Ursula Iturrarán-Viveros

The Classic Garvin’s Problem Revisited

The exact analytical solution for surface displacements due to a volumetric line source disturbance buried in an elastic homogeneous and isotropic half- space is attributable to W. W. Garvin. These results are in the time domain but the final expressions are only valid for a step-time variation of the load. We give a summary of Garvin’s work and extend it for virtually any given time signal. By analytical and numerical integration of the exact analytical solution we implicitly consider a ramp source function (this simple mathematical trick allows for regular waveforms). This solution can be used as a practical tool to test numerical techniques. Some examples are presented, and synthetic seismograms and polarigrams are displayed.

The Gamma test applied to select seismic attributes to estimate effective porosity

We discuss the use of the Gamma test as a powerful tool for selecting the best combination of seismic attributes to predict porosity (φe). The data consists of four wells with conventional logs which tie to a 3-D seismic volume. A formation evaluation was done. Both well-logs and seismic data are used to train an artificial neural network to get estimates of effective porosity, φe. The validation based on leave-one-out was poor. We then generated a complementary set of synthetic data (from the original well-log data), varying the effective porosity and applying the Gassmann’s equation for fluid substitution. The synthetic well-logs we obtained were used to train the neural networks giving better validation and more accurate results.

Scattering of SH Waves in Media with Cracks and Elastic Inclusions

We study scattering effects caused by 2-D cracks and elastic inclusions. To this aim we use two different numerical approaches. On the one hand we apply the Indirect Boundary Element Method (IBEM) to model the diffraction of SH waves by arbitrary shaped, zero-thickness cracks. We validate the IBEM with an analytic solution for a simple case. On the other hand we use the Direct Solution Method (DSM) to study scattering of SH waves by elastic inclusions. The DSM is based on solving the weak form (Galerkin formulation) of the elastic equation of motion. Although both methods work in the frequency domain, we show results in the time domain obtained by means of the Fast Fourier Transform.