Detection of Seismic Stress-Drop Anomalies in the Mendocino
Transform Using Coda-Derived Spectra

Gilead Wurman and Douglas S. Dreger


The Berkeley Digital Seismic Network (BDSN) records many regional-scale events in Northern California each year. At present, only a few of these events are assigned moment magnitudes due to the limitations of moment tensor (MT) inversion codes in use today (Pasyanos et al., 1996). Complete-waveform MT inversions require good records at several stations (usually three or more) to obtain well-constrained solutions. Due to high signal to noise levels for small events such coverage is not possible, limiting the reliability of $M_{w}$ estimates. In the regional context of Northern California this applies to small events with $M_{w} \le 3.5$, and here the goal is to create a continuous $M_{w}$ scale over as broad a range of magnitudes as possible. Additionally, there is interest in getting stable $M_{w}$ determinations in other, sparsely instrumented regions, where reliable MT inversions cannot be done for events of even moderate magnitude.

The moment magnitude and seismic stress drop of an event can be quickly and accurately determined by fitting the decay rate of $L_{g}$ or $S_{n}$ phase coda via the method of Mayeda et al. (2003). The coda is composed of seismic waves which are multiply randomly scattered by 3-D inhomogeneities in the upper crust, and sample a broader swath than direct waves. As a result, path and distance corrections can take the form of average crustal properties and simple geometrical spreading relations, and source radiation patterns are washed out. After a station is calibrated for site response the correction holds for all future events. Because the coda method uses a continuum of arrivals rather than a small number of discrete direct arrivals a single station gives a much more robust measurement of $M_{w}$ than a single station MT inversion. In a densely instrumented region like Northern California coda-derived $M_{w}$ determinations can then be made over a much broader range of earthquake sizes (from $M_{w} \approx 2$ through $8$). The coda method also provides stable determinations of earthquake moment-rate spectra, which can be used to examine $E_{s}/M_{0}$ scaling in the study region.

Coda Decay Method

The coda method measures the narrowband envelopes of the horizontal component of ground motion and fits them to the relation (given a narrow frequency band and epicentral distance)

{\scriptstyle A_{c}(t\vert f,r)=A_{0}\cdot

where $H$ is the Heaviside step function, $v$ is the group velocity as a function of distance, and $b$ and $\gamma$ are decay functions of distance representing average crustal properties of logarithmic and power decay. These three variables are fixed by fitting theoretical functions to data from multiple calibration events at (ideally) multiple stations. Then for each event at each station the amplitude coefficient $A_{0}$ can be fit, representing the power received in that narrow passband. A range of passbands is processed, providing broadband analysis. This power needs to be corrected for site response, and this is done by taking several calibration events (events with good MT solutions) and forcing level spectra at frequencies below the theoretical corner frequency for the corresponding magnitude. Making such corrections over a range of magnitudes yields overall spectra that resemble Brune-model theoretical spectra in corner frequency, DC level and $\omega^{-2}$ falloff beyond the corner frequency (Brune, 1970).

When the calibration for region and individual stations is complete, any subsequent event must be processed into narrowband envelopes, and $A_{0}$ must be fit at each passband. $M_{w}$ can then be determined from the low frequency power level (lowest two passbands), and energy release and Orowan stress drop can be calculated (Figure 19.1) by integrating the square of the moment-rate spectrum of the event (Mayeda and Walter, 1996).

Performance in the Mendocino Area

Figure 19.1: Moment-energy scaling relationship for events in the Mendocino region. Dashed lines represent constant Orowan stress drop. Inset: typical source spectra for events in the Mendocino region (averaged over stations WDC and YBH).

Figure 19.2: Complete-waveform $M_{w}$ vs. Coda-derived $M_{w}$ from station YBH (a) and averaged over stations YBH and WDC (b).

The coda method has been applied to 88 offshore events in the Mendocino transform and the Gorda plate with reasonable success. Due to possible source anomalies in transform events the list of good calibration events is fairly small (10 events). The method has been applied with more success in Northern California (Mayeda, unpub. data).

A significant number of events in the Mendocino transform exhibit source spectra which depart from the Brune model in characteristic ways. These events exhibit significant enrichment in low-frequency content (below 0.5 Hz) and low corner frequencies for a given $M_{w}$. These events have low Orowan stress drops and have been characterized as slow earthquakes (Abercrombie and Ekström, 2003), which may indicate lubrication of faults (e.g., Okal and Stewart, 1982).

After calibrations are performed on BDSN stations WDC and YBH, the rms magnitude discrepancy between coda and complete-waveform $M_{w}$ is 0.14 above $M_{w}$ 3.5 for events that were not in the calibration (Figure 19.2). This scatter is probably due to uncertainties in both methods arising from the anomalous source physics noted above.

Real-Time Applications

The method, described briefly above, currently requires extensive user input at various stages, in particular to pick the start and end of the coda, and for quality control in the final results. The method could be modified to procedurally pick the coda based on slope, coda length and signal to noise constraints. While the calibration phase would still require human input, subsequent detections and measurement of $M_{w}$ and stress drop could be done automatically, yielding results within five minutes. The coda method needs approximately 20 minutes of coda to make good measurements, and taking into account telemetry and other processing delays, a robust magnitude determination can be made within 30 minutes of an earthquake.


The authors gratefully acknowledge the help of Kevin Mayeda and Fumiko Tajima in creating the codes to process the raw NCEDC data into the final results. This project was funded through IGPP grant no. 03-GS-031.


Abercrombie, R.E. and G. Ekström, Earthquake slip on oceanic transform faults, Nature (London), 410, 74-77, 2001.

Brune, J.N., Tectonic stress and the spectra of seismic shear waves from earthquakes, J. Geophys. Res., 75, 4997-5009, 1970.

Mayeda, K. and W.R. Walter, Moment, energy, stress drop, and source spectra of Western United States earthquakes from regional coda envelopes, J. Geophys. Res. B, 101, 11,195-11,208, 1996.

Mayeda, K., A. Hofstetter, J.L. O'Boyle and W.R. Walter, Stable and transportable regional magnitudes based on coda-derived moment-rate spectra, Bull. Seism. Soc. Am., 93, 224-239, 2003.

Okal, E.A. and L.M. Stewart, Slow earthquakes along oceanic fracture zones: evidence for aesthenospheric flow away from hotspots?, Earth Planet. Sci. Lett., 57, 75-87, 1982.

Pasyanos, M.E., D.S. Dreger and B. Romanowicz, Towards real-time estimation of regional moment tensors, Bull. Seism. Soc. Am., 86, 1255-1269, 1996.

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