This thesis has several aspects related to the problem of basin modeling towards oil and gas exploration, and with two general divisions: parameter estimation, and pressure prediction. For the structure of this work, the first topic is related to velocity analysis and effective media, where estimated a distribution for the P wave velocity in time, the transformation to depth, and the use an effective model for the density and for the S wave velocity distributions. The reason for initially focusing on these estimations is because they represent one of the most basic information that one can have from the seismic domain, from where the other seismic parameters can be calculated, and from where the second part of this is totally based. The second topic is related to computing stress, strain and pressure distribution in the subsurface using the information from the P and S wave velocities and the density models, in order to localize areas of high and low pressures that act as natural suction pumps for the mechanics of oil and gas accumulation into productive zones and layers. We have highlighted this second part for the final work presentation, and call attention to the sensitivity of pressure mapping to the velocity and density variations. We also classify the first division as dedicated to the conventional seismic processing and imaging, and have clled the second division as post-imaging stressstrain-pressure prediction. As for the final aim of geophysics is to create images of the subsurface under different properties, the stress calculation only makes total sense for real data, and this makes mandatory the acquired seismic data be three component. As an important conclusion from the numerical experiments, we show that pressure does not have a trivial behavior, since it can decrease with depth and create natural pumps that are responsible for accumulating fluids. The theory of porous media is based on integral geometry, because this mathematical discipline deals with collective geometrical properties for real reservoirs. It was shown that such collective properties are namely for porosity, specific surface, average curvature and Gaussian curvature. For example, cracked media has, as a rule, small porosity, but very large specific surface area that creates anomalous high 𝛾 = 𝑣𝑆/𝑣𝑃 ratio, what means a negative 𝜎 Poisson coefficient. Another conclusion is related to calculating discontinuity in pressure between solid and fluid, what depends on the structure of pore space.
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