The finite difference method consists in the numerical resolution of differential equations and one of its applications is a solution of the wave equations or elastodynamics, by replacing the partial derivatives in space and time by their approximations of finite differences. The present work consisted in the accomplishment of the seismic modeling using the method of the finite differences, to acoustic and elastic case. Then, we performed the seismic imaging, to acoustic case, in a model that simulates an iron ore deposit area of N4WS, located in the mineral province of Carajás, in the state of Pará. We found a heterogeneous, isotropic and bidimensional velocity model to acoustic and elastic cases. In order to generate the synthetic seismogram, we executed the program FDSKALAR, to acoustic case, and SOFI2D, to elastic case, using fourth-order approximation of the equation of acoustic and elastic wave in space and time. For a validation of the programs of finite differences and aid in the interpretation of the events, we compared the results with the travel times obtained by the ray theory. After the seismic modeling, we accomplished the processing of the data generate, using the open-source software package Seismic Unix, to obtain an image of the reflector contained in the mineral model. In this way, we searched a better understanding and control on the problems of seismic modeling and imaging, contributing to an interpretation of seismic data and understanding about a seismic wave propagation in environments where there are significant heterogeneities. In addition, we sought to demonstrate the application of seismic methods in the study and delimitation of mineral bodies.
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