Advancements in Full Wavefield Migration

Abstract

Seismic imaging is a method for generating images of the subsurface of the Earth without the need to drill down to observe it directly. Using a seismic source, high-amplitude acoustic waves are generated, which propagate through the Earth. When these waves encounter interfaces between different layers, part of their energy is reflected, traveling back upwards. At the surface, these scattered waves are recorded using an array of sensors. These recorded wavefields are then used as input for a seismic imaging algorithm, which attempts to reconstruct an accurate image of the subsurface based on these measurements.
While many different seismic imaging methods exist, this thesis focuses specifically on Full-Wavefield Migration (FWM). FWM is a least-squares migration method, based on iteratively updating the image in order to minimize the misfit between the recorded data and the forward modelled wavefield at the surface. Using this iterative approach, FWM is able to incorporate multiple scattering effects into the imaging process, increasing the accuracy of the resulting images. Also, by using explicit convolutional operators based on the one-way wave equation, the computational cost of FWMis reduced compared to alternative iterative imaging methods based on finite-difference modelling.
In this thesis, we describe a number of recent advancements to the FWM method. Our main focus is the extension of the FWM method to include converted waves. In order to take these effects into account, we need accurate reflection and transmission operators. However, the true, elastic reflection and transmission operators are notoriously non-linear, making them difficult to work with. Therefore, we introduce a novel set of approximations of these operators, which we name the extended Shuey approximations. To benchmark these approximations, we apply them in a simple, 1.5D scenario. This test shows that the extended Shuey approximations yield improved results for forward modelling and imaging, compared to the conventional Shuey approximation.
We then use these extended Shuey approximations to derive accurate reflection and transmission operators for the 2D case. Combining these operators with the existing theoretical framework of FWM we develop a robust imaging algorithm which takes converted waves into account. We then apply this algorithm, which we name elastic FWM, to two synthetic models. We show that, for these models, the elastic FWM method out-performs the conventional, acoustic FWM method. We also demonstrate that, using this method, additional information regarding the elastic medium parameters of the subsurface can be recovered.
Finally, we examine the known issue of slow convergence for the conventional, acoustic FWM algorithm. We introduce a novel preconditioner, based on approximating the pseudo-inverse using Proper Orthogonal Decomposition (POD). Using this preconditioner, we demonstrate improved convergence for the synthetic Marmousi model and a field data set from the Vøring basin in Norway.