Compression approaches for reducing computational complexities of nonlinear inversion algorithms

Friday, April 27, 2012 - 1:25pm - 2:25pm
Aria Abubakar (Schlumberger-Doll Research)
In this presentation we discuss compression approaches for improving the efficiency and reducing the memory usage of seismic full-waveform inversion as well as nonlinear electromagnetic inversion algorithms.

The first approach is the so-called source-receiver compression scheme. By detecting and quantifying the extent of redundancy in the data, we assemble a reduced set of simultaneous sources and receivers that are weighted sums of the physical sources and receivers used in the survey. Because the number of these simultaneous sources and receivers can be significantly less than those of the physical sources and receivers, the computational time and memory usage of any gradient-type inversion method can be tremendously reduced. The scheme is based on decomposing the data into their principal components using a singular value decomposition approach and the data reduction is done through the elimination of the small eigenvalues. Consequently this will suppress the effect of noise in the data.

The second approach is the so-called model compression scheme. In this scheme, the unknown model parameters (seismic velocities or conductivty) are represented by using basis functions such as Fourier, cosine, or wavelet. By applying a proper truncation scheme, the model may then be approximated by a reduced number of basis functions, which is usually much less than the number of model parameters in the regular spatial domain representation. This model compression scheme accelerates the computational time as well as reduces the memory usage of most nonlinear inversion algorithm, especially the Gauss-Newton method.

As demonstrations, we show and discuss both synthetic and field data inversions. The results show that by employing these compression scheme we are able to significantly reduce the algorithm computational complexity by a few orders of magnitude without compromising the quality of inverted models.

This work is a joint work with T. M. Habashy, M. Li, Y. Lin, and G. Pan

Aria Abubakar was born in Bandung, Indonesia, on August 21, 1974. He received M.Sc. degree (Cum Laude) in electrical engineering and the Ph.D. degree (Cum Laude) in technical sciences, both from the Delft University of Technology, in 1997 and 2000, respectively. From September 2000 until February 2003 he was with the Laboratory of Electromagnetic Research and Section of Applied Geophysics, Delft University of Technology. Currently he is a Scientific Advisor and Program Manager with Schlumberger-Doll Research, Cambridge, Massachusetts, USA. At present, his main research activities include solving forward and inverse problem in acoustic, electromagnetic, and elastodynamic. He is currently an Associate Editor of Radio Science and Geophysics. He holds 7 US patents and has published 1 book, 4 book chapters, over 70 scientific articles in refereed journals, over 130 conference proceedings papers, and 41 conference abstracts. He has also presented over 200 invited and contributed talks in international conferences and institutes/universities.