TY - JOUR

T1 - One dimensional acoustic direct nonlinear inversion using the Volterra inverse scattering series

AU - Yao, Jie

AU - Lesage, Anne Cécile

AU - Bodmann, Bernhard G.

AU - Hussain, Fazle

AU - Kouri, Donald J.

PY - 2014/7/1

Y1 - 2014/7/1

N2 - Direct inversion of acoustic scattering problems is nonlinear. One way to treat the inverse scattering problem is based on the reversion of the Born-Neumann series solution of the Lippmann-Schwinger equation. An important issue for this approach is the radius of convergence of the Born-Neumann series for the forward problem. However, this issue can be tackled by employing a renormalization technique to transform the Lippmann-Schwinger equation from a Fredholm to a Volterra integral form. The Born series of a Volterra integral equation converges absolutely and uniformly in the entire complex plane. We present a further study of this new mathematical framework. A Volterra inverse scattering series (VISS) using both reflection and transmission data is derived and tested for several acoustic velocity models. For large velocity contrast, series summation techniques (e.g., Cesàro summation, Euler transform, etc) are employed to improve the rate of convergence of VISS. It is shown that the VISS method with summation techniques can provide a relatively good estimation of the velocity profile. The method is fully data-driven in the respect that no prior information of the model is required. Besides, no internal multiple removal is needed. This one dimensional VISS approach is useful for inverse scattering and serves as an important step for studying more complicated and realistic inversions.

AB - Direct inversion of acoustic scattering problems is nonlinear. One way to treat the inverse scattering problem is based on the reversion of the Born-Neumann series solution of the Lippmann-Schwinger equation. An important issue for this approach is the radius of convergence of the Born-Neumann series for the forward problem. However, this issue can be tackled by employing a renormalization technique to transform the Lippmann-Schwinger equation from a Fredholm to a Volterra integral form. The Born series of a Volterra integral equation converges absolutely and uniformly in the entire complex plane. We present a further study of this new mathematical framework. A Volterra inverse scattering series (VISS) using both reflection and transmission data is derived and tested for several acoustic velocity models. For large velocity contrast, series summation techniques (e.g., Cesàro summation, Euler transform, etc) are employed to improve the rate of convergence of VISS. It is shown that the VISS method with summation techniques can provide a relatively good estimation of the velocity profile. The method is fully data-driven in the respect that no prior information of the model is required. Besides, no internal multiple removal is needed. This one dimensional VISS approach is useful for inverse scattering and serves as an important step for studying more complicated and realistic inversions.

KW - Volterra renormalization

KW - acoustic scattering

KW - direct nonlinear inversion

KW - inverse scattering series

KW - series summation techniques

UR - http://www.scopus.com/inward/record.url?scp=84905186889&partnerID=8YFLogxK

U2 - 10.1088/0266-5611/30/7/075006

DO - 10.1088/0266-5611/30/7/075006

M3 - Article

AN - SCOPUS:84905186889

VL - 30

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 7

M1 - 075006

ER -