Least-squares wave-equation migration/inversion

This thesis presents an acoustic migration/inversion algorithm that inverts seismic reflection data for the angle dependent subsurface reflectivity by means of least-squares minimization. The method is based on the primary seismic data representation (single scattering approximation) and utilizes one-way wavefield propagators ('wave-equation operators') to compute the Green's functions of the problem. The Green's functions link the measured reflection seismic data to the image points in the earth's interior where an angle dependent imaging condition probes the image point's angular spectrum in depth.;The proposed least-squares wave-equation migration minimizes a weighted seismic data misfit function complemented with a model space regularization term. The regularization penalizes discontinuities and rapid amplitude changes in the reflection angle dependent common image gathers---the model space of the inverse problem. 'Roughness' with respect to angle dependence is attributed to seismic data errors (e.g., incomplete and irregular wavefield sampling) which adversely affect the amplitude fidelity of the common image gathers. The least-squares algorithm fits the seismic data taking their variance into account, and, at the same time, imposes some degree of smoothness on the solution. The model space regularization increases amplitude robustness considerably. It mitigates kinematic imaging artifacts and noise while preserving the data consistent smooth angle dependence of the seismic amplitudes.;In least-squares migration the seismic modelling operator and the migration operator---the adjoint of modelling---are applied iteratively to minimize the regularized objective function. Whilst least-squares migration/inversion is computationally expensive synthetic data tests show that usually a few iterations suffice for its benefits to take effect. An example from the Gulf of Mexico illustrates the application of least-squares wave-equation migration/inversion to a real-world dataset. The efficient implementation of the algorithm is a challenge and had to be confined to two spatial dimensions (i.e., 2-D earth). Fortunately, distributed computing accelerates the computational turnaround of least-squares migration/inversion greatly. Therefore, given the rapidly evolving computer technology, it is conceivable that 3-D least-squares migration/inversion will become amenable to a practical implementation in the near future.