Abordagens para imageamento eficiente na inversão acústica linear e não-linear

Abstract

Attempts to obtain information from the Earth's subsurface usually require accurate numerical simulations of the wave equation, essential in the inversion processes which has as final goal the construction of the velocity model or the seismic imaging. In this thesis, topics are addressed that aim to make both the linear inversion, which uses the Born approximation as well as the nonlinear inversion, which uses the complete wave equation more efficiently or can produce better resolved images when compared to conventional methods. In the nonlinear inversion case, the question addressed here is based on its application to a reduced portion of the velocity model, a common situation where the geoscientist is interested in the variations of physical properties in the vicinity of the reservoir, and how these variations occur in subsequent surveys, such as in 4D seismic analyses, for example. Comparing two different strategies to calculate the wavefield locally, it was noted that calculating it in a numerically exact way did not bring significant improvements, when compared to inversion that neglects iterations of the local wavefield with the external model, being more sutable to stop at the simplest implementation of the finite differences injection method. On issues addressed to improve performance of the least-squares reverse time migration, two ways of improving the spatial resolution were addresed, the first focused on using the directional wavefield in conjunction with the commonly used pressure field. Since the adjoint of the Born modeling operator when properly handling this directional data, uses the energy of the receiver ghost during imaging, attenuating the noise commonly seen in data with low receiver coverage. This technique has been applied before for conventional reverse time migration and for the full waveform inversion, this thesis extends this approach to the least-squares reverse time migration. The second proposed approach to accelerate convergence also in the least-squares reverse time migration, consisted of applying a stochastic optimizer that takes into account an approximation of the Hessian, and was originally proposed for machine learning problems. In this case, the Devito framework was used, as it is capable of generating as efficient code involving the discretization of differential equations, including the use of GPUs. Being Devito written in Python language makes it convenient to use it along with techniques involving the quite popular machine learning.