58 GS11 Abstracts

58 GS11 Abstracts IP1 tional perspective. Multiscale Model Reduction Techniques for Flows in High-contrast Heterogeneous Media and Appli- Jörn Behrens cations KlimaCampus University Hamburg The development of numerical algorithms for simulations [email protected] of flow processes in large-scale highly heterogeneous porous formations is challenging because properties of natural ge- ologic porous formations (e.g., permeability) display high IP3 variability and complex spatial correlation structures which Recent Advances in Full Waveform Global Seismic can span a hierarchy of length scales. It is usually necessary Tomography of the Earth’s Mantle to resolve a wide range of length and time scales, which can be prohibitively expensive, in order to obtain accurate pre- Over the last 20 years, several generations of global tomo- dictions of the flow, mechanical deformation, and transport graphic models of the earth’s mantle elastic structure have processes under investigation. In practice, some types of been developed, relying on simple theoretical approxima- coarsening (or upscaling) of the detailed model are usually tions to the 3D wavefield (i.e. ray theory and first order performed before the model can be used to simulate com- normal mode perturbation theory). Now, it is possible to plex processes. Many approaches have been developed and compute accurate synthetics in spherical geometry for ar- applied successfully when a scale separation adequately de- bitrary 3D structures using numerical approaches, such as scribes the spatial variability of the subsurface properties the Spectral Element Method, which is particularly well (e.g., permeability) that have bounded variations. The suited for global waveform tomography. The challenge has quality of these approaches deteriorates for complex het- been shifted from theoretical limitations to the length of erogeneities without scale separation and high contrast. In computations involved. I will discuss and illustrate current this talk, I will describe multiscale model reduction tech- steps towards the development of next generation, high res- niques that can be used to systematically reduce the de- olution whole mantle models. grees of freedoms of fine-scale simulations and discuss ap- Barbara Romanowicz plications to preconditioners. Numerical results will be University of California, Berkeley presented that show that one can improve the accuracy [email protected] of multiscale methods by systematically adding new coarse basis functions and obtain contrast-independent preconditioners for complex heterogeneities. IP4 Yalchin Efendiev Computational Challenges in Applications of Cou- Dept of Mathematics pled Reservoir Geomechanics Texas A&M University Recent years have seen dramatic increase in the application [email protected] of coupled hydro-thermo-mechanical numerical solutions to petroleum industry. In this context they are often referred IP2 to as Coupled Reservoir Geomechanics, and involve coupled solution of multiphase, thermal flow in porous me- The Role of Applied Computational Mathematics dia, stress and deformation, and fracture mechanics. This in the end-to-end Near-field Tsunami Early Warn- growing discipline encompasses diverse problems such as ing System in Indonesia wellbore stability, sand production, hydraulic fracturing, In the aftermath of the 2004 Indian Ocean Tsunami, the compaction and subsidence, fault reactivation etc. Such German Federal Government funded the development of a applications invariably involve large, complex fields and new near-field tsunami early warning system (GITEWS) they pose serious computational challenges. This talk will for Indonesia as a multi-national multi-institutional sci- discuss some of them, including: Current state of the iter- entific collaboration. The system is in operation since ative strategies for the flow and stress coupling Grid con- November 2008 and is being handed over to the Indonesian struction, grid repair and generation of the geomechani- Government in the days of the SIAM Geosciences Meeting. cal grid from the flow grid Creation and upscaling of the Several tsunami events have occurred since the inaugura- geomechanical characterization and dealing with complex tion of the system and have demonstrated the performance media (such as naturally fractured reservoirs) Scale issues of this highly sophisticated and integrated tool for mitigat- and dealing with local accuracy requirements All of these ing the effects of natural disaster. In the core of the system, topics will be illustrated by examples of actual studies from several mathematical and computational techniques and studies of petroleum reservoirs and CO2 sequestration in procedures play a key role to interpret earth observation aquifers. data and to make use of the information gained. Simulat- Antonin Settari ing the specific components of the earth system is just the University of Calgary start of the chain of mathematical processes involved. A Taurus Reservoir Solutions rigorous (but simple and robust) uncertainty propagation [email protected] and reduction model helps in determining the potential im- pact of a rupture. Statistical methods are used to develop hazard maps and define risk zones. The presentation will IP5 give an overview of the diverse technical components and 3-D Finite-element Simulation of Transient Elec- societal considerations involved in the GITEWS Tsunami tromagnetics in Complex Earth Media Early Warning System. An emphasis will be laid on the computational mathematics aspects and their core role in The diffusion of low frequency EM fields in conductive solving the problem of near-field tsunami detection and media is the basis for controlled-source electromagnetic early warning. From this development, and the constraints (CSEM) remote sensing of Earths subsurface. Over the of real-time robust operational service, several conclusions past decade, there have been many numerical approaches can be drawn for a more general geo-scientific computa- developed for simulating CSEM in complex geological GS11 Abstracts 59 media, including direct implementation of the coupled CP1 Maxwells equations, the popular double-curl electric field Seismic Velocity Modeling Using Genetic Algo- formulation, and the coupled vector and scalar potentials rithms, Binary Versus Real Valued Searches formulation derived under the Coulomb gauge condition. In this talk, we present a new formulation that uses a From a statistical view seismograms are interpreted as ran- variation of the Lorenz gauge that is well suited to finite- dom variables. The random component can be attributed element (FE) modeling. Our formulation decouples the to sources such as distant-dependent measurement error, vector and scalar potentials into a separate diffusion equa- human error in picking arrival phases, and random noise tion for the vector potential and Poissons equation for the attributed to travel path. Stochastic modeling of such phe- scalar potential. It reduces the larger FE system that re- nomenon quantifies these random processes. Genetic algo- sults from the Coulomb gauge into two smaller decoupled rithms are iterative stochastic models that evaluate pro- systems of FE equations. Moreover, this Lorenzian-gauge gressively improved mathematical models. We explore the formulation retains the advantages of both the double-curl benefits of using binary versus real valued based genetic electric field and the Coulomb-gauge approaches; the re- algorithms in modeling seismic velocity structures. sulting FE system not only has the minimum number of unknowns but also can be used in the static limit using K B. Boomer an iterative solver. We illustrate the method for large 3-D Bucknell University geophysical CSEM problems and compare results with the [email protected] finite-element double-curl electric field approach and the finite-difference Maxwell equation approach. Richard A. Brazier The Pennsylvania State University Dubois Campus Jerry M. Harris Commonwealth College (Math Division) Stanford University [email protected] [email protected] CP1 IP6 Appropriate Formulation of the Objective Function Atmospheric Convection in Weather and Climate for a Better Integration of 4D Seismic Data to Con- Simulations strain Reservoir Models. Convection in the atmosphere, whether driven by heat- Calibrating reservoir models to flow data involves history ing of the earth’s surface or by condensational heating in matching processes. Model parameters are iteratively ad- clouds, is one of the most difficult processes to represent justed to minimize the misfit between the real data and the in our climate and weather models, and representing these corresponding simulated responses. The current formula- processes is critical given the large uncertainty associated tion used to quantify the seismic data mismatch is neither with clouds in climate assessments and weather prediction. representative of the difference between two images, nor of Convective updrafts are not resolved in climate model sim- matching quality. We describe an alternative formulation, ulations that use horizontal mesh spacings of 0(100 km), using methods rooted in image processing, to extract rel- and they are severely under-resolved in weather prediction evant information from seismic images and compute their where the smallest horizontal mesh spacings are O(1 km). dissimilarity. The issues associated with representing convection have significant implications for the design of the Navier-Stokes Ratiba Derfoul solvers used atmospheric

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