Abstract
- 1. ABSTRACT This study developed and tested the idea of representing two-dimensional seismic velocity fields using the two-dimensional Haar wavelet series. The method presented simplifies the strategy and the computing steps used in the parameterisation of the referred fields when compared to methods used in previous studies where the same goal was reached using poly- nomial or 1D wavelet series parameterisation. We considered seismic velocity fields obtained from the following geological models: Layered, Compressional Fault, Normal Fault, Anticlinal and Salt Dome. Once the models have been discretised and available numerically, the models of the velocity fields are approximated using the two-dimensional Haar wavelet series algorithm to generate the parameterised fields and the resulting data is presented using a total and reduced number of coefficients in the series. The research findings indicate that, as predicted, the velocity fields are satisfactorily param- eterised using the two-dimensional Haar wavelet series, though the number of coefficients was high. The generation of coefficient values using their average in subintervals, on the other hand, allowed for the reduction in the total number of coefficients by a maximum of 90%, which guarantees the simplification of the representations. Although this work only deals with the parameterisation of seismic velocity field models, the findings also supported the possibility of expanding the study in the field of seismics through the development of reflection travel time modelling and ray tracing for each velocity field parameterised using the Haar wavelet series; furthermore the representation with a reduced number of coefficients allows for the further development of seismic tomography and migration methods using this parameterisation. iv