At the University of Houston, most of my students work on some form of seismic interpretation topic. This can be fairly basic (horizon mapping in 3D seismic for CO2 sequestration) or very advanced (seismic simulation from flow simulator output, or deep amplitude anomalies in the Gulf of Mexico).
My published work includes a textbook, peer reviewed publications, dozens of meeting abstracts, and many general-audience articles (World Oil contributing editor for 2010). There are two central themes to my peer-review published body of work.
First is the broad field of wave propagation, including phenomena, numerical modeling, and inversion. The second theme is digital data analysis including seismic data processing, multichannel time series analysis, and image processing.
My earliest work centered on a wave equation framework for prestack partial migration (also known as dip moveout, or DMO), a theory that formed important middle ground between poststack and prestack migration during the 1980s as computer power was ramping up to handle the full prestack imaging problem. Earlier researchers had established the kinematics, or travel time, aspects of DMO, but amplitude was not previously related to the physics of wave propagation. A side benefit of my DMO work was an amplitude preserving relationship for inverse DMO that can be used for interpolation or regularization of prestack data.
In the theory of DMO amplitude, one comes across the idea of 2.5 dimensional wave propagation. The concept is a wave in the coordinate system of a 2D seismic line, but having accurate 3D amplitude behavior. In the course of my investigations, I discovered a 2.5D wave equation with exactly these properties. It turned out to be a form of the Klein-Gordon equation well known in quantum mechanics. It is not often one finds an unpublished, fundamental wave equation in the field of classical wave theory.
Another discovery relates to Rayleigh waves. There were three ways of computing the wave speed for the constant-parameter isotropic case: Analytically solve the Rayleigh polynomial, numerically solve it, or use a rough approximation that Rayleigh wave speed is 92% of the shear wave speed. The first two are tricky because the polynomial has multiple roots that may contribute to the solution, while the 92% rule is not accurate. I was able to expand the Rayleigh polynomial about the 92% rule and derive an expression for the wave speed that is accurate across the entire range of parameters encountered in seismic exploration. The new expression is far better than the 92% rule and more straightforward than computing Rayleigh's polynomial.
In 2002 I became interested in time-frequency methods and their application to seismic processing and analysis. This is the topic of my SEG Distinguished Instructor Short Course (DISC) to be given worldwide in 2012, including a book in preparation with the working title of Seismic Dispersion. Working in 2004 with PhD student Chun-Feng Li (now Tongji University), the continuous wavelet transform was used to generate a seismic attribute we termed SPICE (spectral imaging of correlative events). The idea is computation of a pointwise estimate of singularity strength (Hölder exponent) at every time level and every trace in a 2D or 3D migrated data volume. The result is a remarkable view of geologic features in the data that are difficult or impossible to interpret otherwise. SPICE was patented by the University of Tulsa and commercialized by Fairfield Industries.
In a series of papers between 2006 and 2009 I worked with Saudi Aramco colleagues on layer-induced anisotropy, anisotropic prestack depth migration, and near-surface parameter estimation. In particular, I was able to show modern full wave sonic logs, that deliver both P-wave and S-wave velocities, are ideally suited to estimation of anisotropy parameters through a method originally published by Backus in 1962. The estimated anisotropy parameters were shown to improve prestack depth migration results.
A fundamental area of current research is carbon capture and sequestration. In 2008 I stepped in as principal investigator on a CO2 sequestration site characterization project and have since been lead CO2 sequestration researcher at the University of Houston. Our DOE-funded study site in Ness County, Kansas, involves 3D seismic, over 140 wells, digital well logs, production data, etc. My CO2 research team has progressed from seismic interpretation through geological model building, to scenario testing (cap rock integrity, fault and well bore leakage), and flow simulation spanning several hundred years. Site characterization and monitoring will rely heavily on geophysics as carbon capture begins on a large scale in the United States and worldwide. In 2010 I initiated research coordination with the CIUDEN carbon capture and sequestration project in Spain, one of the largest in Europe.
Time-frequency methods are central to ongoing areas of research. In a recent paper with B. Bodmann, we re-examined a 1937 result by A. Wolf showing that reflection from a vertical transition zone results in a frequency-dependent reflection coefficient. Using modern analytical tools and methods, we showed how such phenomena could be detected and mined for important information. Another significant time-frequency application I developed is direct imaging of group velocity dispersion curves for observed data in shallow water settings around the world. Phase velocity dispersion curves have been imaged since 1981, but this was the first reported method to image the group velocity curves that contain rich information about seafloor properties.
A theory of full-bandwidth signal recovery from zero-crossings of the short-time Fourier transform is now under development in collaboration with B. Bodmann. The first paper was delivered at a 2010 American Mathematical Society meeting.
My research will continue in the broad field of advanced seismic interpretation, wave propagation, signal analysis, and time-frequency methods to develop new tools and deeper insight into petroleum seismic data, CO2 sequestration problems, and near surface characterization.