General Earthquake Models:

Claude Allegre, IPG & French Science Ministry, Paris, France

John B. Rundle, University of Colorado, Boulder, CO

The construction of numerical and computational algorithms and specific environment(s) needed to carry out large scale simulations of these nonlinear physical processes over a geographically widely distributed, heterogeneous computing network; and

The development of a testbed for earthquake "forecasting" & "prediction" methodologies which uses modern Object Oriented techniques and scalable systems, software and algorithms which are efficient for both people and computational execution time.

1. Developing algorithms for solving computationally difficult nonlinear problems involving ("discontinuous") thresholds and nucleation events in a networked parallel (super) computing environment, adapting new "fast multipole" methods previously developed for general N-body problems;
2. Leveraging the Los Alamos ACL Infrastructure, including the POOMA object oriented framework, which is already being applied to computationally related adaptive particle mesh problems; and
3. Developing a modern problem solving environment to allow researchers to rapidly integrate simulation data with field and laboratory data (visually and quantitatively). This task is becoming increasingly important with the exponential increase in seismic, as well as space-based deformation data. The idea is to design a sufficiently flexible computational interface so that new physics can be added to the models easily, for example, new friction laws, enhanced wave propagation algorithms, new inelastic bulk constitutive properties, and so forth.

 

Problem(s) in earthquake source physics:

 

Short Term Focus: The group will focus on a problem similar to that described by Rundle (1988), which was associated with earlier work by Stuart (1986), and later work by Ward and Goes (1993). This effort used what would now be considered to be simple simulations that of the San Andreas fault system using 80 fault segments embedded in an elastic lithosphere overlying a Maxwell viscoelastic half space. This model used a modified CA algorithm for a friction law, in which changes in fault normal stress were included in the CA version of Amonton's law of friction. Fault displacement rates for the major faults were inputs into the model, allowing synthetic earthquake histories to be computed from the viscoelastic stress Green's functions. Kinematic viscoelastic Green's functions were then used to calculate the surface deformation for comparison to GPS, trilateration, and other surface deformation data, using in part far field displacement rates obtained from rigid plate motion models. Additionally, the geometric configuration of the faults was held fixed in time, which for short time intervals is probably a good first approximation. The simulations clearly show that field data can be simulated to as realistic an extent as is desired for comparison with natural, observed data.

 

At the GEM workshop, the subgroup in charge of the short term problem focus recommended that the Rundle (1988) work would be a viable starting point. The emphasis would then be on efforts such as:

1. Constructing better and more versatile stress Green's functions, such as including poroelasticity, general dipping faults, and heterogeneous media;
2. A more general friction law interface so that arbitrary friction laws could be used;
3. Computational efficiencies and enhancements so that more fault segments, particularly those in northern California could be modeled;
4. Construction of more general graphical and user friendly interfaces so that general users would find the codes useful, and so forth.

 

As discussed in detail in the full GEM proposal, objective of the calculations is to, for example, identify:

1. Catalogs of space-time patterns of activity at various spatial-temporal scales for comparison to, and validation by, data;
2. Identification of correlated activity involving several faults, so that enhanced probabilities of activity following a large event could be estimated;
3. Methods for initializing codes with historic activity so that projections of future activity could be made with a view to forecasting future events;
4. Roles of sub-grid scale faults and physical processes in space-time pattern selection; and so forth.

 

Intermediate-to-Long Term Focus: The longer term focus will be upon several geophysical and computational issues that will allow us to develop much larger and more general simulations than previously possible. For example, in an N-body simulation, the phase-space density distribution is represented by a large collection of "particles" which evolve in time according to some physically motivated force law. Direct implementation of these systems of equations is a trivial programming exercise. It is simply a double loop. It vectorizes well and it parallelizes easily and efficiently. Unfortunately, it has an asymptotic time complexity of O(N2). As described above, each of N left-hand-sides is a sum of N-1 right-hand-sides. The fact that the execution time scales as N2 precludes a direct implementation for values of N larger than a few tens of thousands, even on the fastest parallel supercomputers. Special purpose machines (such as GRAPE) have been succesfully used but these do not seem appropriate in an evolving field like GEM while we are still in the prototyping phase.

 

Several methods have been introduced which allow N-body simulations to be performed on arbitrary collections of bodies in time much less than O(N2), without imposition of a lattice (Appel, 1985; Barnes and Hut, 1986; Greengard and Rokhlin, 1987; Anderson, 1992). They have in common the use of a truncated expansion to approximate the contribution of many bodies with a single interaction. The resulting complexity is usually determined to be O(N) or O(N log N) which allows computations using orders of magnitude more particles. These methods represent a system of N bodies in a hierarchical manner by the use of a spatial tree data structure. Aggregations of bodies at various levels of detail form the internal nodes of the tree (cells). Making a good choice of which cells interact and which do not is critical to the success of these algorithms (Salmon and Warren, 1994). N-body simulation algorithms which use adaptive tree data structures are referred to as "treecodes" or "Fast Multipole" methods. By their nature, treecodes are inherently adaptive and are most applicable to dynamic problems with large density contrasts, while fast multipole methods have been mostly non-adaptive and applied to fairly uniform problems. It is likely that this distinction will blur in the future, however.

 

Other foci will be on developing an understanding of

1. the role of subgrid scale processes, such as small unmodeled faults, heterogenous media properties, and boundaries;
2. how to incorporate wave and fully inertial dynamics into simulations having boundaries and complex three dimensional structure, and evaluating the extent to which such are necessary to achieve a full understanding of the physics of earthquake rupture; and
3. the extent to which the physics of seismicity on small space-time scales is representative of the physics on larger and longer spatial and temporal scales.

 

Proposed interfaces with SCEC's existing science and outreach programs:

 

We anticipate that interfacing with SCEC's existing science and outreach programs will be straightforward. In fact, it is fortunate that such a vigorous effort already exists, because it would have to be developed for GEM otherwise. The GEM group will in fact be able to provide at some scale, a user friendly modeling/simulation/data interpretation capability that may turn out to be a useful product for the informed public. In particular, these kinds of computational efforts have proven to be invaluable in the atmospheric sciences community for communicating the excitement and promise of the science, not to mention the risks, to the public at large, and to political groups such as city, state, and national government officials. One can only imagine how such communication efforts could be enhanced by the availability, following a moderate event, of calculations and maps detailing some of the future consequences of the event, including enhanced/depressed rates of fault creep on nearby faults, faster/slower deformation rates, and advanced/retarded seismic "clock" times.

 

Anticipated scientific/computational products:

 

The primary product will be a computional tool(s) that will be useful for simulating seismicity and earthquakes, crustal deformation and stress changes, pore pressure changes, and eventually, changes in fault geometry and configurations, and other physical and chemical processes, in whatever spatial and temporal detail is desired, or at least to whatever detail is computationally feasible. These simulations could, with various obvious caveats, be used to "forecast" or "predict" future activity, as well as to analyze space time patterns of events, understand the physics of earthquakes, and so forth.

 

As such, these products will be of considerable value, IF NOT MISUSED, to governmental and corporate entities such as insurance companies, earthquake engineering consulting firms, the PEER center, and others, that need this kind of input to evaluate seismic risk.

 

Anticipated outreach products as they pertain to earthquake hazard reduction:

 

The major outreach product(s) that will flow from the above include the computational tools in their fully operational form, or perhaps simplified versions of same that may be useful for educational or other purposes.

 

Proposed timelines for above:

 

For short term focus models: 1-3 years depending on level of effort

 

For long term focus models: 5-10 years depending on level of effort

 

Anticipated funding and computational resources external to SCEC:

 

Likely to be substantial, since it will now be possible to tap into sources such as:

 

1. DOE funding: Order of $1 million year from geosciences/ASCI/HPCC sources
2. NSF/KDI CISE funding: Order of $3 million/year. We intend to submit to new KDI initiative, proposal due in March
3. NSF EAR: Order of several hundred thousand/year
4. Foundation Funding: Possibility of $1+ million/year of funding from Keck, Packard, etc.
5. Insurance Industry: Unknown. Perhaps might be willing to pay several millions/year or more for tools to forecast risk

Location and organization of the GEM "activity center":