Extended Imaging and Tomography under Two-way Operators

Seismic images reconstructed by migration from seismic data recorded at the surface represent the earth structure at every location in the subsurface. The data are remapped into the subsurface by using a wave equation and an estimate of the earth velocity. The velocity model is of great importance for obtaining accurate seismic images and for understanding the subsurface reservoir properties and conditions. In this thesis, I focus on structure and velocity estimation from surface seismic data. In order to invert for the velocity model, I seek to improve the synchronization and consistency of the extrapolated surface seismic data inside the subsurface. I use correlation functions to measure the synchronization of seismic wavefields with extended images in the image-domain, and with local correlations in the data-domain. Both correlation methods are conceptually similar and yield, after penalization, the estimate of synchronization. The penalty operator objective is to highlight areas of the correlation gathers that need to be improved through optimization of the model parameters. I incorporate, in both subsurface and data correlations, a penalty operator that takes into account the geometry of the data and its bandwidth. Another important aspect of the subsurface imaging process are the wavefields themselves. Most of the wavefields used in imaging and tomography disregard internal and surface-related multiples. Conventional methods fail to handle multiple scattered waves; hence, the multiples act as noise in the conventional and extended images producing an important bias towards low velocities as an outcome. I compute extended images using wavefields reconstructed with single scattering assumptions and wavefields that correctly handle multiple scattered waves. I show how the extended images with multiples contain similar sensitivity to the background velocity model as the conventional extended images. Additionally, the obtained extended images do not introduce a bias towards low velocities as is the case with conventional extended images.