Ph.D Thesis


Ph.D StudentPereg Deborah
SubjectThree-Dimensional Seismic Imaging and Sparse Inversion
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Israel Cohen
Full Thesis textFull thesis text - English Version


Abstract

Exploration seismology aims to produce a three-dimensional (3D) image representing a 3D earth section at depth. Similarly to other imaging techniques, the overall objective is to give insight into the internal structure of a medium or an object. One of the major challenges in imaging systems is to improve the spatial resolution. Resolution limits are inherently determined by the wave length and fundamentally limited by diffraction. In practice, the actual resolution is far below optimal, due to acquisition conditions and limited data processing tools. This research has been dedicated to the exploration 3D seismic imaging and sparse inversion methods. Our broad goal is to develop simpler and efficient ways of processing of large amounts of seismic data, in pursuit of optimal methods for 3D imaging, super-resolution and noise reduction.


First, we present a multichannel method for recovery of 3D reflectivity images from 3D seismic data. The algorithm is designed to promote the sparsity of the solution, while taking into account the attenuation and dispersion propagation effects of reflected waves, and considering the relations between spatially-neighboring traces. We provide theoretical guarantees for stable recovery, in the case of horizontal layered sub-terrain, and demonstrate the robustness of the proposed technique via synthetic and real data examples.


Secondly, we propose a different approach for solving the seismic deconvolution problem. That is, by means a recurrent neural net (RNN). We postulate that each point in the reflectivity image can be inferred by the neural net from an analysis patch of seismic data. During training, the RNN learns to predict each reflectivity point value, from local time and space data relations. We study the system's behavior for different training and testing scenarios, with synthetic data and real data.


The third part is dedicated to the problem of prestack seismic time migration velocity analysis (MVA). Accurate imaging of seismic data requires knowledge of the velocity of the propagating waves at all points along the reflection paths. Currently, MVA is an iterative time consuming process of two stages, where the data is alternately imaged by prestack migration, and the velocity function is updated based on the migration results. We present the basic theory and definitions, and establish two variations of an automated technique for MVA using RNNs. The proposed methods are evaluated via real data experiments.


Lastly, we focus on convolutional sparse coding, with application to seismic reflectivity estimation. In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Recently both data-driven and model-driven feature extracting methods have become extremely popular and have achieved remarkable results. However, practical implementations are often too slow to be plugged in real-time applications. We present a fast alternative to existing sparse coding iterative thresholding algorithms. The performance of the proposed solution is demonstrated via the seismic inversion problem in both synthetic and real data scenarios. We also provide theoretical guarantees for perfect support recovery, under certain conditions, within the first iteration of the algorithm.