Paul A. Rydelek

Earth science: Is earthquake rupture deterministic?

Arising from: E. L. Olson & R. M. Allen 438, 212–215 (2005); Olson & Allen replyIt is essential in an earthquake early-warning system to be able rapidly to determine the size and location of an earthquake. Olson and Allen claim that the size of large earthquakes (magnitude (M) greater than 5.5) can be estimated from the seismic energy radiated during the first several seconds of fault rupture, implying that the earthquake process is deterministic. But here we analyse waveform data from more than 50 events (M≥6.0) recorded by the Japanese Hi-net seismic network and find no evidence that earthquake magnitude can be estimated before the rupture has completed. This bears on the difficult problem of understanding the physics of the earthquake process.

Asthenospheric viscosity inferred from correlated land–sea earthquakes in north-east Japan

The viscosity of the Earths mantle has been estimated from studies of post-glacial rebound1,2, post-seismic deformations of the ground following large earthquakes3,4, and aftershock sequences5–7. Here we derive a value for the viscosity of the asthenosphere from a correlation found in the historical catalogue of subduction-induced seismicity between the intraplate (land) and interplate (sea) earthquakes in north-east Japan. The correlation persists since the time of reliably reported earthquakes in AD 1600; land events precede sea events by ∼36 yr, with a mean distance between land–sea pairs of ∼200 km. Because of the visocoelastic coupling of the lithosphere to the asthenosphere, a plausible mechanism to explain the correlation is stress migration, governed by the viscosity of the asthenosphere. Large land shocks generate diffuse-like stress pulses which sweep past, and unlock, the thrust fault in the subduction zone, thus triggering the sea events. The correlation time and distance provide a measure of the speed of diffusion (5.6 km yr−1) and hence an estimate of the viscosity (7 × 1018 Pa s).

Real-Time Seismic Warning with a Two-Station Subarray

One of the most basic problems in seismology is earthquake location. In particular, the ability to quickly locate a large, potentially devastating earthquake is of fundamental importance in a real-time warning system where speed is a key factor in determining the level of success of such systems. We have developed a simple method that uses only the two earliest P -wave arrival times in a seismic array. Assuming a simple velocity model, these arrivals are used to construct a hyperbolic curve on which the approximate epicenter of the earthquake is expected to lie. Epicentral location along this hyperbola is further constrained by using the fact that the P waves arriving at the other stations in the array are not first arrivals. When applied to P -wave seismic data from the Hector Mine earthquake in California and a smaller event in the central United States, model results show agreement with actual earthquake locations. Although there is an inherent uncertainty in the subarray method of locating large earthquakes, this may be an acceptable trade-off in an early warning system in view of the time (a few to tens of seconds) saved by not waiting for other P arrivals. Whereas the main goal of this report is to present the location method, we also show that the station closest to the Hector Mine earthquake had recorded about 0.3 and 1 mm of ground motion within 2 and 3 sec, respectively, of the arrival of the P waves, thus indicating that a large event had occurred. Manuscript received 18 September 2003.

Comment on “Earthquake magnitude estimation from peak amplitudes of very early seismic signals on strong motion records” by Aldo Zollo, Maria Lancieri, and Stefan Nielsen

] An early warning system should determine the loca-tion and magnitude of an earthquake as rapidly as possiblein order to broadcast an alarm to regions that will undergosevere ground shaking. It was recently claimed by Zollo etal. [2006] that earthquake size could be determined fromonly the first 2-seconds of P- or S-wave strong-motion data;this represents a fraction of the rupture time for larger M >7 events. Using this relatively short amount of data, themethod of analysis was to find the peak ground displace-ment (PGD), which was reported to scale with earthquakemagnitude; such rapid information would play an importantand much needed role in an earthquake early warning(EEW) system. Here we perform a similar analysis onstrong-motion data from the KiK-net and K-NET arrays inJapan and find no compelling evidence that the peak grounddisplacement during the first couple of seconds of P-wave isrelated to the eventual size of a large earthquake.[

Seismology: Tectonic strain in plate interiors?

Arising from: R. Smalley Jr, M. A. Ellis, J. Paul & R. B. Van Arsdale 435, 1088–1090 (2005); R. Smalley et al. reply.It is not fully understood how or why the inner areas of tectonic plates deform, leading to large, although infrequent, earthquakes. Smalley et al. offer a potential breakthrough by suggesting that surface deformation in the central United States accumulates at rates comparable to those across plate boundaries. However, we find no statistically significant deformation in three independent analyses of the data set used by Smalley et al., and conclude therefore that only the upper bounds of magnitude and repeat time for large earthquakes can be inferred at present.

Fossil strain from the 1811–1812 New Madrid Earthquakes

Observations of postseismic deformation generally suggest that the effects of postseismic viscoelastic relaxation may persist for many decades after an earthquake. In particular, strain effects from the three great earthquakes that occurred in the New Madrid seismic zone in 1811–1812 may influence present day measurements of ground deformation in this active seismic region of the central United States. Forward calculations using an earth rheology that may be appropriate for a continental intraplate region and a simple fault model for the 1811–1812 sequence suggest that postseismic relaxation may be an important factor in driving the unexpectedly high rate of shear deformation recently observed in the southern New Madrid Seismic Zone.

Comment on “Minimum Magnitude of Completeness in Earthquake Catalogs: Examples from Alaska, the Western United States, and Japan,” by Stefan Wiemer and Max Wyss

Manuscript received 24 January 2002. Wiemer and Wyss [2000] (WW) have analyzed earthquake data from Japan in order to determined the magnitude level ( M c) at which seismic catalogs are complete. Regional and local maps that accurately show the spatial variation of M c are important because they provide helpful guidance in planning for the future deployment of seismic stations. This comment is intended to point out several problems with WWs method of determining M c and to demonstrate that ignoring temporal variations in seismicity can result in erroneous completeness maps. The fundamental assumption made by WW in determining M c is that the distribution of seismic events follows a linear Gutenberg-Richter relation or b -value. Above some lower magnitude limit, WW modeled the observed magnitude-frequency distribution with a linear power law. They constructed a synthetic distribution from their model and then calculated the goodness of fit between the observed and synthetic distributions. Since a shortage of events at small magnitudes (e.g., missing events) will result in a nonlinear curve and therefore a poor fit, WW systematically increased the lower magnitude used in their analysis until about 90% or more of the curve can be modeled by a linear power law, at which point the lower magnitude is considered to be M c. While examples show the Gutenberg-Richter curve may be linear down to small magnitudes (e.g., Abercrombie and Brune, 1994), there are also careful studies that challenge the assumption of linear b -value (Aki, 1987; Umino and Sacks, 1993; Heimpel and Malin, 1998; Iio, 1991 for aftershocks; Watanabe, 1973 for a swarm). Certainly, the a priori assumption of a linear b -value should not be used to discard seismic observations that do not support this assumption. We agree with WW when they concluded …

Migration of large earthquakes along the San Jacinto fault; stress diffusion from the 1857 Fort Tejon earthquake

Abstract. Historic and modern catalogs of seismicity in California suggest a migration of earthquakes (M > 5.6) along the San Jacinto Fault; these events appear to travel down the fault with a migration speed of 1.7 krn/year (Sanders [1993]). This migration is explained by postseismic strain diffusion due to viscoelastic relaxation from the great Fort Tejon earthquake in 1857. We model this postseismic effect and find that significant stress diffuses down the San Jacinto fault for distances in excess of 200 km and the corresponding migration may be a result of Coulomb triggering from this stress perturbation. The level of postseismic stress that seems to be the trigger level for most of the events is of order 1 bar. Since the temporal evolution of the postseismic strain field is mainly dependent on the inelastic properties of the lower crust and uppermost mantle, the observed migration enables a viscosity estimate of -4x10 •8 Pas for this region of California. Introduction Sanders [ 1993] has presented evidence that suggests large earthquakes on the San Andreas fault zone (SAFZ) can influence the seismicity on neighboring faults such as the San Jacinto fault zone (SJFZ). Of particular interest, it was shown that from 1899 to 1987, larger magnitude earthquakes (M > 5.6) along the SJFZ appear to migrate in a southeast direction with a migration rate of 1.7 krn/yr. This led Sanders to

Triggering and inhibition of great Japanese earthquakes: the effect of Nobi 1891 on Tonankai 1944, Nankaido 1946 and Tokai

Abstract There are two unusual features of the most recent great earthquakes off southwest Honshu. The Tonankai and Nankaido earthquakes were relatively early compared to the historical record of past occurrence, and the Tokai section of the Tonankai fault did not fail in 1944 whereas it probably had for the previous ∼1000 years. We show that both phenomena can be explained by postseismic strain diffusion from the great Nobi, Japan, earthquake (M 8.0) in 1891. It is believed to have produced stress changes that influenced the time of occurrence of the great Tonankai (M 7.9) and Nankaido (M 8.0) earthquakes in the mid-1940’s. The pattern of long-term viscoelastic deformation following the Nobi earthquake suggests that the failure threshold was reduced in the southwest section of the Nankai Trough, which may have acted to trigger the Tonankai and Nankaido events. In contrast, the threshold was increased in the eastern Tokai section of the thrust zone and therefore failure of this section may have been inhibited. We model fault failure and show that the stress levels from Nobi are adequate to account for the advance of Tonankai and the inhibition of Tokai.

Determination of the Trajectory of a Fireball Using Seismic Network Data

We present inverse-theory techniques for the determination of the trajectory of a fireball using seismic network data. Assuming that the speed of sound (c) in air is constant and known and that the trajectory is a straight line, the unknowns are the velocity of the fireball (nu), and the following parameters related to the trajectory: the two horizontal coordinates of the end point and the corresponding arrival time (t(0)), the azimuth of its horizontal projection, and the angle with the vertical. As the computation of travel times for a given set of parameters is nonlinear, the inverse problem is solved by use of a standard linearization technique with the resulting linear system of equations solved using damped least squares and the generalized inverse. These two approaches are applied to data from a fireball observed in northeast Arkansas in November 2003 and recorded by stations of the University of Memphis seismic network. We find that nu and t(0) are essentially unconstrained, with the computed values depending on the initial value of nu (and the assigned value of c). However, the two angles that define the trajectory are well constrained. Inversion of realistic synthetic data confirm our observations, which are also supported by analytical considerations. The results obtained for the Arkansas data were used to predict the direction of the ground motion in the horizontal plane, which is in good agreement with the observations. Although this is not the main point of the article, we also noted that the observed ground motion is prograde, which we were able to reproduce with synthetic seismograms.