High Resolution Modeling of Regional Phases

Citation

Song, Xi (1997) High Resolution Modeling of Regional Phases. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/qjr7-9471. https://resolver.caltech.edu/CaltechTHESIS:08302023-200342752

Abstract

It has been a long-time goal of seismologists to decouple source phenomena from propagation effects. This thesis elaborates on our effort towards this goal.

We start by representing earthquakes as point-sources in space and using 1-D synthetics to resolve point-source parameters. Our trial-and-error approach to ob­tain 1-D crustal models is summarized in a set of sensitivity tests, where regional seismograms are decomposed into segments, i.e., the Pnl segment, the SV waves, the Love wave and the Rayleigh wave, so that the impact of model parameters on each segment is the most direct. In these tests, broadband waveform data is studied in a forward modeling approach, with synthetics computed using the reflectivity method and the generalized ray theory. Applying these tests to paths sampling the Basin and Range province, we find that a simple two-layer crustal model is effective in explaining regional seismograms. Our sensitivity tests also serve to help understand, and inter­ pret, the many results of a source estimation method we use to obtain point-source parameters. This method desensitizes the source mechanism result from the crustal model used to generate the 1-D synthetics, by allowing relative time shifts between the various segments. With this method, we obtain source mechanisms and seismic moments for a selection of Northridge aftershocks using broadband and long-period waveform data recorded by the TERRAscope array. The source duration of these earthquakes is measured by comparing the short-period to long-period energy ratio in the data to that in the synthetics. The seismic moment and source-duration are used to estimate the relative stress drop. The depth distribution of the relative stress drop indicates that the largest stress drops are in the depth range of 5-15 km for the 24 Northridge aftershocks in our study.

To obtain more detailed information about large earthquakes, such as fault di­mension and rupture directivity, we develop a new method of using empirical Green's functions (eGf). As an example, the January 17, 1994 Northridge mainshock is studied with one of its aftershocks as an eGf. The source duration of the mainshock, as seen from the regional surface waves observed at various stations, is obtained by searching for the trapezoidal far-field source-time function for each station which, when convolved with the aftershock data, best simulates the mainshock data. Sta­tions to the north see shorter source durations than those to the south. Modeling these with theoretical predictions of rupture on a square fault, we constrain the ef­fective fault dimension to be 14 km with rupture along the direction of the average rake vector. A moment of (1.4 ± 0.9) x 10²⁶ dyne•cm with a stress drop of ~120 bars is obtained for the mainshock from our eGf study.

When empirical Green's functions are not available due to a difference in the source mechanisms or in the source locations, theoretical modeling plays an important role. Our approach to develop high resolution Green's functions is to convert eGfs to pseudo Green's functions (pGf). This is done by modeling the eGfs with the generalized ray theory and consists of two major steps.

The first step is to shift individual ray responses to account for a difference in source location. This ray-shifting technique has its own use in fast generation of synthetic seismograms for finite sources. To study the directivity for a finite source, we discretize the fault region into a set of elements represented as point-sources. We then generate the generalized ray responses for the best-fitting point-source location, and derive for each separate ray the response for neighboring point-sources using power series expansions. The response for a finite fault is then a summation over rays and fault elements. If we sum over the elements first, we obtain an effective far­ field source-time function for each ray, which is sensitive to the direction of rupture. These far-field source-time functions are convolved with the corresponding rays and the results summed to form the total response. A simple application of the above method is demonstrated with the tangential motions observed from the 1991 Sierra Madre earthquake. For this event, we constrain the fault dimension to be about 3 km with rupture towards the west, which is compatible with other more detailed studies.

The second step in the modeling of the eGfs and the development of pseudo Green's functions is to account for variations in model structure by perturbing individual generalized ray responses calculated from a 1-D model. The model is divided into blocks and velocities in the blocks are allowed to vary, which shifts the arrival time of the individual rays. The amplitudes of the rays are perturbed independently to accom­modate local velocity variations in the structure. For eGfs that are moderate-sized earthquakes with known source mechanism and time history, the velocity variation in each block and the amplification factor for individual rays can be optimized using a simulated annealing algorithm. The usefulness of the pGfs is demonstrated with the 1991 Sierra Madre earthquakes as examples. The pGf technique is also useful in retrieving 2-D structure, which is essentially waveform tomography. This is demonstrated with a study of a Tibetan profile.

Thesis Files