Global optimization algorithms with application to constructing seismic images

• Grant number: 06/03360-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: February 01, 2007
• End date: March 31, 2008
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Martin Tygel
• Grantee: Emerson Alexandre de Oliveira Lima
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Efficient and precise methods of optimization play important role in the image construction by seismic processing. In this context, intense activity of research is dedicated to the development of algorithms capable to act on large data sets and reduced computation times. The development of global optimization algorithms represents an interesting challenge, not only in the academic point of view of research advancement, but also in practical application, because the impact the results have to industrial purposes.The process of stacking is one of the most important techniques of the obtention of seismic images. It consists of summing seismic amplitudes throughout curves or surfaces that are constructed for this purpose. These curves or surfaces are defined through parameters that are to be estimated so as to maximize the energy along the stacking. The stacking energy is measured by a coherence criterion (called semblance) associated to each stacking curve or surface.As result of the process, images of the subsurface - known as seismic sections - are generated. These images are, in fact, a kind of subsurface maps, for which at each point a numerical value isassigned. This value is the result of stacking of the curve or optimal surface associated to the point in consideration.The estimated parameters provide, not only the best images, but also valuable geologic information from the subsurface that has beenilluminated.This project investigates the different methods of parameters estimation that are of use to the construction of seismic images by means of the stacking process. The energy associated to eachstacking curve is rather oscillating (that is, it may present several local maxima). As a consequence, the use of global optimization methods is more appropriate for the solution of the problem. The large size of the data and also the noise that are inherent from the seismic surveys, makes the problem a real challenge, for which there still not exists an established solution.