Title:  A finite-difference contrast source inversion method


Speaker:  Aria Abubakar

Affiliation:  Schlumberger-Doll Research, Cambridge, MA, USA

 
Abstract:

In this presentation we present the so-called Finite-Difference Contrast 
Source Inversion (FDCSI) method for solving full non-linear inverse 
scattering problems. The FDCSI method is an iterative inversion algorithm 
and it utilizes the finite-difference frequency-domain approach as the 
forward solver. However, unlike the non-linear Conjugate Gradient (NLCG) 
method and the Gauss-Newton (GN) method, the FDCSI method does not solve 
any full forward problem in each iterative step of the inversion process. 
This feature makes the method very efficient to solve large-scale 
computational problems. We will show that the FDCSI method is able to 
produce inversion results that are comparable with the ones produced by 
the GN method and are better than the ones produced by the NLCG method 
while using a significantly lower computational cost. Another attractive 
feature of the FDCSI method that it is capable to use an inhomogeneous 
medium as the background medium. This feature is very useful when we are 
dealing with time-lapse inversion problems where we would like to monitor 
changes in the Earth subsurface or in the human body.

 

The quality of the inversion results of the FDCSI method may be significantly 
improved with the use of a Total Variation (TV) based regularizer. In our 
work the need for an artificial regularization parameter may be avoided by 
utilizing the TV regularization term as a Multiplicative Regularizer, which 
eliminates the need for an external regularization parameter selection process. 
Further since we prefer to work with a quadratic regularization function we 
employed a variant of the TV based regularizer. This so-called weighted 
L2-norm regularization function has all good features of the TV regularizer, 
however it is still a quadratic function.  

 

As numerical examples we will present some  inversion results for microwave 
biomedical imaging using electromagnetic waves and seismic full-waveform 
inversion applications. We will use  both synthetic and experimental data.