Imaging of the Earth by Iterative Reconstruction Methods

Abstract

Cross borehole imaging (tomography) is an inversion technique that recreates the velocity field between two wells using observed travel times. The standard procedure is based on the decomposition of the cross hole area into a number of square-shaped cells. Two iterative techniques, the Algebraic Reconstruction Technique (ART) and the Simultaneous Iterative Reconstruction Technique (SIRT), are the basis for reconstructing images from observed travel times. These two techniques are compared to show the advantages and disadvantages for image reconstruction using synthetic data.

The initial velocity estimates required for these techniques was found to play a very important role in image resolution and in the speed of convergence to the solution. Here, three different initial velocity estimates are used including averaged, layered and estimated velocities. The layered initial velocity estimate was found to work best for both algorithms. The effects of different initial models on reconstruction are discussed for various models. In order to simulate real data, noise with zero mean and various standard deviations have been added to the travel times.

The results of this study indicate that the ART method converges more rapidly than the SIRT method, but the SIRT method is more stable in the presence of noise.