Because the process of an earthquake cannot be directly observed, we must infer the process by determining source parameters that describe the relative motion between the two sides of the fault, i.e., the kinematics of the rupture. At each point on the fault the source parameters are: 1) the slip-rate time function, characterized by a functional form and generally specified with a few parameters, 2) the rupture time?a time relative to the origin time of the earthquake at which the slip rate function starts and 3) the final slip, a vector with one component along strike and the other up-dip (i.e., perpendicular to the strike component), that gives the relative displacement of one side of the fault with respect to the other. The investigators assume a priori the velocity and attenuation structure of the medium in which the fault is embedded as well as the geometry of the fault and the hypocenter of the earthquake. With this information we can compute the ground motion at any point in space, in particular, at the locations of the seismic and geodetic instruments that recorded the earthquake. To find the source parameters they will solve an inversion problem in which they continuously adjust the source parameters. With each adjustment they will compute ground motion time histories (synthetics) at the recording sites and compare the synthetic time histories with the recorded time histories. At the same time they compute the static displacements for comparison with the geodetic measurements, GPS or InSAR. Using a predetermined cost function that measures the misfit between data and synthetics, we continue the procedure of adjusting the source parameters until we have an acceptable level of misfit.
Until relatively recently the emphasis has been on reducing the misfit between the data and the synthetics. However, that is now being recognized as not the issue because any number of different kinematic descriptions can fit the data. The number of free parameters (i.e., source parameters) is often far greater than the number of independent data making it possible to find nearly perfect agreement between synthetics and data. This raises two questions to be addressed in the proposal: 1) Is there additional data, not yet used, to constrain the source parameters? 2) Rather than measure the misfit between synthetics and data, how can we determine the difference between models? That is, how can we decide if one source description is better than another?
An earthquake is one of the most fundamental phenomena in the natural world. How two massive blocks of earth move past one another in a matter of seconds, tens of seconds, perhaps a few hundred seconds for the very largest earthquakes (e.g., 2004 Sumatra; 2010 Maule, Chile; 2011 Tohoku, Japan) releasing strain energy accumulated over hundreds or thousands of years is a basic scientific question. It is also a societally relevant question. The shaking and subsidiary effects (e.g., tsunamis, landslides) created by an earthquake critically affect the built environment. In order to prepare for future earthquakes it is essential to understand the process of earthquake ruptures. By using the data from an earthquake we can infer some of its behavior. By studying many different earthquakes we can understand what features are common among earthquakes. We can also understand what features of an earthquake contribute most to the strongest shaking and to the subsidiary effects.
Because we cannot directly observe an earthquake, we invert the seismic, geodetic and geologic data created by the earthquake to infer the relative motion between the two blocks of earth. The kinematic source parameters describe how the rupture evolves in time and space, i.e., the time when a point on the fault starts to slip (controlled by the rupture velocity) and the growth of the slip at each point on the fault (controlled by the stress relaxation of the medium). Conceptually the inverting the data is similar to finding the parameters (slope and intercept) of the best fitting line to a group of points. The difficulty with inverting for the source parameters of an earthquake is that the number of parameters being sought exceeds the number of independent data. Thus multiple, best-fitting earthquake models may be found. The problem is assessing how different one model is with respect to other models that fit the data equally well and what features different models have in common. In both respects the information can guide simulations of earthquakes for estimating the range of ground motions from future earthquakes.
