Kinematic artifacts in prestack depth migration.

Strong refraction of waves in the migration velocity model introduces kinematic artifacts¿coherent events not corresponding to actual reflectors¿into the image volumes produced by prestack depth migration applied to individual data bins. Because individual bins are migrated independently, the migration has no access to the bin component of slowness. This loss of slowness information permits events to migrate along multiple incident-reflected ray pairs, thus introducing spurious coherent events into the image volume. This pathology occurs for all common binning strategies, including common-source, common-offset, and common-scattering angle. Since the artifacts move out with bin parameter, their effect on the final stacked image is minimal, provided that the migration velocity model is kinematically correct. However, common-image gathers may exhibit energetic primary events with substantial residual moveout, even with the kinematically accurate migration velocity model

A Differential Semblance Criterion for Inversion of Multioffset Seismic Reflection Data

Mean-square error leading to least-squares inversion of multioffset reflection seismograms is insensitive to velocity trend information except in the immediate vicinity of a kinematically correct model. In contrast, differential semblance retains sensitivity to velocity trend changes over a wide range of models. The differential semblance criterion combines mean-square error with the mean-square differences of inverted models from datasets at neighboring shot positions (or offsets, or slownesses, ...). Differential semblance compares model estimates at nearby acquisition parameters which are similar even when the model velocity trends are incorrect. Because the method inverts the data, so that the estimated model amplitudes are meaningful, simple differences between the (unstacked) model estimates give a reliable measure of velocity error. A mathematical investigation indicates that the differential semblance criterion is smooth and convex over a large range of velocity models. Numerical simulation using synthetic data sets verifies this contention

Advanced High Resolution Seismic Imaging, Material Properties Estimation, and Full Wavefield Inversion for the Shallow Subsurface

Develop and test advanced near vertical to wide-angle seismic methods for structural imaging and material properties estimation of the shallow subsurface for environmental characterization efforts

The Plane-Wave Detection Problem

The plane-wave detection problem is: to estimate the incidence angle and waveform of a transient plane traveling wave, from samples recorded at a linear array of receivers. This simple problem shares several important mathematical features with other inverse problems of wave propagation, and is of interest in its own right as a model problem in ocean acoustic signal analysis. Straightforward formulation as a nonlinear least squares problem yields a nonconvex objective for which the minima are not stably dependent on the data. In contrast, an infeasible point formulation, in which the signal at each receiver is explained to some extent independently, proves to yield a smooth convex optimization problem with stable optima. Numerical experiments illustrate the theoretical results about the infeasible point approach, differential semblance optimization

Hilbert class library: A library of abstract C++ classes for optimization and inversion

AbstractAccording to the Object-Oriented Programming paradigm, a computer program should be organized around the fundamental objects it manipulates. In the C++ programming languages, these objects are embodied in classes. The Hilbert Class Library (HCL) is a collection of C++ classes designed for implementing numerical optimization algorithms in the context of Hilbert spaces. HCL includes base classes for defining vectors, linear operators, nonlinear operators and functionals, and related mathematical objects. Using these base classes, algorithms can be coded in a natural style that does not refer to application-specific details; nonetheless, the code can be applied to arbitrarily complex applications. Thus, HCL is intended to provide a way to bridge the often large gap between sophisticated numerical optimization routines and complicated simulation-based applications

Deflated Krylov Subspace Methods for Nearly Singular Linear Systems

This paper concerns the use of Krylov subspace methods for the solution of nearly singular nonsymmetric linear systems. We show that the Incomplete Orthogonalization Methods (IOM) in conjunction with certain deflation techniques of Stewart and Chan can be used to solve large nonsymmetric linear systems which are nearly singular

Transactional Workflows or Workflow Transactions?

Workflows have generally been accepted as a means to model and support processes in complex organizations. The fact that these processes re-quire robustness and clear semantics has generally been observed and has lead to the combination of workflow and transaction concepts. Many variations on this combination exist, leading to many approaches to transactional workflow support. No clear classification of these approaches has been developed, how-ever, resulting in a badly understood field. To deal w ith this problem, we de-scribe a clear taxonomy of transactional workflow models, based on the relation between workflow and transaction concepts. We show that the classes in the taxonomy can directly be related to specification language and architecture types for workflow and transaction management systems. We compare the classes with respect to their characteristics and place existing approaches in the taxonomy - thus offering a basis for analysis of transactional workflow support