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One approach to determining the amount of seismic coupling uses the energy release in individual earthquakes to estimate rupture areas and slips, and then to accumulate the slips of overlapping rupture areas. Available earthquake catalogs give estimates of energy release in such forms as event magnitudes and moments. These values can be used to determine estimates of rupture area and average slip based on generalized fault models and selected parameters. Fault models for rectangular and circular faults have been in use for some time. Rectangular fault models are appropriate for large events which rupture the entire seismogenic zone in depth and have some known lateral extent. Lateral extent may be inferred by using the location of aftershocks to delimit the region of rupture. For smaller earthquakes which do not rupture the entire seismogenic zone and those lacking information to determine the lateral extent of rupturing, a circular fault model is commonly used to estimate earthquake rupture area and average slip.

Several common earthquake catalogs exist, such as the: International Seismological Centre catalog, or ISC catalog, the United States Geological Survey's Preliminary Determination of Epicenter catalog, or PDE catalog, the Harvard Seismology Centroid-Moment Tensor Catalog, or HCMT catalog, and Abe's catalog of large historical earthquakes, as well as others. Solutions in the HCMT catalog provide details of earthquake parameters not available in other catalogs. However, Abe's catalog covers the longest duration. Thus the HCMT catalog is chosen as the primary resource used here due to its uniform treatment of events, soundness of methods, high quality and detail of solutions, global coverage, and availability. Abe's catalog is chosen as the secondary source because of its long duration of coverage since the seismic cycle may be much longer than the period covered by the HCMT catalog.

In addition to the two sources selected above, some additional information was selected from papers containing pertinent geological and geophysical information relevant to the New Hebrides Trench and Vanuatu Archipelago. These include specific analyses of significant earthquakes and earthquake sequences.

The Department of Earth and Planetary Sciences at Harvard University maintains and updates a freely available electronic catalog of earthquake centroid-moment tensor solutions (Harvard Seismology Centroid-Moment Tensor Catalog) determined using methods developed by Dziewonski et al. (1981, 1983) and Woodhouse et al. (1984). The catalog contains centroid-moment tensor solutions and other pertinent information for moderate and large earthquakes with moment magnitudes (Mw) greater than approximately 5.0 from around the globe. It currently contains solutions for events first occurring in 1976 through the very recent past. The catalog is updated periodically through the year as new solutions are computed. The release used in this analysis includes solutions for events through the end of December of 1997 (or 22 years) and contains solutions for nearly 14,900 events(actually 14,465). Although information identical to that contained in the electronic catalog is also published periodically in academic journals (e.g., Dziewonski et al., 1998), publication of recent solutions lags the release of updates to the electronic catalog.

The centroid-moment tensor, or CMT, solution is the result of inversion of recorded seismograms to determine parameters of a best fitting point source earthquake. Parameters include: epicentral coordinates, focal depth, origin time, nodal plane dip, strike and slip, among others. Here "best fitting" refers to a minimization of recorded seismogram to synthetic seismogram cross correlation in the least-squares sense. Since first introduced, the CMT method has been refined to take advantage of the latest radial attenuation and lateral heterogeneity models. This method has been proven to show good agreement with fault planes inferred by other methods and is believed to provide better estimates of size than surface wave magnitude alone (Dziewonski et al., 1983).

The search of the HCMT catalog for events that fall near the New Hebrides Trench and Vanuatu Archipelago region of 165° to 171° longitude and -12° to -22° latitude reveals 563 events occurring between January of 1976 and December of 1997. These events are plotted in figure 3 and pertinent details are listed in appendix A2.

Selected earthquakes from the HCMT catalog were sorted based on several criteria. The events were first separated into the four categories: reverse, normal, transform, and odd using methods developed by Frohlich and Apperson (1992). Frohlich and Apperson show that the dominant character of an earthquake can be determined by plotting the earthquake in a triangle diagram using the

plunge angles of the three mutually perpendicular axes of the moment tensor solution. Events having a T axis with a dip of 50° or greater are reverse events, those with P axis dips of 60° or greater are normal events, those with B axis dips of 60° or greater are transform events, and all other events are considered odd. Here the P, T, and B axes represent the axes of maximum compressive stress, minimum compressive stress, and intermediate compressive stress respectively (Lay and Wallace, 1995, pp. 346-350). These are also commonly known as the compressional, tensional and null axes of the moment tensor solution. The distribution of events from the HCMT catalog considered here using a triangle diagram is shown in figure 4 below.

Figure 4. Triangle diagram of HCMT earthquakes.

Perusal of the distribution of event epicenters as plotted in figure 3 shows dense clustering along a deep linear feature, the trench axis, but also some dispersed seismicity further away. To investigate the subduction interface, we require only reverse events associated with the subduction process. To this end, event distances from the trench axis are required and parameters of the trench axis must be defined. A visual inspection of bathymetric maps of the region of interest, such as that presented in figure 1, reveals that the general trend of the trench axis is roughly 19° west of north and passes through the intersection of 166° longitude and -13° latitude. A geometrical approach to estimate event normal distances from a linear trench axis is described in appendix A1. These distances have been calculated and used in plotting the reverse event profile shown in figure 5 below.

Figure 5. HCMT reverse earthquake focal depth profile along trench axis.

In figure 5, the profile along the trench axis of the event focal depths shows that the solutions for these events range in depth from 10 kilometers to nearly 324 kilometers, with higher concentrations occurring at shallower depths. The near-trench seismicity is confined to within approximately 70 or 80 kilometers in depth and approximately 75 to 100 kilometers of lateral distance from the trench. There is also a significant grouping of shallow back-arc seismicity approximately 75 to 175 kilometers east of the trench axis. Histograms showing the event focal depth and distance distributions are shown in figure 6.

Figure 6. HCMT reverse earthquake depths and distances.

Plotting focal depths of the solutions for these reverse events shows a somewhat bi-modal distribution with a high concentration of events near the surface, a less concentrated and varied grouping some distance below that, and only very few events at great depths. Decreased activity between the two shallower groups occurs with a minimum at approximately 80 kilometers depth with the clustering of reverse events ending short of 70 kilometers depth. Utilizing this information, a value of 70 kilometers, is used to distinguish between shallow events, less than 70 kilometers depth, and deep events, greater than 70 kilometers depth. Table 3 summarizes the categorization of events from the HCMT catalog.

Table 3. Classification of events from the HCMT catalog.

In figure 6, the histogram of event distances from the trench axis shows a high concentration within approximately 100 kilometers of the trench axis and a lesser grouping further east. The assumption here of a linear trench axis, although reasonable in this situation, does not ideally characterize the sinuous nature of the trench axis. To allow for the mild curvature of the actual trench axis and possible inaccuracies in event location determination, all reverse events west of the assumed linear trench axis (i. e. those with negative distances) that are within reasonable proximity to the trench axis will be included in later slip calculations.

A cursory inspection of depth plots of hypocenters for event solutions culled from the HCMT catalog reveals a peculiarity of the CMT method. This is an unusual clustering of events in the 10 to 15 kilometer depth range and no events shallower than 10 kilometers depth. This can be seen in the histogram of event focal depths, figure 6. The CMT method involves matching synthetic and observed seismograms, including surface reflections. Parameters of the synthetic seismograms are varied within limits until a least-squares best match for all is found. However, the solution for the moment tensor becomes unstable as the source used to model the event approaches the surface. Therefore, by convention, the focal depth used to generate the synthetic seismograms in the CMT method is constrained to depths of 10 kilometers or greater (Dziewonski et al., 1983).

Also, upon more detailed inspection, some events in the HCMT catalog were found not to be ideal candidates for the analysis being performed. Some of the event solutions of the HCMT catalog may not sufficiently accurately model a given seismic event. That is, some complex source or multiple source events are not modeled well using the single point source assumption of the HCMT method. A measure of the Compensated Linear Vector Dipole, or CLVD, component relative to the double couple component can be used to recognize these events. This is given by (Lay and Wallace, 1995, p. 346):

Here, the deviatoric eigenvalues of the moment tensor solution used to calculate the above are related by:

These are the Teig, Beig, and Peig eigenvalues as supplied in the HCMT catalog. Values of e = 0 represent a pure double couple and indicate a seismic source adequately modeled with a double couple point source, and e = ± 0.5 represent a pure CLVD and a source that would be poorly modeled with a double couple point source. Although this amounted to only a few events, reverse events from the HCMT catalog with a significant CLVD component were excluded from the accumulated slip calculations of later sections.

In contrast to the HCMT catalog, Abe's earthquake catalog is a compilation of available information on large, historical earthquakes compiled by the seismologist Katsuyuki Abe (1981, 1982, 1984). It contains information on over 1500 events that have occurred from the turn of the century through 1980. Since much of the information is taken from sources prior to the widespread distribution of high quality seismometers, event parameters may be less precise when compared with current standards. It does, however, represent the best available information for this extended period. Abe's Catalog includes only the most basic parameters such as: event date, epicentral coordinates, depth, and estimates of magnitude. Where the Harvard Catalog represents very detailed, high quality information for recent seismic events, Abe's Catalog is a compendium of available information on large historic events. Since little information other than size is available for the events in the catalog, there is no direct way to determine whether the events are interplate as opposed to intraplate earthquakes. An assumption made here is that all of the events contained in Abe's Catalog that fall within reasonable proximity of the trench axis are reverse interplate events. Evidence from analyses by Scholz, et al., (1986) suggests that the majority of large near trench events at subduction zones are reverse in nature.

Abe's catalog was searched using similar criteria and procedures as the HCMT catalog with the exception of the event type classification. No nodal plane information is available in Abe's catalog so this type of classification is not possible. Also, events with no size or depth information present an additional problem with hypocentral location. As such, events lacking size information were excluded from further processing while those lacking depth information were arbitrarily set to 30 kilometers depth for later modeling purposes. Lastly, since Abe's catalog overlaps the HCMT catalog for the years of 1976 through 1980, for duplicated events, information from the HCMT catalog was preferred over that of Abe's catalog. The events selected from Abe's catalog include 89 events occurring in the years 1901 through 1976. These events are plotted in figure 7 and listed in appendix A3 with pertinent statistics summarized in table 4.

Table 4. Classification of events from Abe's catalog.

The HCMT and Abe's catalog data were augmented with information available in the more detailed analysis of Chinn and Isacks (1983). Only events not already included in the HCMT catalog were considered and as previously, where events were duplicated in the additional data and Abe's catalog, information from Chinn and Isacks was preferred. These events have been included in figure 7 previously and detailed information for modeling is listed in appendix A4.

To put the differences in the data sources in proper perspective, figure 8 below shows a comparative view of event sizes in time. For events with moment magnitudes, M_w, greater than 6.7, both Abe’s catalog and the HCMT catalog show a similar event frequency of approximately one large event every two years. Therefore, from the perspective of large events, the catalogs are consistent. The fact that Abe’s catalog is incomplete in that it does not include smaller events, indicates that it likely underestimates seismic energy release. Using the 260 reverse events from the HCMT catalog, 248 events have moment magnitudes smaller than 6.7 but these account for only 16% of the total moment release. Thus the missing small magnitude earthquakes in the Abe catalog are not likely to bias total slip calculations by a significant amount.

Figure 8. Reverse event size comparison. 'x' symbols are events from Abe's Catalog, 'o' symbols are events from Chinn and Isacks (1983), and '+' symbols are events from the HCMT Catalog.

© jlundy@wyoming.com 20 June 2003