Earth Resources Laboratory :: Abstracts

Nonlinear Refraction and Reflection Traveltime Tomography

Jie Zhang

Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on January 10, 1997 in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Abstract

We develop three traveltime techniques that utilize refraction/reflection data recorded on the surface. They include nonlinear refraction traveltime tomography, joint refraction traveltime migration and tomography, and joint nonlinear refraction and reflection traveltime tomography. These techniques are applicable to a large range of geological investigation problems, from imaging the shallow earth structure to deep crustal soundings. We implement these techniques on a regular velocity grid, which can well represent any complex velocity structure in the earth.

We first describe a wavefront raytracing algorithm for calculating the first arrival refractions and later reflections, and for downward continuing the traveltime curves for the refraction migration purpose. The method simulates wave propagation by expanding a wavefront in terms of traveltimes, accounting for various wave effects. In addition, it is more accurate and efficient than several existing methods.

We develop a nonlinear refraction traveltime tomography method that accounts for several fundamental physical issues in the refraction problem. The inversion jointly minimizes the misfits of the average slownesses (ratios of traveltimes to the corresponding ray lengths) and the apparent slownesses (derivatives of traveltimes with respect to distance). We apply the Tikhonov regularization method to obtain a stable solution. To measure the reliability of the solution, we perform uncertainty analysis and calculate its posterior model covariance by way of nonlinear Monte Carlo inversions.

To enhance resolution of the tomographic image when large velocity contrasts occur in the Earth, we conduct joint refraction traveltime migration and tomography. Refraction traveltime migration that downward continues the forward and reverse traveltimes reconstructs the location (image) of a refractor for a given velocity model, while traveltime tomography resolves a velocity structure with a curvature constraint constructed from the migration image. We present two algorithms to solve this joint imaging problem. Numerical experiments and real cases prove that both methods are useful for reconstructing a velocity model with sharp interfaces.

We also develop a joint nonlinear refraction and reflection traveltime tomography method on a regular-velocity grid. Similar to the nonlinear refraction traveltime tomography, we explicitly invert the average slowness and the apparent slowness data that are converted from the refraction and reflection traveltimes. The approach is beneficial to this joint inverse problem, because it modifies traveltimes associated with long rays and short rays in the refractions and the reflections to the same order of magnitude, and combines two types of data on the basis of their physical information rather than using an arbitrary weighting factor. We show that the inclusion of the first-arrival refractions can be very helpful to reduce the undermined features in the slowness field in the reflection traveltime problem.

For imaging the shallow earth, utilizing the first-arrival traveltimes is practical and reliable. Nonlinear refraction traveltime tomography is useful for imaging complex velocity variations. For cases with sharp refraction interfaces, the joint refraction traveltime migration and tomography proves more applicable. When we image the deep earth structure for which the deep reflections can be readily identified, performing joint refraction and reflection traveltime tomography appears to be more attractive.

We demonstrate applications to three real cases. The first case in South Boston, Massachusetts is to determine the bedrock topography in a complex near-surface area for an engineering project. The second real case is to image the shallow velocity structure surrounding the Bala Kimberlite which is partially exposed at the surface in Riley County, Kansas. Our interest is to understand the structure of the kimberlite plug in the subsurface. We apply nonlinear refraction traveltime tomography and joint refraction traveltime refraction traveltime migration and tomography techniques to both cases. The results are consistent with other geophysical information. The third case is to image the crustal structure of California Borderland using marine OSB data and joint refraction and reflection traveltime tomography technique. The results show that most of the anomalous variations seen in the traveltimes are due to the shallow complex velocity structure. The deep crust is relatively simple, and the Moho at the depth of about 23 km with slightly lateral variation is found along two survey lines.