Imageamento sísmico: aplicação eficiente da RTM causal, FLSRTM com algoritmos SVD estocásticos e WEM baseado na aproximação de Jacobi-Anger.

Abstract

This thesis addresses the development of techniques related to seismic migration, aiming overcome the limitations and challenges present in traditional methodologies. The three chapters of this work present solutions that enhance computational efficiency, accuracy in seismic imaging, and the ability to handle complex subsurface models. In chapter 1, we focus on the separation of the wavefield into upgoing and downgoing components, a crucial step in the processing of multicomponent data, wavefield propagation, and seismic imaging. We propose an alternative method for computing the analytical wavefield using the first-order partial equation in time, solving the wave equation only once. This approach allows for the explicit separation of wavefields at each time step, making it more computationally efficient and enabling the application of the causal imaging condition in reverse time migration (RTM). Results from synthetic models indicate that the proposed method achieves a decomposition similar to that obtained by the conventional method, which requires two \-propagations, with potential applications in 3D cases. Moreover, the method effectively removes low-frequency noise present in RTM images that use the cross-correlation imaging condition. In chapter 2, we investigate frequency-domain least-squares RTM (FLSRTM), which is capable of producing high-resolution reflectivity models. However, storing the Green's functions needed for gradient computation and the scattered wavefield via Born modeling may be unfeasible due to their size. We propose a FLSRTM scheme using low-rank Green's functions obtained through randomized (rSVD) and compressed (cSVD) singular value decomposition algorithms. These algorithms allow for efficient storage of Green's functions in memory, using less space and reducing computational time. Evaluations on synthetic models demonstrate that the proposed scheme generates migrated sections identical to those produced by the FLSRTM scheme using the original Green's functions while utilizing less memory and computational time. In chapter 3, we address the limitations of conventional depth migration operators based on downward continuation of the acoustic wavefield, such as the undesired generation of evanescent waves, imaging in media with strong velocity contrasts and steeply dipping reflectors, and the stability of the one-way propagator. We propose a depth migration algorithm based on an one-way wave equation that is both stable and efficient. To achieve this, we use a spectral projector to suppress evanescent modes from the Helmholtz operator and apply the coupled Schulz iterative scheme to compute the square root of this filtered operator. Finally, we introduce the Jacobi-Anger expansion to approximate the exponential matrix operator, enabling the stable construction of the propagator. Impulse response tests, as well as field data applications, demonstrate that our algorithm is more accurate and effective for imaging in media with strong lateral velocity variations, surpassing the quality of images obtained by conventional methods.