Richard Gibson

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.

Ray methods are useful for the calculation of Green's tensors for three-dimensional, anisotropic media because they are much faster than more exact algorithms such as finite differences. At the same time, there are significant challenges because of difficulties in implementation, particularly those related to the solution of the two-point problem. Classical shooting methods often either fail to determine a solution

... the eikonal equations using finite difference, graph theoreti-cal, or other approaches to rapidly compute traveltimes throughout the volume of a regular discretization of an earth model (Vidale, 1990; Van Trier and Symes ... dxi dτ = aijkl pl gj gk dpi dτ = − 1 2 ∂anjkl ∂xi pn pl gj gk. ...

... approaches to rapidly compute traveltimes throughout the volume of a regular discretization of an earth model (Vidale, 1990; Van Trier and Symes ... ODEs) that are integrated to determinate ray trajectories and traveltimes (Cervený, 1972; Cervený, 2001): dxi dτ = aijkl pl gj gk dpi ...

The propagation of seismic waves through heterogeneous sediments is a topic of major importance , particularly in reservoir exploration. In order to develop a better understanding of wave propagation through sediments, we employ a numerical model based on the discrete element method (DEM) used in modeling granular materials. An advantage of this method is that one can readily explore a large range of heterogeneity in grain properties, such as size and bulk modulus, as well as a variety of spatial distributions of those properties. Discrete element models (e.g. Cundall and Strack, 1979) have been used to study the deformation of granular materials under a wide variety of conditions. In this method, a small (103 to 104) set of simple (2D circular) model grains is defined. The pore space between the grains is taken to have zero bulk modulus, so these models represent drained sediments. Grain interact with specified elastic and frictional forces. The elastic forces can be both repulsive...

Marine multi-channel seismic (MCS) profiles provide important constraints on crustal structure beneath the sea floor. MCS data usually provide good images of the upper part of the oceanic crust, especially in sedimentary layers. In contrast, it is often difficult to interpret deeper layers, especially those within the igneous basement, which is often nearly seismically transparent. That difference in interpretability occurs because sediments typically have continuous, well-layered and easily-traced structural features, whereas volcanic materials are characterized by smaller features with poorer lateral continuity and often with weak impedance contrasts. Since the basement tends to create weaker reflections, the signal-to-noise ratio decreases, creating additional difficulties that can be exacerbated by the presence of multiples generated by the sea floor and other sources of noise. However, it is still important to characterize the basement accurately to better understand oceanic cr...

Seismic velocities in rocks increase with pressure, a pattern often explained by changes in cracks within the rock volume. Specifically, the width of microcracks will decrease, increasing the contact area of crack surfaces, which in turn leads to increased stiffness of the crack. This causes P- and S-wave velocities to increase, and having accurate models of this behavior is important in many applications where it is important to related stress changes and observed seismic velocities, such as investigations of both fault zones and changing conditions in geothermal fields or hydrocarbon reservoirs. Several different models have been proposed to explain and quantify the relationship between confining pressure and the physical properties of cracked rocks, including a number of solutions describing cracks as ellipsoidal voids (penny-shaped cracks) of with varying aspect ratios that close at different pressures. Differential effective medium theories based on this model will typically us...

ABSTRACT The sequestration of CO2 into geologic formations, specifically existing and depleted oil and gas reservoirs, is a promising solution for reducing environmental hazards from the release of greenhouse gases into the earth's atmosphere. A critical component of long-term sequestration will be our ability to adequately monitor the movement of CO2 fronts in the subsurface. In this article, we examine the viability of time-lapse seismic monitoring using an integrated modeling of fluid flow, including chemical reactions and seismic response. Modeling of CO2 injection is complicated by the various interactions between CO2, reservoir fluids, and the minerals in the formation. These interactions change fluid and bulk rock properties with time, which in turn impact the seismic signatures. We perform a comprehensive simulation of the gas injection process accounting for the phase behavior of CO2-reservoir fluids, the associated precipitation/dissolution reactions, and the accompanying changes in porosity and permeability. The simulation results are then used to model the changes in seismic response with time. The general observation is that gas injection decreases bulk density and wave velocity of the host rock system. Seismic amplitude attributes therefore change with time as well, and these effects provide a tool for tracking the movement of the CO2 front. Analysis of the results also confirms that much of the change can be attributed to chemical effects that should therefore be considered in studies of long-term sequestration projects.

Summary Seismic data provide essential information for guiding reservoir development. Improvements in data quality hold the promise of improving performance even further, provided that the value of these data exceeds their cost. Previous work has demonstrated value-of-information ...

... In contrast, finite difference solutions of the eikonal equation and graph theoretical methods solve this problem by computing travel times on uniform grids (Vidale, 1990; Van Trier and Symes, 1991; Moser, 1991; Zhang and ... dxi dτ = aijkl pl gj gk dpi dτ = − 1 2 danjkl dxi pn pl gj gk ...

Hybrid Ray-Propagator Matrix Modeling of Complex Stratified Reservoirs Hung-Liang Lai∗ and Richard L. Gibson, Jr., Texas A&M Univ., College Station ... Instead of the direct com-putation of the plane layer responses, the reflectivity method (Kennett and Kerry, 1979; Booth and ...

Time-lapse seismic monitoring of CO 2 injection into a hydrocarbon reservoir can be important for either enhanced recovery or CO 2 sequestration tasks. In the latter case, over long time periods, the interaction of CO 2 with in-situ brine and host rock minerals ...

Knowledge of the orientation and spatial distribution of fractures in rocks is important for predicting the flow of fluids. Masihi et al.(2007) developed a new method of modeling these distributions beginning with theoretical results from the physics of fracturing. We ...

VSP data were collected in the Larderello geothermal field in Italy in order to attempt to image reflective features below the depth of current geothermal production with the goal of extending and better developing the reservoir. The shallow geologic structures, which are ...

We investigate the sedimentary and volcanic structure of the Tuamotu Plateau with multichannel seismic, seismic refraction, and gravity data along a ship track crossing the plateau near 15°S. The volcanic basement of the central portion of the plateau is capped with a 1 to 2-km-thick sediment layer composed of two compositional sequences. The uppermost sequence, with semblance-derived P wave velocities