André K. Takahata

Unsupervised Processing of Geophysical Signals: A Review of Some Key Aspects of Blind Deconvolution and Blind Source Separation

This article reviews some key aspects of two important branches in unsupervised signal processing: blind deconvolution and blind source separation (BSS). It also gives an overview of their potential application in seismic processing, with an emphasis on seismic deconvolution. Finally, it presents illustrative results of the application, on both synthetic and real data, of a method for seismic deconvolution that combines techniques of blind deconvolution and blind source separation. Our implementation of this method contains some improvements overthe original method in the literature described.

Blind extraction of the sparsest component

In this work, we present a discussion concerning some fundamental aspects of sparse component analysis (SCA), a methodology that has been increasingly employed to solve some challenging signal processing problems. In particular, we present some insights into the use of l1 norm as a quantifier of sparseness and its application as a cost function to solve the blind source separation (BSS) problem. We also provide results on experiments in which source extraction was successfully made when we performed a search for sparse components in the mixtures of sparse signals. Finally, we make an analysis of the behavior of this approach on scenarios in which the source signals are not sparse.

2D Spiking Deconvolution Approach to Resolution Enhancement of Prestack Depth Migrated Seismic Images

Complex velocity models, limitations in acquisition geometry and frequency bandwidth, give rise to distortions in prestack depth migrated (PSDM) images. Such distortions can be modelled as the 2D convolution between the actual reflectivity and a resolution function. In the case of Born scattering, the resolution function is referred to as point spread function (PSF). The PSFs can be calculated with relatively low computational effort by ray tracing. In this work, we review the basic idea of the PSF and its relationship with seismic images generated by PSDM. With the help of the PSF concept, we propose the use of 2D spiking deconvolution with the aim of minimizing these image distortions. Finally, the potential and limitations of the proposed method are explored with applications on controlled synthetic data.

Multiple Contribution Traveltime Equation in the MCG Domain

Multiple attenuation is a crucial phase in the processing of marine seismic data. In specific, free surface multiples (waterair interface) that reflect from near water bottom layers are so strong that they mask reflections from lower geological layers. Surface Related Multiple Elimination (SRME) process is composed of two steps: prediction and adaptive subtraction. This paper deals with the prediction step. We analyze the signals that are registered on the Multiple Contribution Gather (MCG) domain and how they can be processed in order to obtain better prediction results. The better the prediction, the better the adaptation and subtraction. We suggest an approximation to the Multiple Contribution Traveltime (MCT) equation in the MCG domain. We use this equation to correct and filter the signals on the MCG domain.