Paul E. Murray

High-resolution multicomponent seismic imaging of deepwater gas-hydrate systems

Multicomponent seismic data have unique value for studying near-seafloor geology in deepwater environments. When properly processed, PP (compressional) and PS (converted-shear) images made from multicomponent seismic data acquired in deepwater with seafloor sensors show near-seafloor geology with impressive detail. These high-resolution images are invaluable for studying deepwater gas-hydrate systems.

Finite element analysis of diffusion with reaction at a moving boundary

Abstract We consider the model problem of mass transport by diffusion with chemical reaction at a moving boundary. The objective is to model the chemical process by predicting the location of the boundary as the reaction proceeds in time. A finite element analysis is formulated in one dimension using moving elements to follow the boundary motion, and an iterative linearization method is developed to uncouple and solve the diffusion and reaction equations. The semidiscrete system for the transport process is integrated using a predictor-corrector scheme and its accuracy and stability are examined in numerical experiments. Numerical results are compared with an analytic solution for the quasi-steady case in which diffusion is very rapid in comparison to reaction and to a perturbation solution for the unsteady case. Other supporting numerical studies are made to examine the sensitivity of the solution and boundary motion to changes in diffusion and reaction rate for both linear and nonlinear reactions.

Depth registration of P-wave and C-wave seismic data for shallow marine sediment characterization, Gulf of Mexico

Multicomponent seismic data, combining P-wave and converted P-to-SV wave (C-wave) wavefields, provide independent measurements of rock and fluid properties. Unlike P waves, C waves are minimally affected by changes in pore fluids, and in cases of azimuthal anisotropy, will be split into two modes (fast and slow) with differing polarization. The 4C, 3D ocean-bottom cable (OBC) multicomponent seismic data discussed here were acquired in shallow water (<300 ft) offshore Louisiana over approximately 455 miles2 (Figure 1). Because these data are still being marketed to interested oil and gas operators, only data above targeted oil and gas reservoirs (<5000 ft) were used. The P-wave migrated data extend to only 1 s and the C-wave migrated data volume to only 2 s.

Determination of interfacial stress during thermal oxidation of silicon

We develop a theoretical model to obtain the stress in oxide films occurring during thermal oxidation of silicon. The model results in a prediction of 4.5×109 dyn/cm2 for the interfacial stress, in excellent agreement with laboratory measurements. Moreover, we establish generally that the interfacial stress is proportional to 1−γ, where γ is the molar volume ratio of reactant to product. For silicon oxidation, γ=4/9, and the resulting stress is compressive.

Evaluation of deepwater gas-hydrate systems

The worlds offshore continental margins contain vast reserves of gas hydrate, a frozen form of natural gas that is embedded in cold, near-seafloor strata. Published estimates suggest that the energy represented by gas hydrate may exceed the energy available from conventional fossil fuel by a factor of 2 or more. Understanding marine hydrate systems has become critical for long-term worldwide energy planning. Groups in several nations are attempting to evaluate the resource and to define seafloor stability problems across hydrate accumulations.

Multicomponent seismic data registration for subsurface characterization in the shallow Gulf of Mexico

Using multicomponent ocean-bottom seismic technology, it is possible to obtain robust estimates of several subsurface parameters. We apply an automatic data registration (warping) algorithm to find a mapping between P-wave and convertedwave migrated images. The algorithm improves the matching of the two seismic volumes obtained by previous manual interpretation. There are two main products of this process. First, it improves a combined interpretation of the gas cloud zones that are obscured in the conventional one-component (P-wave) seismic images. Second, interval Poisson ratios get extracted directly from the warping function. This extraction provides a petrophysical characterization of the subsurface at a resolution unobtainable by other methods. Introduction Multicomponent seismic exploration with ocean-bottom technology opens new possibilities for improving seismic imaging and for extracting valuable additional information about subsurface physical characteristics (Stewart et al, 2003). The benefits of using multicomponent data have been proven for imaging through gas clouds and identifying shallow gas hazards (Granli et al, 1999; Englehart et al, 2001; Knapp et al, 2001). Joint interpretation of multiple image components (P-P and P-S images) depends on our ability to identify and register reflection events from similar reflectors. This task is especially challenging in shallow sediments, where the high ratio of Pand S-velocities causes large differences in the corresponding traveltimes. DeAngelo et al (2003) describe a careful strategy of joint P-P and P-S interpretation with application to subsurface characterization in the shallow Gulf of Mexico. In this study, we extend the registration procedure with an accurate automatic algorithm for representing P-S reflection events in the corresponding P-P time. By examining the algorithm performance on simple synthetic data, we observe that the differences in the frequency content of the P-wave and converted-wave data have a major impact on the registration accuracy. We implement a non-stationary spectral balancing method to take these differences into account. Balanced images are then automatically registered (warped) to estimate a point-by-point correlation function. The time derivative of this function produces the time-variable ratio of the P and S seismic velocities. This ratio and the related Poisson ratio are major physical attributes useful for interpreting subsurface structures. Our method enables extracting them directly from time-migrated P-P and P-S images. Application of this technique to data from the Gulf of Mexico reveals the structure of sediments around shallow gas clouds with a resolution unobtainable by other methods. Theory If we denote a P-P seismic image as a function of the vertical P-P traveltime t as P(t) and the corresponding converted-wave image as a function of the vertical P-S traveltime τ as C(τ), then the relationship between the two images can be expressed as P(t) ≈ a(t) C(w(t)) , (1) where w(t) is the warping function establishing the correspondence of reflection events in the two images, and a(t) is the amplitude gain function compensating for the difference in reflectivity. We assume the reflection events to be correctly positioned laterally in the migrated images so that the differences can be explained by vertical transformations only. The depth-dependent ratio of the P and S velocities expressed in the P-P traveltime coordinate is simply related to the derivative of the warping function γ(t)= 2 w’(t)-1. (2) Equation (2) is usually applied in the form of an interval relationship γ = 2 ∆τ/∆ t – 1 for a layer of time thickness ∆ t (Stewart et al, 2002). It extends naturally to the continuous case, providing continuous depth-variable values of the interval γ that convert into related Poisson’s ratio σ, as follows: σ(t) = 1⁄2 (γ2(t)-2) / (γ2(t)-1) (3)

Defining P-wave and S-wave stratal surfaces with nine-component VSPs

Nine-component vertical seismic profile (9C VSP) data were acquired across a three-state area (Texas, Kansas, Colorado) to evaluate the relative merits of imaging Morrow and post-Morrow stratigraphy with compressional (P-wave) seismic data and shear (S-wave) seismic data. 9C VSP data generated using three orthogonal vector sources were used in this study rather than 3C data generated by only a vertical-displacement source because the important SH shear mode would not have been available if only the latter had been acquired. The popular SV converted mode (or C wave) utilized in 3C seismic technology is created by P-to-SV mode conversions at nonvertical angles of incidence at subsurface interfaces rather than propagating directly from an SV source as in 9C data acquisition.

Perturbation analysis of the “Shrinking core”

Abstract An improved perturbation analysis for the shrinking-core model describing diffusion and reaction for combustion of a spherical “particle” is developed. The analysis employs several transformations to recast the problem to a form suited to perturbation solution using regular expansions for concentration and core boundary in terms of a small parameter. Results are compared with highly accurate numerical solutions using finite elements and shown to be a slight improvement over an earlier approximate perturbation result. This improved analysis and the finite-element solution are new and show that the earlier results appear adequate for a representative problem.

Estimating Pore Pressure Using Compressional and Shear Wave Data from Multicomponent Seismic Nodes in Atlantis Field, Deepwater Gulf of Mexico

Summary Pore pressures for the shallow sub-seafloor sediments at the Atlantis field are estimated by analysis of P and S wave velocities observed seismic data recorded by a patch of ocean-bottom multicomponent nodes. A modified Eaton’s algorithm for pressure prediction is applied, and estimated overpressure locations are compared to known hazardous shallow water flow zones evaluated from a batch-set drilling project.

OBC Sensor Response and Calibrated Reflectivity

Summary Given deep-water OBC data, we can combine hydrophone (P) and vertical-geophone (Z) data to separate upgoing and downgoing acoustic wavefields. By using the downgoing wavefield to estimate the seismic wavelet, we can recover compressional-wave reflectivity and provide an acoustic impedance log for the near-seafloor sedimentary section. This procedure requires the calibration of geophone response to hydrophone response with an appropriate matching filter (z2p). P and Z data containing only upgoing energy can be provided in several ways to estimate z2p and p2z filters. Alternatively, the multiple/primary ratio (in the frequency domain) can be used to obtain calibrated reflectivity from the hydrophone alone or from the geophone alone, with no sensor calibration required. We apply these methods to a deep-water OBC line. We obtain consistent results by all of the methods. By combining low-frequency (5–70 Hz) z2p filters based on energy arriving before the direct arrival, with high-frequency (25–180 Hz) z2p filters based on near-offset reflection data, we can provide broadband (5–180 Hz) calibrated reflectivity and impedance of shallow seafloor sediments.