APPARATUS AND METHOD FOR SEISMIC IMAGING USING WAVEFORM INVERSION SOLVED BY CONJUGATE GRADIENT LEAST SQUARES METHOD

• US 20110267923A1
• Filed: 09/24/2010
• Published: 11/03/2011
• Est. Priority Date: 04/30/2010
• Status: Abandoned Application

• Current Assignee: Seoul National University R&DB Foundation (Seoul National University)
• Original Assignee: Seoul National University R&DB Foundation (Seoul National University)
• Inventors: SHIN, Changsoo
• Application Number:
  US12/890,278
• Publication Number:
  US 20110267923A1
• Time in Patent Office: Days
• US Class Current: 367/49
• CPC Class Codes: G01V 1/30 Analysis G01V1/50 takes precedence

Abstract

Provided is an apparatus for seismic imaging by using waveform inversion in the frequency domain. The seismic imaging apparatus includes: a waveform inversion unit obtaining an equation by applying a Gauss-Newton method to an objective function consisting of residuals of logarithmic wavefields in frequency-domain waveform inversion and then obtaining a parameter vector, which minimizes the objective function, by solving the equation using a conjugate gradient method; and a subsurface structure display unit generating subsurface structure information using the parameter vector obtained by the waveform inversion unit and displaying the generated subsurface structure information.

Claims

1. A seismic imaging apparatus comprising:

a waveform inversion unit obtaining an equation by applying a Gauss-Newton method to an objective function consisting of residuals of logarithmic wavefields in the frequency-domain waveform inversion and then obtaining a parameter vector, which minimizes the objective function, by solving the equation using a conjugate gradient method; and

a subsurface structure display unit generating subsurface structure information using the parameter vector obtained by the waveform inversion unit and displaying the generated subsurface structure information.

2. The apparatus of claim 1, wherein the waveform inversion unit comprises:

a coefficient matrix calculation unit calculating coefficient matrices of a linear matrix equation obtained by applying the Gauss-Newton method; and

a conjugate gradient processing unit iteratively solving the linear matrix equation, which has the coefficient matrices calculated by the coefficient matrix calculation unit, by using the conjugate gradient method.

3. The apparatus of claim 2, wherein the conjugate gradient processing unit performs matrix multiplication using a back-propagation method when iteratively solving the linear matrix equation

4. The apparatus of claim 2, wherein the coefficient matrices calculated by the coefficient matrix calculation unit are defined by H=V^TS⁻

1₀U_a(S<sup>−

1</sup>₀V)* and g=V^TS<sup>−

1</sup>₀e_a, where S₀ is a coefficient matrix of a linear wave equation, V is a matrix assumed as a virtual source in an equation obtained by differentiating the linear wave equation with respect to a parameter vector, and U is a matrix, and e_a is a transformed residual vector.

5. The apparatus of claim 4, wherein the coefficient matrix calculation unit comprises a first coefficient matrix calculation unit which calculates the coefficient matrix H by sequentially back-propagating a first virtual source vector for first modeling vectors.

6. The apparatus of claim 4, wherein the coefficient matrix calculation unit comprises a second coefficient matrix calculation unit which calculates the coefficient matrix g by sequentially back-propagating a second virtual source vector for second modeling vectors.

7. The apparatus of claim 4, wherein the matrix assumed as the virtual source is defined by V=[v₁ v₂ . . . v_m]

8. The apparatus of claim 4, wherein the transformed residual vector is given by

9. A seismic imaging method comprising:

obtaining an equation by applying a Gauss-Newton method to an objective function consisting of residuals of logarithmic wavefields in frequency-domain waveform inversion and then obtaining a parameter vector, which minimizes the objective function, by solving the equation using a conjugate gradient method; and

generating subsurface structure information using the obtained parameter vector and displaying the generated subsurface structure information.

10. The method of claim 9, wherein the obtaining of the equation and the obtaining of the parameter vector comprises:

calculating coefficient matrices of a linear matrix equation obtained by applying the Gauss-Newton method; and

iteratively solving the linear matrix equation, which has the calculated coefficient matrices, by using the conjugate gradient method.

11. The method of claim 10, wherein in the iterative solving of the linear matrix equation, matrix multiplication is performed using a back-propagation method in the process of iteratively solving the linear matrix equation

12. The method of claim 10, wherein the calculated coefficient matrices are defined by H=V^TS⁻

1₀U_a(S<sup>−

1</sup>₀V)* and g=V^TS<sup>−

1</sup>₀e_a, where S₀ is a coefficient matrix of a linear wave equation, V is a matrix assumed as a virtual source in an equation obtained by differentiating the linear wave equation with respect to a parameter vector, and U is a matrix, and e_a is a transformed residual vector.

13. The method of claim 12, wherein the calculating of the coefficient matrices comprises calculating the coefficient matrix H by sequentially back-propagating a first virtual source vector for first modeling vectors.

14. The method of claim 12, wherein the calculating of the coefficient matrices comprises calculating the coefficient matrix g by sequentially back-propagating a second virtual source vector for second modeling vectors.

15. The method of claim 12, wherein the matrix assumed as the virtual source is defined by V=[v₁ v₂ . . . v_m]

16. The method of claim 12, wherein the transformed residual vector is given by

17. A computer-readable recording medium on which a program for executing the method of claim 9 is recorded.