Travel Time Inversion in Seismic Tomography

The word tomography finds its origins in the two Greek words tomos, meaning section, and graphy, which translates as drawing. There are many different types of tomography used in many sciences such as medicine, biology, materials science and geology. The basic idea of tomography in all of its uses is to obtain a cross-section of an object which will then be used to infer various facts regarding the particular object’s internal structure. In processing seismic data the earth internal parameters of velocity and density play a critical role. Seismic imaging methods all require an accurate parameter estimation process. For imaging algorithms which are based on depth rather than time for the output, it is essential that the interval velocities be determined in a cellular type of model rather than the traditional layered model. The approach used in tomography is a natural for cellular seismic model building. In this paper we present a dipping layer, gridded cell, ray trace tomographic system built at Memorial University for determining reflection tomograms and well based tomograms. Based on Java it runs on both Windows and Linux machines and the code is open source which allows for modifications for research purposes. The second author is the primary developer of the code. More general systems are available but we feel the benefits of a graphical user interface and the open source code will allow for development of more sophisticated tools during the life of this project. Further, typically available codes are not written for parallel computation of the rays and the method used here is ideal for using hundreds, if not thousands of processors for the ray tracing and the linear algebra of the least squares problem. Both of these issues will be important when the seismic processing parameters are from three dimensional problems. We will illustrate the raytracing aspects of the three dimensional tomographic problem using the large screen visualization system in the Earth Sciences Department at Memorial University. As a part of the development effort we are build into the ray tracing methodology a mechanisms simulate converted waves, compute the relative amplitudes for compressional and shear waves in models that allow for acoustic, elastic, and density parameters. The research areas include allowing certain regions in the model to be anisotropic, highly fractured, or to be visco-acoustic in nature. In the following sections we review the notion of seismic tomography, how and why travel times are computed, the forward and inverse modeling problem, how a cellular model is developed, how the raytracing works, the linear algebra of the travel time equation, solving the least squares problem using conjugate gradients, why the matrix is sparse, and some examples of ray tracing using the Java code and an example of the user interface.