GEM MEETING AT JPL
4/22/99
John's model
earthquake: elastic stuff sits over viscoelastic. Build up stress through plate motion until earthquake. Fault represented as a topological surface of displacement discontinuity; shear displacement modelled by distribution of dipole pairs (double-couples) on fault surface. Yay, we know about dipoles. To calculate displacements, use Green's f'ns. This kernel f'n is derivative of the Somigliana tensor, based on point force & point displacement.
SO: u(y) = Integrate[ delta-u T_ikl(y-x) dsigma(x)]
We also need the stress Green's function to propagate stress through medium.
So if you have a fault, you can find the displacement everywhere. Beware of notiation differences. Swapping of T and G exists! anyway, you convolve slip with T/G to get sigma/u. Slip is time-dependent. For a point fault, T dies off as 1/r^3. Quasistatic problem: given slip, we calculate stress and [surface] disp. Solution of problem: elastic stress equated with cohesive (friction) stress. Loading/forcing is applied & shows up in elastic stress. Cohesive forces should be not just friction but sliding/rolling/boiling/shearing/welding/etc.
Lots of friction laws. Stick-slip, rate-state, slip-dependent (TDW)
Faults have many orientations (fixed). How do we load the faults? Clever trick: given that stress decreases when slip increases, we can replace slip in integral with slip deficit function s -> s0 - vt
[phenomenologically represents simple sliding friction. required input: long-term slip rate on faults observables: well, surface things, basically. assumption that faults follow their long-term slip rates is an assumption and is at some level wrong.]
This trick avoids fault evolution questions. What we are looking at with this model are space-time patterns of activity; looking for correlations, triggering, scaling, etc.
Seth McGinnis' Model
Fault patch model...Mohr-Coulomb model with cohesive stress...use point source Green's functions. Prescribe loading rate for any element in the model. Discussion of Green's functions equations. Discussions of images and Boussinesq terms. Source process...images plus Boussinesq stress leads to non-elementary integrals. Question from Salmon about how best to calculate Green's functions. What is the most efficient way to calculate the displace- ments in response to applied forces.
Terry Tullis
Parkfield Model...rate and state, boundary conditions determine stressing rate. Use Green's functions as well. Steadily slipping San Andreas fault... No slip allowed on locked part from 1857. "Tan" parts of model all moving at 35 mm/yr, nominal San Andreas rate. Then each individual cell has constitutive properties. Use properties of serpentine or granite with somewhat arbitrary transition. Initial conditions correspond to an earthquake...slip at 1 mm/s. Each earthquake takes certain number of computational time steps. Each earthquake pretty much looks like each other. Adaptive time step sizes...fifth order Runge Kutta....from Numerical recipes in Press' book. Calculate derivatives in advance...know velocities from last time step. Calculate full time step as well as half time steps, compare answers to see if you need finer time steps. Question of whether 5th order Runge Kutta techniques makes matters worse in that higher derivatives are more unstable...not intended for use to decide on whether you need a finer time steps.
John Salmon
Fast multipoles...a Green's function relation...can be written as a matrix multiplication. Lumped parameter matrix multiplications...sum of near field plus far field terms. recursive matrix multiplies. get to order log_8 (N) instead of N^2 ...depth of an Oct-tree. Error bounds must be acceptable but will not be machine accuracy. Question of how much accuracy do we need. see vugraphs. Need to build the Oct-tree that sits above the mass distribution. We need Quad-trees instead of Oct-trees.
Jay Parker
Discussion of VISCO 3D code. Inversion code for fault elements based upon finite elements with split nodes. Used for examples such as Northridge earthquakes.
Jin-Fa Lee
Adaptive finite element mesh refinement for electromagnetic problems. Error estimation is very important for these problems. See vugraphs.
Geoffrey Fox
Discussed basic simulation modules. What about other parts of environment. In particular, what about computing environment. Distributed computing module. An object broker grabs a simulation code or a source of data. For example a web page is a source of data. Object has properties, registered, addressed, located. E.g., Databases are objects, can be registered on a web site, for example. XML is a generalization of HTML, can build an ASCII structure for any code or object. Display object in HTML, map to XML. Metadata should be stored in XML. XML is equivalent to a database. Instead of formats or information, should be in XML....similar in philosophy to FORTRAN NAMELISTS. Tags for XML..which attaches to lists of data. Specifies the object.
List of Actions
Acting as code repository is no big deal broker at JPL? issues of currency of codes JPL nominated as code repository.
Step 1 Code inventory
What does that mean? Need description of what metainfo is desired. Should include standards: comments, test run? This can be established later. G. Fox wants to compile list of acessible codes w/out any analysis yet. Categorization, etc, comes later. First, just a list. Then a paper talking about them. Follow with accessible code site later.
"Proto-objects"
Fox *
Step 2 Simulation Initiative
Code/project demonstration committee. Simple, benchmarky sorta problem. Basically, see if we can get some of these models to run with the Fast Multipole approach. Which we appear to be ready to jump into doing.
Step 3 Integration of Data with Simulation
(But we haven't had the discussions about this yet) Plan a more integrated approach (establish protocols) Computational environments, setup thoughts about NASA RFI, longer-term thing.
Step 4 Computational Environment & Visualization
It seems one of the ultimate goals is for people in this field to generate code tools that can be used by others, so we're not all perpetually reinventing the wheel. Simulation infrastructure. [standard argument: doing science vs creating a tool to work together to do science, hinging this time on how much $]
Comparison: specialize codes to straight faults, compare Rundle/Tullis?
Compare codes to a system with an analytic solution? (Jin-fa Lee)
Step 5 Program Committee
People to respond to things like NASA RFI, etc.
* = committee chairs