It is possible to use the waveform data not only to derive the source mechanism of an earthquake but also to establish the hypocentral coordinates of the ‘best point source’ (the centroid of the stress glut density) at a given frequency. Thus two classical problems of seismology are combined into a single procedure. Given an estimate of the origin time, epicentral coordinates and depth, an initial moment tensor is derived using one of the variations of the method described in detail by Gilbert and Dziewonski (1975). This set of parameters represents the starting values for an iterative procedure in which perturbations to the elements of the moment tensor are found simultaneously with changes in the hypocentral parameters. In general, the method is stable, and convergence rapid. Although the approach is a general one, we present it here in the context of the analysis of long-period body wave data recorded by the instruments of the SRO and ASRO digital network. It appears that the upper magnitude limit of earthquakes that can be processed using this particular approach is between 7.5 and 8.0; the lower limit is, at this time, approximately 5.5, but it could be extended by broadening the passband of the analysis to include energy with periods shorter that 45 s. As there are hundreds of earthquakes each year with magnitudes exceeding 5.5, the seismic source mechanism can now be studied in detail not only for major events but also, for example, for aftershock series. We have investigated the foreshock and several aftershocks of the Sumba earthquake of August 19, 1977; the results show temporal variation of the stress regime in the fault area of the main shock. An area some 150 km to the northwest of the epicenter of the main event became seismically active 49 days later. The sense of the strike-slip mechanism of these events is consistent with the relaxation of the compressive stress in the plate north of the Java trench. Another geophysically interesting result of our analysis is that for 5 out of 11 earthquakes of intermediate and great depth the intermediate principal value of the moment tensor is significant, while for the remaining 6 it is essentially zero, which means that their mechanisms are consistent with a simple double-couple representation. There is clear distinction between these two groups of earthquakes.

Determination of earthquake source parameters from waveform data for studies of global and regional seismicity

Data from the Global Digital Seismograph Network were used to obtain ‘centroid-moment tensor’ solutions using the method of Dziewonski et al. (1981). Results were obtained for 201 earthquakes ranging in seismic moment from 7×1023 to 3×1027 dyne-cm. The wide dynamic range of the SRO/ASRO stations allows us to investigate, using the same algorithm, series of events among which the smallest and the largest may differ in moment by a factor as large as 1000. Among the events studied is a particularly interesting series, in January 1981, off the island of Honshu. The main shock was preceded by three foreshocks and followed by four aftershocks all falling within the range of our analysis. There is an indication that the source mechanism changes with the size of the event. Statistical analysis of the results for all earthquakes reveals that the half duration of shallow and intermediate events is approximated by 1.6×10−8 M01/3. The shifts in origin time for deep-focus earthquakes are indicative of the general complexity of these events, which depends only weakly on the seismic moment. The extreme departures from a double couple mechanism seem to depend both on the moment and on the focal depth. While for shallow earthquakes these departures decrease, from a maximum at about 1025 dyne-cm, with increasing moment, the reverse appears to be true with respect to deep-focus earthquakes. Shallow earthquakes north of New Guinea and along the Solomon Islands show systematic and substantial departures from the double couple mechanism.

An experiment in systematic study of global seismicity: Centroid-moment tensor solutions for 201 moderate and large earthquakes of 1981

[1] Crustal deformation patterns are affected by multiscale granulation and healing processes associated with phase transitions between continuum and discrete states of rocks. The ongoing continuum-discrete transitions are accompanied by progressive evolution of disordered fault networks to dominant localized fault zones, development of bimaterial interfaces, and increasing dynamic weakening of fault surfaces. Results on individual fault zones point to three general dynamic regimes. The first is associated with broad range of heterogeneities, little dynamic weakening, power law frequency-size statistics, temporal clustering of intermediate and large events, and accelerated seismic release before large earthquakes. The second is associated with relatively uniform localized structures, significant dynamic weakening, characteristic earthquake statistics, and quasi-periodic temporal occurrence of large events without precursory accelerated release. For a range of conditions, the fault zone response can switch back and forth between the foregoing two dynamic regimes. Higher temperature, fluid content, and thickness of sedimentary cover reduce the seismic coupling in a region and change the properties of local earthquake sequences. Brittle regions with high seismic coupling have few foreshocks and long-duration aftershock sequences with high event productivity, whereas more viscous regions with low seismic coupling have increased foreshocks activity and low-productivity aftershock sequences or swarms. The results provide criteria for organizing data in classes associated with different evolutionary stages and different regional conditions. An ability to recognize the dynamic regime of a given fault zone or a region can increase the information content of the data and lead to improved strategies for seismic hazard assessment.

Collective behavior of earthquakes and faults: Continuum-discrete transitions, progressive evolutionary changes, and different dynamic regimes

A review of a moment tensor for describing a general seismic point source is presented to show a second order moment tensor can be related to simpler seismic source descriptions such as centers of expansion and double couples. A review of literature is followed by detailed algebraic expansions of the moment tensor into isotropic and deviatoric components. Specific numerical examples are provided in the appendices for use in testing algorithms for moment tensor decomposition.

A Student’s Guide to and Review of Moment Tensors

Use of long-period surface waves for rapid determination of earthquake-source parameters

Models of earthquake sources that have no volume change, no net force, and no net torque as criteria for the radiation of first motions, have five degrees of freedom in their spatial orientation. The usual double-couple model has only three degrees of freedom. The most general source of high-frequency seismic motions must be a linear combination of a double couple and another source called the compensated linear-vector dipole. A radiation pattern of amplitudes of first motions on the focal sphere cannot be uniquely decomposed into the radiation patterns due to the two sources.

M. J. Randall

Papers

The compensated linear-vector dipole: A possible mechanism for deep earthquakes