David D. Jackson

Space geodetic measurement of crustal deformation in central and southern California, 1984-1992

A laboratory type of analyzer for quantitatively determining the percent third element content of a hydrocarbon sample. A unique rhodium/americium radioactive source is disclosed.

Contemporary crustal deformation in east Asia constrained by Global Positioning System measurements

Global Positioning System (GPS) measurements collected since the early 90s allow us to derive geodetic velocities at 16 permanent stations in east Asia and 68 campaign mode sites in north China. The resulting velocity field shows the following: (1) Contrary to the early inferences that the Shanxi Rift has accommodated significant right-slip motion, our results suggest that the rift system, at least in its northern part in north China, is under ESE-WNW extension at a rate of 4±2 mm/yr. The velocity field also suggests that an ESE-WNW trending left-lateral shear zone deforming at a rate of 2±1 mm/yr may exist along the north rim of north China at the latitude of ∼40°N, separating actively extending north China in the south from relatively stable Mongolia in the north. (2) Central and east China move at a rate of 8–11 mm/yr east-southeast with respect to Siberia, implying that the overall east-southeastward motion is the dominant mode of deformation in east China. (3) The India plate moves at a rate of 6±1 mm/yr slower than the NUVEL-1A model prediction relative to the Eurasia plate. (4) Significant eastward motion (20±2 mm/yr) with respect to Siberia occurs in southeastern Tibet. About half of this eastward motion (∼11 mm/yr) is absorbed by structures along the eastern boundary of the Tibetan Plateau.

Seismic Gap Hypothesis: Ten years after

The seismic gap hypothesis states that earthquake hazard increases with time since the last large earthquake on certain faults or plate boundaries. One of the earliest and clearest applications of the seismic gap theory to earthquake forecasting was by McCann et al. (1979), who postulated zones of high, medium, and low seismic potential around the Pacific rim. In the 10 years since, there have been over 40 large (M ≥ 7.0) earthquakes, enough to test statistically the earlier forecast. We also analyze another forecast of long-term earthquake risk, that by Kelleher et al. (1973). The hypothesis of increased earthquake potential after a long quiet period can be rejected with a large confidence. The data suggest that, contrary to these forecasts, places of recent earthquake activity have larger than usual seismic hazard, whereas the segments of the circum-Pacific belt with no large earthquakes in recent decades have remained relatively quiet. The “clustering” of earthquake times does not contradict the plate tectonic model, which constrains only the long-term average slip rate, not the regularity of earthquakes.

Crustal deformation along the Altyn Tagh fault system, western China, from GPS

We collected GPS data from the southern Tarim basin, the Qaidam basin, and the western Kunlun Shan region between 1993 and 1998 to determine crustal deformation along the Altyn Tagh fault system at the northern margin of the Tibetan plateau. We conclude from these data that the Altyn Tagh is a left-lateral strike slip fault with a current slip rate of ∼9 mm/yr, in sharp contrast with geological estimates of 20-30 mm/yr. This contrast poses an enigma: because the GPS data cover a wider region than the geologic data, they might be expected to reveal somewhat more slip. We also find that the Tarim and Qaidam basins behave as rigid blocks within the uncertainty of our measurements, rotating clockwise at a rate of ∼11 and ∼4.5 nrad/yr, respectively, with respect to the Eurasia plate. The rotation of the Tarim basin causes convergence across the Tian Shan, increasing progressively westward from ∼6 mm/yr at 87°E to ∼18 mm/yr at 77°E. Our data and other GPS data suggest that the Indo-Asia collision is mainly accommodated by crustal shortening along the main Himalayan thrust system (∼53%) and the Tian Shan contractional belt (∼19%). Eastward extrusion of the Tibetan plateau along the Altyn Tagh and Kunlun faults accommodates only ∼23% of the Indo-Asia convergence.

Comparison of Short-Term and Time-Independent Earthquake Forecast Models for Southern California

We have initially developed a time-independent forecast for southern California by smoothing the locations of magnitude 2 and larger earthquakes. We show that using small m 2 earthquakes gives a reasonably good prediction of m 5 earthquakes. Our forecast outperforms other time-independent models (Kagan and Jackson, 1994; Frankel et al., 1997), mostly because it has higher spatial resolution. We have then developed a method to estimate daily earthquake probabilities in south- ern California by using the Epidemic Type Earthquake Sequence model (Kagan and Knopoff, 1987; Ogata, 1988; Kagan and Jackson, 2000). The forecasted seismicity rate is the sum of a constant background seismicity, proportional to our time- independent model, and of the aftershocks of all past earthquakes. Each earthquake triggers aftershocks with a rate that increases exponentially with its magnitude and decreases with time following Omoris law. We use an isotropic kernel to model the spatial distribution of aftershocks for small (m 5.5) mainshocks. For larger events, we smooth the density of early aftershocks to model the density of future aftershocks. The model also assumes that all earthquake magnitudes follow the Gutenberg-Richter law with a uniform b-value. We use a maximum likelihood method to estimate the model parameters and test the short-term and time-independent forecasts. A retro- spective test using a daily update of the forecasts between 1 January 1985 and 10 March 2004 shows that the short-term model increases the average probability of an earthquake occurrence by a factor 11.5 compared with the time-independent forecast.

Long-term probabilistic forecasting of earthquakes

We estimate long-term worldwide earthquake probabilities by extrapolating catalogs of seismic moment solutions. We base the forecast on correlations of seismic moment tensor solutions. The forecast is expressed as a map showing predicted rate densities for earthquake occurrence and for focal mechanism orientation. Focal mechanisms are used first to smooth seismicity maps to obtain expected hazard maps and then to forecast mechanisms for future earthquakes. Several types of smoothing kernels are used: in space domain we use the 1/distance kernel for the distribution of seismicity around any epicenter. The kernel is parameterized using two adjustable parameters: maximum distance and directivity (distribution of seismicity around an epicenter with regard to the focal mechanism of an earthquake). For temporal prediction we use the Poisson hypothesis of earthquake temporal behavior. We test these forecasts: we use the first half of a catalog to smooth seismicity level, and the second half of the catalog is used to validate and optimize the prediction. To illustrate the technique we use available data in the Harvard catalog of seismic moment solutions to evaluate seismicity maps for several seismic regions. The method can be used with similar catalogs. The technique is completely formal and does not require human operator intervention, hence the prediction results can be objectively tested. Moreover, the maps can be used as the Poisson null hypothesis for testing by the likelihood method against any other prediction model which shares the same sample space (the same zones, time window, and acceptance criteria).

New seismic gap hypothesis: Five years after

We use earthquake data from 1989–1994 to test a forecast by Nishenko based on the seismic gap theory. We refer to this forecast as the “New Seismic Gap” hypothesis, because it is the first global forecast based on the seismic gap hypothesis that considers the recurrence time and characteristic earthquake magnitude specific to each plate boundary segment. Nishenkos forecasts gave probabilities that each of about 100 zones would be filled by characteristic earthquakes during periods of 5, 10, and 20 years beginning on the first day of 1989. Only the first of these can be tested now. We used three tests based on (1) the total number of zones filled by characteristic earthquakes, (2) the likelihood that the observed list of filled zones would result from a process with the probabilities specified in Nishenkos hypothesis, and (3) the likelihood ratio to that of a Poissonian null hypothesis. The null hypothesis uses a smoothed version of seismicity since 1977 and assumes a Gutenberg-Richter magnitude distribution. We used both the Harvard Centroid moment tensor and the National Oceanic and Atmospheric Administration preliminary determination of epicenters catalogs in our test. We also used several different magnitude cutoffs in our tests, because Nishenkos forecast did not specify a clear relationship between the characteristic earthquake magnitude and the threshold magnitude for a successful prediction. Using a strict interpretation, that only earthquakes equal to or larger than the characteristic magnitude should be counted, both catalogs show only two qualifying earthquakes in the entire area covered by the forecast. The predicted number is 9.2, and the discrepancy is too large to result from chance at the 99% confidence level. The new seismic gap hypothesis predicts too many characteristic earthquakes for three reasons. First, forecasts were made for some zones specifically because they had two or more earthquakes in the previous centuries, biasing the estimated earthquake rate. Second, open intervals before the first event and after the last event are excluded in calculation of recurrence rate. Third, the forecast assumes that all slip in each zone is released in characteristic earthquakes of the same size, while in fact considerable slip is released by both smaller and larger earthquakes. The observed size distribution of earthquakes is inconsistent with the characteristic hypothesis: instead of a deficit of earthquakes above the characteristic limit, earthquake numbers are distributed according to the standard Gutenberg-Richter relation. By lowering the magnitude threshold for qualifying earthquakes, it is possible to reduce the discrepancy between the observed and predicted number of earthquakes to an acceptable level. However, for every magnitude threshold we tried, the new seismic gap model failed the test on the number of filled zones, or the likelihood ratio test, or both, at least at the 95% confidence level.

Southern California Permanent GPS Geodetic Array: Continuous measurements of regional crustal deformation between the 1992 Landers and 1994 Northridge earthquakes

The southern California Permanent GPS Geodetic Array (PGGA) was established in 1990 across the Pacific-North America plate boundary to continuously monitor crustal deformation. We describe the development of the array and the time series of daily positions estimated for its first 10 sites in the 19-month period between the June 28, 1992 (Mw=7.3), Landers and January 17, 1994 (Mw=6.7), Northridge earthquakes. We compare displacement rates at four site locations with those reported by Feigl et al. [1993], which were derived from an independent set of Global Positioning System (GPS) and very long baseline interferometry (VLBI) measurements collected over nearly a decade prior to the Landers earthquake. The velocity differences for three sites 65–100 km from the earthquakes epicenter are of order of 3–5 mm/yr and are systematically coupled with the corresponding directions of coseismic displacement. The fourth site, 300 km from the epicenter, shows no significant velocity difference. These observations suggest large-scale postseismic deformation with a relaxation time of at least 800 days. The statistical significance of our observations is complicated by our incomplete knowledge of the noise properties of the two data sets; two possible noise models fit the PGGA data equally well as described in the companion paper by Zhang et al. [this issue]; the pre-Landers data are too sparse and heterogeneous to derive a reliable noise model. Under a fractal white noise model for the PGGA data we find that the velocity differences for all three sites are statistically different at the 99% significance level. A white noise plus flicker noise model results in significance levels of only 94%, 43%, and 88%. Additional investigations of the pre-Landers data, and analysis of longer spans of PGGA data, could have an important effect on the significance of these results and will be addressed in future work.

The 2004 Parkfield Earthquake, the 1985 Prediction, and Characteristic Earthquakes: Lessons for the Future

The 1985 prediction of a characteristic magnitude 6 Parkfield earth- quake was unsuccessful, since no significant event occurred in the 95% time window (1985-1993) anywhere near Parkfield. The magnitude 6 earthquake near Parkfield in 2004 failed to satisfy the prediction not just because it was late; it also differed in character from the 1985 prediction and was expectable according to a simple null hypothesis. Furthermore, the prediction was too vague in several important respects to meet the accepted definition of an earthquake prediction. An event occurring by chance and meeting the general description of the predicted one was reasonably probable. The original characteristic earthquake model has failed in comprehensive tests, yet it is still widely used. Modified versions employed in recent official seismic hazard calculations allow for interactions between segments and uncertainties in the parameters. With more adjustable parameters, the modified versions are harder to falsify. The characteristic model as applied at Parkfield and elsewhere rests largely on selected data that may be biased because they were taken out of context. We discuss implications of the 2004 event for earthquake prediction, the characteristic earthquake hypothesis, and earthquake occurrence in general.

High-Resolution Long-Term and Short-Term Earthquake Forecasts for California

We present two models for estimating the probabilities of future earth- quakes in California, to be tested in the Collaboratory for the Study of Earthquake Predictability (CSEP). The first is a time-independent model of adaptively smoothed seismicity that we modified from Helmstetter et al. (2007). The model provides five- year forecasts for earthquakes with magnitudes M ≥ 4:95. We show that large earthquakes tend to occur near the locations of small M ≥ 2 events, so that a high- resolution estimate of the spatial distribution of future large quakes is obtained from the locations of the numerous small events. We further assume a universal Gutenberg- Richter magnitude distribution. In retrospective tests, we show that a Poisson distri- bution does not fit the observed rate variability, in contrast to assumptions in current earthquake predictability experiments. We therefore issued forecasts using a better- fitting negative binomial distribution for the number of events. The second model is a time-dependent epidemic-type aftershock sequence (ETAS) model that we modified from Helmstetter et al. (2006) and that provides next-day forecasts for M ≥ 3:95. In this model, the forecasted rate is the sum of a background rate (propor- tional to the time-independent model rate) and of the expected rate of triggered events due to all prior earthquakes. Each earthquake triggers events with a rate that increases exponentially with its magnitude and decays in time according to the Omori-Utsu law. An isotropic kernel models the spatial density of aftershocks for small (M ≤ 5:5) events, while for larger quakes, we smooth early aftershocks to forecast later events. We estimate parameter values by optimizing retrospective forecasts and find that the short-term model realizes a probability gain of about 6.0 per earthquake over the time-independent model. Online Material: Identification of explosions and ETAS parameters.