Master Thesis Defense Pedro Martínez Saiz

Title: Deterministic wavelet estimation methods in the tie-to-well approach

Abstract:
Wavelets are wave-like functions with short extension, i.e., they oscillate over a short distance and damp very fast. Their main value over the whole domain is zero. These properties give wavelets the localization power, useful in a wide range of disciplines.

In seismology, the wavelets are hidden in the seismic data. Seismic processing methods are aimed at removing the wavelets from the seismic data to yield the response of the Earth to an initial perturbation: the reflectivity. The reflection coefficient series carry information about the structure of the subsurface. The aim of the project is to exploit deterministic inversion tools to estimate the wavelet function (our unknown) hidden in the data.

Deterministic inversion theory covers those minimization problems that are solved using least squares approaches. During the project we will see that the least squares fit, in its simplest form, is not robust enough, and needs to be reformulated. More specifically, we will deploy Tikhonov regularization to render the problem robust and stable. Dumped Tikhonov regularization will be presented too as need of introducing prior information about the wavelets.

A forward model that parametrizes the problem is required. The convolutional model will be employed as the connecting bridge between the data space and the parameter space. Our parameters will be the wavelet itself, which must fulfil the foregoing requisites. We will explore its limitations, as well as up to which extent it works. We will simulate our own data using the SPECFEM software.

Supervisor: Klaus Mosegaard

Censor: Thomas Mejer Hansen