Paper IV

Spectral amplitude grouping and the state of stress: A study of
microearthquake activity before the November 13, 1998, magni-
tude 5.0 earthquake in Ölfus, Iceland

Introduction
The sequel to PRENLAB is PRENLAB-2, and the Uppsala SIL group continued its participation in the project. Remembering that PRENLAB is an earthquake prediction research project, it was obvious to us that the methods developed in Paper II and III should be applied to a study of microearthquakes before a larger earthquake. We chose the November 13, 1998, $M_L = 5.0$ earthquake in Ölfus, southwestern Iceland, and studied the seismicity one year prior to the main event.

Summary
We analyzed microearthquakes occurring in the Ölfus area between November 1, 1997 and November 13, 1998, seven hours after the main shock. All events with at least four recording stations, 18 amplitude components, one polarity reading and $M_L \geq 0$ were included in the study, resulting in a catalogue of 2943 events. Using relative relocations we know that the main event, a right-lateral strike-slip event, took place on a N-S striking fault and that many of the events in our study also occurred on N-S striking faults.

In this paper we decided to use the name Spectral Amplitude Grouping (SAG) for the correlation and grouping technique developed in Paper III. We also split the second mode of operation from Paper III into two, where mode 2 is equivalent to the second mode above but where mode 3 now is the mode used to produce batches of a predetermined number of reduced events. The mode 2 of SAG has in this paper also been further developed to accommodate a variable size of the correlation memory. In Paper II, all events were retained in the correlation memory implying that early events were correlated with very few events and later events were correlated with almost the entire event catalogue. Now it is possible to choose the number of events to retain in the correlation memory, i.e. SAG can act as a moving window filter.

In order to study the repeating pattern of the Ölfus seismicity, and test the influence of the length of the correlation window, we ran SAG twice on the Ölfus data, see Figure 20.

Figure: Spectral amplitude grouping (SAG) results, or repeating patterns, for the Ölfus seismicity. Eq1 is the $M_L = 5.1$ event north of the study area, Eq2 is the main November event. A) The entire catalogue is used as correlation memory. Number of solitary events (solid line) and number of groups (dashed line) versus time. B) Same as in A but now plotted versus the number of processed events. C) Using a 250 event moving window as correlation memory. Number of solitary events (solid line) and number of groups (dashed line) versus time. D) Same as in C but now plotted versus the number of processed events. In B and D the start of each month is indicated by short, solid lines down from the top of the frames.

In the first run, in Figures 20A and B, we retained all events in the correlation memory. Figure 20A indicates that there is a steady increase in the number of solitary events with time, until we reach November and the foreshocks to the main event, when the number of solitary events increase rapidly. What is less noticeable is the rapid increase in the number of groups at Eq1, where there is a large number of aftershocks occurring as the result of a $M_L = 5.1$ earthquake to the north of the study area. We, hence, have two different responses to an increase in seismicity, in June the aftershocks are almost all repeating events that group very well, whereas the November foreshocks are mostly solitary events. The repeating pattern becomes clearer, we avoid the influence of the seismicity rate, if the number of solitary events is plotted versus event number, Figure 20B. We now have a more detailed view, the number of solitary events first increase until mid March, where the increase rate levels off. In June the rate is almost flat, most of the seismicity consists of repeated events, and then, in late August, early September, the rate of the number of solitary events increases dramatically. There is some decrease in the rate after the November event but it is not until further into the aftershocks that the rate of solitary events decreases substantially. How is this repeating pattern affected by the size of the correlation memory? In Figures 20C and D are the results of a 250 event correlation memory. Note that the first 250 events should not be included in the analysis since we are filling up the correlation memory and the solitary event rate will be high. The large scale pattern is generally the same, but we see that we have substantially increased the time resolution. Decreases in the number of solitary events are caused by two mechanisms; new events correlating well with older, solitary, events and old, solitary events leaving the correlation memory. Figure 20D shows that the seismicity after mid-March are repeating events and that there is a small increase in the number of solitary events immediately after the June main event but that the aftershocks soon are very similar. With this resolution we also note that the onset of a different type of seismicity occurs already in July and that the the number of solitary events peaks on the main November event. There is a small trough immediately before the main November event, as if the seismicity settled into a repeating pattern before the main event occurred. After the main event there is a short increase in the number of solitary events and then the aftershocks seem to localize, or stabilize, and become repeating events. Using a 100 event correlation memory produces approximately the same pattern, including the trough at the November event, whereas a 500 event memory seems a little too long and does not decrease as quickly after the main event as do the shorter memory sizes.

Using the spectral amplitude grouping technique in mode 3 we produced 76 batches of 40 reduced events for stress tensor inversion. The batches overlap by 20 reduced events. We also ran SAG in mode 1 on a data set where the aftershocks to the June event and the fore- and aftershocks to the November event were taken out, producing a list of 438 reduced events for the year. The list was used to estimate the background state of stress for the studied year.

The background stress state was estimated to an oblique strike-slip state with a normal faulting component. The least principal stress, $\sigma_{3}$, is subhorizontal in the direction $\mathrm{N}{51}^{\circ}\mathrm{W}$, in agreement with the $\mathrm{N}{63}^{\circ}\mathrm{W}$ direction of spreading across south Iceland [Sigmundsson et al., 1995]. The maximum horizontal stress is in the direction $\mathrm{N}{36}^{\circ}\mathrm{E}$. The stress state is very well constrained with small confidence areas and, surprisingly, we find that none of the principal stresses are vertical.

We estimated one stress state for each of the 76 batches of reduced events and in Figure 21 we show, as an example of the results, the direction of maximum horizontal stress, A and B, and the magnitude of the maximum horizontal stress relative to the vertical stress, C and D.

Figure: Results of stress tensor inversions of batches of 40 reduced events. Eq1 is the time of the June 5.1 event, Eq2 is the November 5.0 event. Solid squares are the optimum solutions for each batch and the hatched band is the 68% confidence limits. A) Directions of maximum horizontal stress in degrees east of north versus time. B) Same as in A but plotted against the batch number for clarity. C) Variation of the magnitude of the maximum horizontal stress during the studied time period. In order to estimate the stress magnitudes we used a coefficient of friction $\mu = 0.6$, hydrostatic pore pressure and normalized the magnitudes to the weight of the overburden. D) Same as in C but plotted against the batch number.

The first order impression of the direction of maximum horizontal stress, $\sigma_{H}$, is a rather stable direction around $\mathrm{N}{30}^{\circ}\mathrm{E}$, with a 68% confidence limit of ${30}^{\circ}$ - ${40}^{\circ}$, during the year. There are some batches that have a deviation which is significant at the 68% level with respect to other batches, such as batch 52 with respect to batch 11, 22, 66 and 69. There are temporal variations in the confidence limit, which is sometimes very well constrained and sometimes very large, indicating perhaps inhomogeneity in the stress field. There is some indication of a rotation in the horizontal stress towards N-S around November 9. Assuming a coefficient of friction of $\mu = 0.6$, hydrostatic pore pressure and a vertical stress that equals the weight of the overburden, we can estimate the magnitudes of the maximum horizontal stress. These magnitudes may be incorrect, but the pattern of magnitudes relative each other is constant. We see in Figure 21 that there is no systematic variation in the horizontal stress magnitudes but that there are indications of variations. Most pronounced is the group of four batches in July and the rather well constrained decrease after the mainshock in November.

We studied the sizes of the 68% confidence limit areas and the differences in deviation angle between the chosen and the rejected nodal planes from the stress inversions. We also separated the data set into two sets, group 2 containing the area of most intense aftershocks activity from the June event, and group 1 with the remaining events. The SAG of group 1 show the same repeating patterns as in Figure 20, but without the June peak. In group 2 the June pattern again shows how similar the events are. Stress inversion of batches of 40 events show an interesting feature. The June aftershock seismicity seems to be influenced by a more NE-SW trending maximum horizontal stress. The inversions of group 1 events show that the stress states are generally more well constrained than for the entire data set. There is, again, an indication of a rotation of the direction of maximum horizontal stress from N-S towards NE-SW around the main event.

Concluding remarks
The spectral amplitude grouping results are very interesting and show that SAG in mode 2 can provide a new view of the temporal evolution of seismicity. Further, the large anomaly in the latter part of the study seems to be associated with the main November event. This opens up interesting prospects of SAG as a monitoring instrument. I will analyze a longer series of events from the Ölfus area in order to obtain more information on the normal variations in repeating patterns.

There seems to be very little correlation between the repeating pattern from SAG and the estimated stress states. I have not performed any rigorous significance tests on the fluctuations in e.g. the direction of maximum horizontal stress, so I am uncertain of the significance of the variations observed.