A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...

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The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

Preliminary reference earth model

The nearly coincident forms of the relations between seismic moment M_0 and the magnitudes M_L, M_S, and M_w imply a moment magnitude scale M = ⅔ log M_0 - 10.7 which is uniformly valid for 3 ≲ M_L ≲ 7, 5 ≲ M_s ≲ 7½, and M_w ≳ 7½.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/JB084iB05p02348%4010.1002/%28ISSN%292169-9356.FAULT1

A moment magnitude scale

We have developed an efficient method to determine high-resolution hypocenter locations over large distances. The location method incorporates ordinary absolute travel-time measurements and/or cross-correlation P-and S-wave differential travel-time measurements. Residuals between observed and theoretical travel-time differences (or double-differences) are minimized for pairs of earthquakes at each station while linking together all observed event-station pairs. A least-squares solu- tion is found by iteratively adjusting the vector difference between hypocentral pairs. The double-difference algorithm minimizes errors due to unmodeled velocity struc- ture without the use of station corrections. Because catalog and cross-correlation data are combined into one system of equations, interevent distances within multiplets are determined to the accuracy of the cross-correlation data, while the relative lo- cations between multiplets and uncorrelated events are simultaneously determined to the accuracy of the absolute travel-time data. Statistical resampling methods are used to estimate data accuracy and location errors. Uncertainties in double-difference locations are improved by more than an order of magnitude compared to catalog locations. The algorithm is tested, and its performance is demonstrated on two clus- ters of earthquakes located on the northern Hayward fault, California. There it col- lapses the diffuse catalog locations into sharp images of seismicity and reveals hor- izontal lineations of hypocenters that define the narrow regions on the fault where stress is released by brittle failure.

/pdf/a-double-difference-earthquake-location-algorithm-method-and-13ttz2fahg.pdf

A Double-Difference Earthquake Location Algorithm: Method and Application to the Northern Hayward Fault, California

The conventional magnitude scale M suffers saturation when the rupture dimension of the earthquake exceeds the wavelength of the seismic waves used for the magnitude determination (usually 5–50 km). This saturation leads to an inaccurate estimate of energy released in great earthquakes. To circumvent this problem the strain energy drop W (difference in strain energy before and after an earthquake) in great earthquakes is estimated from the seismic moment M_0. If the stress drop Δσ is complete, W = W_0 = (Δσ/2μ)M_0 ∼ M_0/(2×10^4), where μ is the rigidity; if it is partial, W_0 gives the minimum estimate of the strain energy drop. Furthermore, if Orowan's condition, i.e., that frictional stress equal final stress, is met, W_0 represents the seismic wave energy. A new magnitude scale M_w is defined in terms of W_0 through the standard energy-magnitude relation log W_0 = 1.5M_w + 11.8. M_w is as large as 9.5 for the 1960 Chilean earthquake and connects smoothly to M_s (surface wave magnitude) for earthquakes with a rupture dimension of about 100 km or less. The M_w scale does not suffer saturation and is a more adequate magnitude scale for great earthquakes. The seismic energy release curve defined by W_0 is entirely different from that previously estimated from Ms. During the 15-year period from 1950 to 1965 the annual average of W_0 is more than 1 order of magnitude larger than that during the periods from 1920 to 1950 and from 1965 to 1976. The temporal variation of the amplitude of the Chandler wobble correlates very well with the variation of W_0, with a slight indication of the former preceding the latter. In contrast, the number N of moderate to large earthquakes increased very sharply as the Chandler wobble amplitude increased but decreased very sharply during the period from 1945 to 1965, when W_0 was largest. One possible explanation for these correlations is that the increase in the wobble amplitude triggers worldwide seismic activity and accelerates plate motion which eventually leads to great decoupling earthquakes. This decoupling causes the decline of moderate to large earthquake activity. Changes in the rotation rate of the earth may be an important element in this mechanism.

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The energy release in great earthquakes

Can the time, location, and magnitude of future earthquakes be predicted reliably and accurately? In their Perspective, Geller et al.9s answer is “no.” Citing recent results from the physics of nonlinear systems “chaos theory,” they argue that any small earthquake has some chance of cascading into a large event. According to research cited by the authors, whether or not this happens depends on unmeasurably fine details of conditions in Earth9s interior. Earthquakes are therefore inherently unpredictable. Geller et al. suggest that controversy over prediction lingers because prediction claims are not stated as objectively testable scientific hypotheses, and due to overly optimistic reports in the mass media.

Earthquakes Cannot Be Predicted

A data set of 41 moderate and large earthquakes has been used to derive scaling rules for kinematic fault parameters. If effective stress and static stress drop are equal, then fault rise time, τ, and fault area, S, are related by τ = 16S^(1/2)/(7π^(3/2)β), where β is shear velocity. Fault length (parallel to strike) and width (parallel to dip) are empirically related by L=2W. Scatter for both scaling rules is about a factor of two. These scaling laws combine to give width and rise time in terms of fault length. Length is then used as the sole free parameter in a Haskell type fault model to derive scaling laws relating seismic moment to M_S (20-sec surface-wave magnitude), M_S to S and m_b (1-sec body-wave magnitude) to M_S. Observed data agree well with the predicted scaling relation. The “source spectrum” depends on both azimuth and apparent velocity of the phase or mode, so there is a different “source spectrum” for each mode, rather than a single spectrum for all modes. Furthermore, fault width (i.e., the two dimensionality of faults) must not be neglected. Inclusion of width leads to different average source spectra for surface waves and body waves. These spectra in turn imply that m_b and M_S reach maximum values regardless of further increases in L and seismic moment. The m_b versus M_S relation from this study differs significantly from the Gutenberg-Richter (G-R) relation, because the G-R equation was derived for body waves with a predominant period of about 5 sec and thus does not apply to modern 1-sec m_b determinations. Previous investigators who assumed that the G-R relation was derived from 1-sec data were in error. Finally, averaging reported rupture velocities yields the relation v_R = 0.72β.

Scaling relations for earthquake source parameters and magnitudes

SUMMARY Earthquake prediction research has been conducted for over 100 years with no obvious successes. Claims of breakthroughs have failed to withstand scrutiny. Extensive searches have failed to find reliable precursors. Theoretical work suggests that faulting is a non-linear process which is highly sensitive to unmeasurably fine details of the state of the Earth in a large volume, not just in the immediate vicinity of the hypocentre. Any small earthquake thus has some probability of cascading into a large event. Reliable issuing of alarms of imminent large earthquakes appears to be effectively impossible. Key word: Earthquake prediction.

Earthquake prediction: a critical review

We study four ML - 2.7 earthquakes on the San Andreas Fault in Central California. The first two events occurred within five minutes of each other in November 1978; the two events in January 1979 occurred within a nine hour period. The CALNET (USGS local array) seismograms of these four events display only some general similarity. However, when low - pass filtered below 5 Hz, the four events have nearly identical seismograms. The similarity is even more striking in the pass-band below 2 Hz. This suggests that all four events are within a radius of no more than a quarter wavelength, or about 200 - 400 m.

Although no definitive conclusion can be reached from a study of only four earthquakes, our results strongly suggest that the following hypothesis should be further tested: Small to moderate earthquakes may commonly be much more tightly clustered in both hypocentral location and depth than is suggested by routine locations from local arrays. The physical basis of this clustering is that the earthquakes represent repeated stress release at the same asperity, or stress concentration, along the fault surface. Identification of such asperities might be useful in understanding the sequence of events leading to the initiation of a larger earthquake.

Robert J. Geller

Papers

Earthquakes Cannot Be Predicted

Scaling relations for earthquake source parameters and magnitudes

Earthquake prediction: a critical review

Four similar earthquakes in central California

Why earthquake hazard maps often fail and what to do about it