28, 2011Slide2
A brief introductionData domain vs. depth domain
Sensitivity Kernel for Migration Velocity Analysis
The Inversion SystemVelocity model partitioning and sensitivity kernel storageNumerical ResultConclusions
OutlineSlide3
A brief introductionData domain vs. depth domain
Sensitivity Kernel for Migration Velocity Analysis
The Inversion SystemVelocity model partitioning and sensitivity kernel storageNumerical ResultConclusions
OutlineSlide4Slide5Slide6Slide7
arg(u/u0) =
imag
(U/u0)u0/ u0u / u0
U / u
0
df
=
arg
(
u
/
u
0
)
u
0
u
U
Imag
RealSlide8Slide9Slide10
In applied seismology
Huge data size. Efficiency is crucial. Suggested methods could be one-way propagator or Gaussian beam method.Complex background models. The velocity perturbations overlapped on the initial model are large (some times are more than 100%). Including not only transmitted observations, where the information is from the surface data, but also reflection type observation
, where the information is collected in image
domain. Slide11
A brief introductionData domain vs. depth domain
Sensitivity Kernel for Migration Velocity Analysis
The Inversion SystemVelocity model partitioning and sensitivity kernel storageNumerical ResultConclusions
OutlineSlide12Slide13
A synthetic shot record. The shot is located above relatively complicated structures. There are many complicated features in this synthetic section.
▼
Complexity in data domainSimplicity in depth domainSlide14
A brief introductionData domain vs. depth domain
Sensitivity Kernel for Migration Velocity Analysis
The Inversion SystemVelocity model partitioning and sensitivity kernel storageNumerical ResultConclusions
OutlineSlide15
The incoherence information are RMOs from different common image gathers. Offset index CIG
Shot index CIG
Angle index CIGMigration velocity updatingSourceTarget
Data
Measuring incoherence in image
Back project to modify the velocity
The methods that converting the RMO into velocity corrections.
Parameterized semblance
Ray-based tomography
Wave-equation based inversionSlide16
How the RMO sense the velocity perturbation: --- Direct measurementsSlide17
The actual sensitivity map for a shot image (how the depth image senses the V-model error). To generate this map, we use an velocity error patch to scan the model. At each location, we conduct a migration and measure the RMO from the depth image. The RMOs are then presented in the model to show the sensitivity of the depth image to the velocity error. The sensitivity map is very complex. A positive error can generate either positive or negative RMOs; the sensitivity area is much broader than the ray based theory predicted. Our goal is to derive theoretical equations to express this sensitivity map and use it for velocity updating.Slide18
Direct measured sensitivity maps for shots at different locations
in 2D SEG/EAGE salt modelSlide19
Source side kernel
Receiver side kernel
Source
Image point
Imaginary sourceSlide20
The GB Green’s functions used to construct the sensitivity kernel for migration velocity analysis. (a) Down-going Green’s function , (b) up-going Green’s function , and (c) Green’s function .Slide21
Comparison of different kernels for a shot gather
The sketch of a ray-based kernel
The sensitivity kernel calculated using the finite-frequency theoryThe actual sensitivity map directly measured from migrationSlide22
A brief introductionData domain vs. depth domain
Sensitivity Kernel for Migration Velocity Analysis
The Inversion SystemVelocity model partitioning and sensitivity kernel storageNumerical ResultConclusions
OutlineSlide23
∫
dV
=Sensitivity kernelVelocity model error
δ
v/v
RMOSlide24
Comparison between inversions using a finite-frequency sensitivity kernel and a ray kernel
Sketch illustrating the relative residual moveout measurement from a pair of shots
The differential sensitivity kernel for a pair of shots. Note the complexity and volumetric distribution of a finite-frequency kernel The ray based kernel for a pair of shots. Note the sensitivity distribution is unrealistic and the uneven ray distribution can cause singularities in inversions.Slide25
Differential RMO
Differential kernelSlide26
A brief introductionData domain vs. depth domain
Migration Velocity Analysis
The Inversion SystemVelocity model partitioning and sensitivity kernel storageNumerical ResultConclusions
OutlineSlide27
A 5-layer velocity model used to demonstrate the migration velocity analysis. Slide28
How to partition the model?
How to store huge amount of kernels?Slide29Slide30
Actual output and stored
kernels
Unknown perturbation at cell corners
Parameter matrixSlide31
Stored parameter a1. The 4 groups of kernels are for 4 reflectors; the horizontal coordinate is for different image points and the vertical coordinate is for different sources. Model grid size 10m x 10mCell size 500m x 500m31shot x 31 imaging point x 4 reflectors, 32x10 cells spend 286Mb.Slide32
A brief introductionData domain vs. depth domain
Sensitivity Kernel for Migration Velocity Analysis
The Inversion SystemVelocity model partitioning and sensitivity kernel storageNumerical ResultConclusions
OutlineSlide33
migration velocity updating process (1) Conduct the migration using an initial model.
(2)
Calculate the RMOs from the shot-index CIGs.(3) Pick the reflector position from the initial depth image. (4) Use the initial model and reflector locations to calculate sensitivity kernels. (5) Input the RMOs and the sensitivity kernels to the inversion system to do the tomography. (6) Use the inverted errors to update the initial model and use it
for the next iteration. Slide34
A 5-layer velocity model used to demonstrate the migration velocity analysis. Slide35
Comparison between the theoretically calculated kernels (left column) and actually measured sensitivity maps (right column). From top to bottom are for different reflectors.Slide36
Coverage of sensitivity kernels in the model. Panels (a) to (d) are kernel coverage for image points on the 4 reflectors. Panel (e) is the coverage from all kernels. Shown here is the summed positive parameter FK1.Slide37
Velocity models in updating process, with (a) initial model and (b) model after two iterations. Slide38
Depth image improved in the velocity updating process. (a) Image calculated using the initial model and (b) image calculated using the updated velocity model. Slide39
CIGs before and after the velocity updating, with (a) CIGs in the initial model and (b) CIGs in the updated velocity model.Slide40
A brief introductionData domain vs. depth domain
Sensitivity Kernel for Migration Velocity Analysis
The Inversion SystemVelocity model partitioning and sensitivity kernel storageNumerical ResultConclusions
OutlineSlide41
SummaryBased on the
finite-frequency sensitivity theory
, we present a migration velocity analysis method. The new approach is a wave-equation based method which naturally incorporates the wave phenomena and is best teamed with the wave-equation based migration for velocity analysis.The finite-frequency sensitivity kernel is used to link the observed shot gather RMO with the errors in the migration velocity model. Angle domain decomposition is not required.(3) We developed method to calculate the broadband sensitivity kernel in complex velocity models and for irregular reflectors.Slide42
Summary (continues)(4) A new velocity model partitioning approach
is tested. This method partitions the model into small cells and uses
interpolation function to represent the velocity model within cells. (5) To store the sensitivity kernels, we use interpolation functions as basis and expanded kernels to these basis. Thus we only need to store the expansion coefficients. The accuracy of the kernel is adaptive to the required accuracy of the velocity model. In this way, we significantly reduce the storage space of sensitivity kernels while without losing the required accuracy. Slide43
Summary (continues)(6) Using this approach, we
demonstrate the velocity model
updating. The updated velocity model improves the depth image by both flattened the common image gather and bring the image to the original location of reflectors. Slide44
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