Apparatus and method for imaging a subsurface using frequency-domain elastic reverse-time migration

Patent metadata

Field	Value
Publication number	US-8953411-B2
Application number	US-201113160913-A
Country	US
Kind code	B2
Filing date	Jun 15, 2011
Priority date	Aug 24, 2010
Publication date	Feb 10, 2015
Grant date	Feb 10, 2015

Abstract

Provided are an apparatus and method for imaging a subsurface using frequency-domain reverse-time migration in elastic medium. The subsurface imaging method represents a frequency-domain imaging condition as convolution of measured data and a partial derivative wavefield. That is, the subsurface imaging method applies a back-propagation algorithm to represent an imaging condition as convolution of a virtual source and a back-propagated wavefield. Then, the subsurface imaging method divides a virtual source vector and the back-propagated wavefield represented by a displacement vector into P- and S-wave potentials through Helmholtz decomposition, thereby providing a new imaging condition.

First claim

What is claimed is:

1. An apparatus of imaging a subsurface, comprising:
a plurality of receivers configured to receive a seismic data from a region to be observed;
a signal processor configured to estimate sources from measured data measured by the receivers, and to process the seismic data so as to generate a migration image signal for imaging a subsurface of the region to be observed, wherein:
the signal processor generates migration images for a P-wave and a S-wave of a seismic signal, by convolving a virtual source vector and a wavefield displacement vector obtained by back-propagating the seismic signal, with a divergence operator and a curl operator, and
imaging conditions for generating the migration images for the P-wave and the S-wave are represented as equations E-1 and E-2, respectively:
(φ k ) PP =∫Re{∇·[( v ke ) T ]∇·[S e −1 {tilde over (d)} e *]}dω and  (E-1)

(φ k ) SS =∫Re{∇×[( v ke ) T ]∇×[S e −1 {tilde over (d)} e *]}dω,   (E-2)

where (φ k ) PP is the imaging condition for P wave, (φ k ) SS is the imaging condition for S wave, (v ke ) p , (v ke ) s is the virtual source vector for the P and S wave velocity for the kth model parameter respectively, {tilde over (d)} e is the observed data, Re is the real part of the complex number, ∇· is divergence operator, ∇× is curl operator, T is transpose, * is complex conjugate, ω is angular frequency, and S e −1 is the inverse matrix of the complex impedance matrix in an elastic medium.

2. The apparatus of claim 1 , wherein the virtual source vector is defined as equations (E-3) and (E-4) for the P-wave and the S-wave, respectively:

(

v
ke

)

p

=

-

∂

S
e

∂

v
p

⁢

u
~

e

,
and

(

E
⁢

-

⁢
3

)

(

v
ke

)

s

=

-

∂

S
e

∂

v
s

⁢

u
~

e

,

⁢
where

⁢

⁢

∂

S
e

∂

v
p

=

2
⁢
ρ
⁢

⁢

v
p

⁢

∂

S
e

∂
λ

,

∂

S
e

∂
λ

,

∂

S
e

∂

v
s

-

4
⁢

⁢
ρ
⁢

⁢

Assignees

• Shin Changsoo
• Snu R&Db Foundation

Inventors

• Shin Changsoo

Classifications

• G01V1/28 Primary

  Processing seismic data, e.g. for interpretation or for event detection (G01V1/48 takes precedence) · CPC title

• G01V2210/51

  Migration · CPC title

• G01V2210/67

  Wave propagation modeling · CPC title