http://science.sciencemag.org/content/sci/181/4102/803.full.pdf

Earthquake Prediction: A Physical Basis

The inverse problem of three-dimensional (3-D) local earthquake tomography is formulated as a linear approximation to a nonlinear function. Thus the solutions obtained and the reliability estimates depend on the initial reference model. Inappropriate models may result in artifacts of significant amplitude. Here, we advocate the application of the same inversion formalism to determine hypocenters and one-dimensional (1-D) velocity model parameters, including station corrections, as the first step in the 3-D modeling process. We call the resulting velocity model the minimum 1-D model. For test purposes, a synthetic data set based on the velocity structure of the San Andreas fault zone in central California was constructed. Two sets of 3-D tomographic P velocity results were calculated with identical travel time data and identical inversion parameters. One used an initial 1-D model selected from a priori knowledge of average crustal velocities, and the other used the minimum 1-D model. Where the data well resolve the structure, the 3-D image obtained with the minimum 1-D model is much closer to the true model than the one obtained with the a priori reference model. In zones of poor resolution, there are fewer artifacts in the 3-D image based on the minimum 1-D model. Although major characteristics of the 3-D velocity structure are present in both images, proper interpretation of the results obtained with the a priori 1-D model is seriously compromised by artifacts that distort the image and that go undetected by either resolution or covariance diagnostics.

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Initial reference models in local earthquake tomography

We have developed a semi-automated method of determining accurate relative phase arrival times and uncertainty estimates for teleseisms recorded on regional networks. Our analysis begins by obtaining preliminary arrival times with a single-trace phase-picking algorithm. For each possible pair of traces we then perform a search for the maximum of their cross-correlation function in order to obtain relative delay times. Depending on event magnitude, the best results are obtained by using correlation windows containing 2 to 4 sec of the initial energy pulse of the phase. The cross-correlation derived delay times are then used to generate an overdetermined system of linear equations whose solution is an optimized set of relative arrival times. We solve for these times using least squares. Cycle skipping is eliminated through the automatic re-evaluation of cross-correlation functions which yield high equation residuals. Quantitative estimates of timing uncertainty are obtained from the variance of equation residuals associated with each trace. 

Using data from the Washington Regional Seismograph Network, we have found that for reasonably high-quality events, the rms uncertainty in arrival time estimates is on the order of the sample interval (0.01 sec). Reproducibility of delay anomalies is excellent for events from the same geographic locations despite significant differences in waveform character. In connection with a study of the deep structure of the Cascadia Subduction Zone, we include a preliminary examination of the variation of residual patterns with azimuth.

Determination of teleseismic relative phase arrival times using multi-channel cross-correlation and least squares

The recent evolution of induced seismicity in Central United States calls for exhaustive catalogs to improve seismic hazard assessment. Over the last decades, the volume of seismic data has increased exponentially, creating a need for efficient algorithms to reliably detect and locate earthquakes. Today's most elaborate methods scan through the plethora of continuous seismic records, searching for repeating seismic signals. We leverage the recent advances in artificial intelligence and present ConvNetQuake, a highly scalable convolutional neural network for earthquake detection and location from a single waveform. We apply our technique to study the induced seismicity in Oklahoma, USA. We detect more than 17 times more earthquakes than previously cataloged by the Oklahoma Geological Survey. Our algorithm is orders of magnitude faster than established methods.

Convolutional neural network for earthquake detection and location

Automatic phase-picking algorithms are designed to detect a seismic signal on a single trace and to time the arrival of the signal precisely. Because of the requirement for precise timing, a phase-picking algorithm is inherently less sensitive than one designed only to detect the presence of a signal, but still can approach the performance of a skilled analyst. A typical algorithm filters the input data and then generates a function characterizing the seismic time series. This function may be as simple as the absolute value of the series, or it may be quite complex. Event detection is accomplished by comparing the function or its short-term average (STA ) with a threshold value (THR), which is commonly some multiple of a long-term average (LTA) of a characteristic function. If the STA exceeds THR, a trigger is declared. If the event passes simple criteria, it is reported. Sensitivity, expected timing error, false-trigger rate, and false-report rate are interrelated measures of performance controlled by choice of the characteristic function and several operating parameters. At present, computational power limits most systems to one-pass, time-domain algorithms. Rapidly advancing semi-conductor technology, however, will make possible much more powerful multi-pass approaches incorporating frequency-domain detection and pseudo-offline timing.

Automatic phase pickers: Their present use and future prospects

A computer program has been developed for the automatic detection and timing of earthquakes on a single seismic trace. The program operates on line and is sufficiently simple that it is expected to work in inexpensive low-power microprocessors in field applications. In tests with analog tapes of earthquakes, the program correctly identified and timed to within 0.05 sec about 70 per cent of the events which would normally be timed in operation of a network. The program evaluates the accuracy of its picks, and its estimates appear to be quite reliable. The algorithm is working at present in a 16-bit minicomputer and appears to be compatible with presently available microprocessors.

Automatic earthquake recognition and timing from single traces

The three largest earthquakes to occur within 50 km of San Francisco during 1970 were centered near the community of Danville, California, and spanned a time interval of 50 sec starting on June 12, at 0330 hr GMT. These earthquakes were greater than magnitude 4.0 and were part of a shallow, tightly-clustered earthquake swarm that persisted for approximately 2 months starting in mid-May 1970. During the same period of time, continuous tilt at tidal sensitivity (10 −8 radian) was being recorded in two vaults at distances of 25 and 45 km west of the epicentral area. Two types of anomalous tilting preceded the principal events: (1) a long-term (1-month) constant tilt rate of 8 × 10 −10 radian/hr that was recorded by both tilt stations and (2) a short-term (1-day) accelerated micro-tilt change which occurred just prior to the events and was most pronounced on the station closest to the epicentral area. Neither type of anomaly was recognized in the post-Danville record. The lack of a strong correlation with meteorological phenomena to account for the long-term coherency between two tilt stations of 25-km separation and the apparent azimuthal correlation of the Berkeley residual tilt vector with the earthquake epicenters suggests that the anomalous tilt preceding the Danville events were tectonic.

Anomalous microtilt preceding a local earthquake

A tiltmeter suitable for operation at tidal sensitivities in a shallow borehole has been designed. Construction is of stress-relieved aluminum and the design is so simple it can be fabricated in most machine shops. The electronic system is built around available modular circuits, both integrated and hybrid. The meter is sensitive, stable and inexpensive. Representative samples of record presented include a 200-hr period in which the instrument was operated adjacent to a 5-meter baselength liquid-level tiltmeter. Drift during this period amounts to no more than a few parts in 10 8 .

Rex V. Allen

Papers

Automatic earthquake recognition and timing from single traces

Automatic phase pickers: Their present use and future prospects

Anomalous microtilt preceding a local earthquake

A borehole tiltmeter for measurements at tidal sensitivity

Tiltmeter observations near a large earthquake