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In this work we apply 2-dimensional seismic tomography techniques to determine the velocity model of the near surface strata in data from the Catatumbo area in Colombia, a zone of complex subsurface. Seismic tomography includes linear and non-linear techniques. Within the linear ones there are the Algorithmic Reconstruction Technique and the Simultaneous Iterative Reconstruction Technique, which require initial velocity models very near to the true velocity to ensure exactness and convergence. On the other side, the non-linear techniques have better theoretical principles and are less based on the initial model, but perhaps require more computational resources. The techniques used are applied to only refraction data. The ray tracing needed by the tomographic algorithms is performed using a hybrid technique based in the minimum travel time problem of graph theory and the ray bending technique. With these tomographic techniques it is also possible to obtain a velocity model of deep strata.

We implemented an elastic reverse time migration based on a coupled system of pure P-and S-wave particle velocities. The system utilizes finite difference wavefields for P-and S-wave particle velocity in vertical and horizontal directions (vpx , vpz , vsx and vsz), and for 2-D displacement divergence and curl (A and B). In contrast with the usual elastic imaging conditions that cross-correlates vertical displacements to obtain the P-wave image and vertical and horizontal displacements to obtain the converted wave image, we devised P-and S-wave imaging conditions using the adjoint state method. The resulting imaging conditions cross-correlate spatial derivatives of A and B wavefields with P-and Swave displacements. The proposed migration shows a better reflector definition and more balanced amplitudes than the usual vertical and horizontal particle displacement cross-correlations.