D19 Method for accurate relative earthquake locations and fault plane identification – IMO

A method for mapping subsurface faults by joint interpretation of relative earthquake locations and their fault plane solutions has been under development by IMO(UPP), and in use at IMO for some time (Slunga et al., 1995, Rögnvaldsson and Slunga, 1994). The method uses cross-correlation of seismic wave forms to determine relative travel times of waves from events to station with increased accuracy. It inverts the time differences between these relative traveltimes and theoretical traveltimes to minimize the time residuals. As such, it is similar to other relative location algorithms (Got et al., 1994; Waldhauser et al., 1999). Due to the 1 ms time accuracy obtained in the Icelandic permanent seismic network, SIL, the relative location accuracies delivered, at their best, can be on the order of tens of meters and thus capable of delineating subsurface fault planes. Joint interpretation of the event distributions with focal mechanisms allows the determination of slip directions on individual faults.

The software has undergone several changes and revisions from its original form to make it more versatile and robust. For example the correlation, which previously was done in the frequency domain is now done in the time domain. In addition, the original procedure was not capable of handling large datasets, but the most recent version of the software can simultaneously handle up to 1800 events. The algorithm for joint interpretation with focal mechanisms is also under constant development. This latest version of the software has not been extesively tested before, hence the presentation of test results here to demonstrate its reliability.

The test data set is from the Hengill region and plotted in Figure 1. It consists of 1339 of the over 80 thousand earthquakes recorded in the Hengill region in the years 1992-2000. In local magnitude, the events range from -1.0 to 4.0, but the majority is within the -0.5 to 1.0 magnitude range. The seismic stations used in the inversion for best locations are also shown and the black box defines the region supplying the earthquakes for this work package. The latitude distribution with time is displayed in Figure 2. It shows how the activity during the period 1992-2000 was defined by swarms at the north and south margins of the South Iceland Seismic Zone (SISZ). The test set, outlined by the green oval, is from a 5-day swarm occurring between May 25 and 30, 1999.

Figure 1 Map showing test data set (red circles) and seismic stations (triangles). The box outlines the Hengill region.

Figure 2 Event locations through time. Width of the SISZ is shown by the blue bar on the right. The test data set is outlined in green.

Before the inversion, the events are ordered into groups of predefined number and spatial dimension and with a pre-defined overlap. Numerous test were run with different group sizes, between 30 and 48 events. Maximum group dimension was fixed at 6 km, but overlap of groups was not; the distance between centers of consecutive groups varied between 2.3 and 3 km. Length of the correlation time-window was changeable, between 1 and 3 seconds. Maximum event-source distance and maximum number of stations used were also parameters that were tested. In the inversion both relative and absolute times are used, so different weights of relative versus absolute times were tested. The results were not strongly dependent upon maximum event-source distance or weighting of absolute vs relative times. Length of the correlation time window had a somewhat greater effect, but the most important parameters were the group dimension and overlap. So that in order for location accuracies to be within acceptable range (on the order of tens of meters), on average, the events had to be in six groups. That means decreasing the inter-group distance from 3 to 2.3 km improved the accuracies. The error estimates from a well constrained inversion test are shown in Figure 3, which shows the median of relative errors in depth (red), latitude (green) and longitude (blue) for each event. The parameters used were: a maximum of 48 events in a group, maximum group diameter of 6 km and inter-group distance of 2.3 km. Correlation time-windows were 1 and 2 seconds long and maximum distance used was 100 km. The figure shows that a few events are not constrained and have large relative errors, but approximately 75% of the events have the median of the relative errors in latitude and longitude < 50 m and in depth < 100 m. The large errors are generally associated with singular events, that is, location outliers and events close in time interfering with each others waveforms.

Figure 3 Median of the relative errors in depth (red), latitude (green) and longitude (blue) for one of the test runs.

The improvement by the relocation can be seen in Figure 4. Where the before (a) and after (b) locations are shown. Also shown are the selected locations (c) with the median of relative errors < 50 m in latitude and longitude and < 100 m in depth. In 4b we can see that after relocation many of the events have collapsed into clusters, some of which have linear shape, indicating fault planes. After the best locations have been selected from the pack, these linear features become even clearer and several faults can be immediately identified; in 4c five faults are identified. We zoom in on the fault labeled 1, and view it in vertical cross sections in Figure 5. There each event is represented by the focal plane, which most closely matches the common plane defined by the event distribution. Each focal plane is obained from the suite of possible fault-plane solutions resulting from the focal mechanism inversion performed for each event. The size of the individual focal planes is proportional to the estimated fault radius of the events. In the upper left, the the events are plotted in map view. The figure shows the intersection of the best fault plane through the hypocenters with the surface, it has a strike of 29° and dip of 90°. On the upper right the events are shown in vertical cross section, viewed along strike from the SW, the events distribution shows a small deviation from the fault plane. On the lower right, the events are viewed perpendicular to the fault plane from the SE, so each event is seen as a disk proportional to its size. The tick mark on each circle shows the slip direction of the event's solution. All events have a consistent slip direction to the left showing that the Eastern side of the fault is moving left, hence the fault is a right-lateral fault.

Figure 4 Event locations before relocation (top) after relocation (middle) and selected events with rel. error in lat., lon<50 m, in depth <100 m (bottom).

Figure 5 (Upper left) Map view of fault 1 showing event distribution and intersection of best fitting fault plane with the surface. Slip direction is right-lateral. (Upper right) Vertical cross section looking along the strike direction. (lower right) Vertical cross section looking in the direction perpendicular to strike. The tick marks on the circles show the slip direction of the eastern half of the fault plane.

References:

Got, J-L, J. Frechet and F.W. Klein, 1994. Deep fault plane geometry inferred from multiplet relative relocation beneath the south flank of Kilauea, J. Geophys. Res., 99, 15375-15386.

Rögnvaldsson, S. Th. and R. Slunga, 1994. Single and joint fault plane solutions for microearthquakes in South Iceland, Tectonophysics, 237, 73-80.

Slunga, R., S. Th. Rögnvaldsson and R. Bödvarsson, 1995. Absolute and relative locations of similar events with application to microearthquakes in southern Iceland, Geophys., J. Int., 123, 409-419.

Waldhauser, F., W.L. Ellswortht and A. Cole, 1999. Slip-parallel seismic lineations on the northern Hayward fault, California, Geophys Res. Lett., 26, 3525-3528.