M.Sc Thesis

M.Sc StudentPereg Deborah
SubjectSparse Seismic Inversion
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Israel Cohen
Full Thesis textFull thesis text - English Version


Seismic deconvolution aims to recover the earth structure hidden in the acquired seismic data. In exploration seismology, a short-duration acoustic pulse is transmitted from the earth surface. The reflected pulses from the ground are then received by a sensor array and processed into a two-dimensional (2D) seismic image. Unfortunately, this image does not represent the actual image of the ground. We will refer to the hidden ground image we are estimating as the reflectivity.

The observed seismic data can be modeled as a convolution between each column in the 2D reflectivity section and a one-dimensional (1D) seismic pulse (wavelet), with additive noise. The reflectivity is assumed to be sparse. Therefore, deterministic deconvolution methods often use sparse inversion techniques.

In this thesis we present two algorithms that perform seismic recovery. We apply both algorithms to synthetic and real seismic data and demonstrate improved performance and robustness to noise, compared to competitive algorithms.

The first algorithm - Multichannel Sparse Spike Inversion (MSSI) - takes advantage of the horizontal spatial correlation between neighboring traces in the reflectivity image. MSSI is an iterative procedure, which deconvolves the seismic data and recovers the earth 2D reflectivity image, while taking into consideration both the desired sparsity of the solution and the dependencies between spatially-neighboring traces. Visually, it can be seen that the layer boundaries in the estimates obtained by MSSI are more continuous and smooth than the layer boundaries in the single-channel deconvolution estimates.

The second algorithm takes into account the attenuation and dispersion propagation effects of the reflected waves, in noisy environment. We present an efficient method to perform seismic Time-Variant inversion considering the earth Q-model. We derive the theoretical bounds on the recovery error, and on the localization error. It is shown that the solution consists of recovered spikes which are relatively close to every spike of the true reflectivity signal. In addition, we prove that any redundant spike in the solution which is far from the correct support will have small energy.