Modeling and Inversion of Scattered Surface waves

In this thesis, we present a modeling method based on a domain-type integral representation for waves propagating along the surface of the Earth which have been scattered in the vicinity of the source or the receivers. Using this model as starting point, we formulate an inversion scheme to estimate properties of scattering objects close to the surface of the Earth. The objectives of the resaerch are to develop an efficient and accurate modeling method for scattering of seismic waves by 3D near-surface heterogeneities close to the receivers or sources and to develop an inversion algorithm to reconstruct scattering-medium parameters from scattered surface waves. Model studies show that we accurately model near-surface scattering effects, which can seriously distort the wave fronts of upcoming reflections. Our method may therefore help in understanding this problem which is of particular interest for the oil industry as the upcoming wave fronts contain the primary information for making images of subsurface structure. For further validation, we compared our modeled data with experimental data collected with similar geometries at the Colorado School Mines (CSM). We have also applied our inversion algorithm to several synthetic data sets. We find that we can get a good estimate of the location and strength of contrasts up to a depth of about one Rayleigh wavelength.Electrical Engineering, Mathematics and Computer Scienc

A new iterative solver for the time-harmonic wave equation

The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can be solved efficiently by a direct method. In three dimensions, direct methods cannot be used for problems of practical sizes because the computational time and the amount of memory required become too large. Iterative methods are an alternative. These methods are often based on a conjugate gradient iterative scheme with a preconditioner that accelerates its convergence. The iterative solution of the time-harmonic wave equation has long been a notoriously difficult problem in numerical analysis. Recently, a new preconditioner based on a strongly damped wave equation has heralded a breakthrough. The solution of the linear system associated with the preconditioner is approximated by another iterative method, the multigrid method. The multigrid method fails for the original wave equation but performs well on the damped version. The performance of the new iterative solver is investigated on a number of 2D test problems. The results suggest that the number of required iterations increases linearly with frequency, even for a strongly heterogeneous model where earlier iterative schemes fail to converge. Complexity analysis shows that the new iterative solver is still slower than a time-domain solver to generate a full time series. We compare the time-domain numeric results obtained using the new iterative solver with those using the direct solver and conclude that they agree very well quantitatively. The new iterative solver can be applied straightforwardly to 3D problems.Electrical Engineering, Mathematics and Computer Scienc