In order to explore and exploit natural resources in México, it is required high performance technology and engineering human capacity, with both it is creating methodologies to offer a better quality results. The exploration of natural resources, it is the area of knowledge in which geophysics and geology are practiced, however for these two sciences to be understood in the same space, subsurface images are needed. So, implementing an efficient method to avoid noise signals caused by the same time reverse migration algorithm is the method of absorbing borders. This method proposes to subdivide the seismic image into borders in order to obtain only the propagation and retro-propagation signal without spurious signals. This implementation in the oil industry is necessary to generate greater effectiveness in the seismic inversion and thus the generation of seismic images with a better interpretation. Without this implementation, we have worked in the oil industry for more than 30 years, which is why it is innovative for our oil field projects in Mexico to carry it out. It can be said that when referring to the images in depth we are talking about deep migration PSDM (Pre-Stack Depth Migration) and its elements are input data, pre-processing, migration algorithm and speed model. Reverse-time migration (RTM) is a pre-stacking migration technique that, unlike the rest of migrations, ignores simplifications and uses the full-wave equation . In the past decades a great variety of absorbent borders have been developed, especially for the modeling of the seismic wave. Subsequently, among the various attempts to improve the classical PML, (Kuzouglu, 1996) and, (Roden, 2000) developed the convolutional PML or CPML (Convolutional Perfectly Matched Layer) for the Maxwell equations and were adapted to the equations of elastodynamics by Komatitsch and Martin, ( ). The latter are used to simulate the direct problem in the present work. The development of the reversal algorithm in time, consisted in the implementation of absorbent borders in the different domains of the seismic image. This implementation considerably improves the seismic image compared to the inverse algorithm without absorbing borders and even with absorbent borders not as elaborate as the development in this thesis work. By means of the implementation of convolutional absorbent borders, it modifies the way of thinking of the current algorithms of programming, for which this thesis work is a clear example of the algorithmic revolution applied to the geophysics of the last decade.


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