Source Parameters Seismic Moment Research Articles

Resolving Differences in the Rupture Properties of M5 Earthquakes in California Using Bayesian Source Spectral Analysis

AbstractThe spectra of earthquake waveforms can provide important insight into rupture processes, but the analysis and interpretation of these spectra is rarely straightforward. Here we develop a Bayesian framework that embraces the inherent data and modeling uncertainties of spectral analysis to infer key source properties. The method uses a spectral ratio approach to correct the observed S‐wave spectra of nearby earthquakes for path and site attenuation. The objective then is to solve for a joint posterior probability distribution of three source parameters—seismic moment, corner frequency, and high‐frequency falloff rate—for each earthquake in the sequence, as well as a measure of rupture directivity for select target events with good azimuthal station coverage. While computationally intensive, this technique provides a quantitative understanding of parameter tradeoffs and uncertainties and allows one to impose physical constraints through prior distributions on all source parameters, which guide the inversion when data is limited. We demonstrate the method by analyzing in detail the source properties of 14 different target events of magnitude M5 in southern California that span a wide range of tectonic regimes and fault systems. These prominent earthquakes, while comparable in size, exhibit marked diversity in their source properties and directivity, with clear spatial patterns, depth‐dependent trends, and a preference for unilateral directivity. These coherent spatial variations source properties suggest that regional differences in tectonic setting, hypocentral depth or fault zone characteristics may drive variability in rupture processes, with important implications for our understanding of earthquake physics and its relation to hazard.

Fast and Robust Earthquake Source Spectra and Moment Magnitudes from Envelope Inversion

ABSTRACTWith the present study, we introduce a fast and robust method to calculate the source displacement spectra of small earthquakes on a local to regional scale. The work is based on the publicly available Qopen method of full envelope inversion, which is further tuned for the given purpose. Important source parameters—seismic moment, moment magnitude, corner frequency, and high-frequency fall off—are determined from the source spectra by fitting a simple earthquake source model. The method is demonstrated by means of a data set comprising the 2018 West Bohemia earthquake swarm. We report moment magnitudes, corner frequencies, and centroid moment tensors inverted from short-period body waves with the Grond package for all earthquakes with a local magnitude larger than 1.8. Moment magnitudes calculated by envelope inversion show a very good agreement to moment magnitudes resulting from the probabilisitc moment tensor inversion. Furthermore, source displacement spectra from envelope inversion show a good agreement with spectra obtained by multiple taper analysis of the direct onsets of body waves but are not affected by the large scatter of the second. The seismic moments obtained with the envelope inversion scale with corner frequencies according to M0∝fc−4.7. Earthquakes of the present data set result in a smaller stress drop for smaller magnitudes. Self-similarity of earthquake rupture is not observed. In addition, we report frequency-dependent site amplification at the used stations.

Don't Call it Stress Drop

O ne of the most battle-weary parameters in seismology today is stress drop. Seismologists argue over everything about this parameter, including its name, meaning, measurement, and scaling with magnitude. The original concept of stress drop was introduced as a static measure of final fault slip, as a fraction of fault dimension (Δσ ∼ u/r ), and was estimated from measurements or inferences of these geologically-based parameters (as, for example, by Kanamori and Anderson, BSSA, 1975, pp. 1,073–1,095). Stress drop became an important earthquake source parameter following Brune's classic paper ( JGR , 1970, pp. 4,997–5,009), showing that the radiated far-field spectrum of shear waves could be interpreted in terms of a simple point-source model with just two source parameters—seismic moment ( M ) and stress drop (Δσ). This paved the way for measurments of stress drop from seismic signals. In Brune's model, the acceleration source spectrum has a simple `omega-squared' shape...

Combined inversion for the three‐dimensional Q structure and source parameters using microearthquake spectra

The estimation of Q values and/or source corner frequencies fc from single‐station narrow‐band recordings of microearthquake spectra is a strongly nonunique problem. This is due to the fact that the spectra can be equally well fitted with low‐Q/high‐fc or a high‐Q/low‐fc spectral models. Here, a method is proposed to constrain this ambiguity by inverting a set of microearthquake spectra for a three‐dimensional Q model structure and model source parameters seismic moment (Mo ) and corner frequency (fc ) simultaneously. The inversion of whole path Q can be stated as a linear problem in the attenuation operator t* and solved using a tomographic reconstruction of the three‐dimensional Q structure. This Q structure is then used as a “geometrical constraint” for a nonlinear Marquardt‐Levenberg inversion of Mo and fc and a new Q value. The first step of the method consists of interactively fitting the observed microearthquake spectra by spectral models consisting of a source spectrum with an assumed high‐frequency decay, a single‐layer resonance filter to account for local site effects, and additional “whole path attenuation” along the ray path. From the obtained Q values, a three‐dimensional Q model is calculated using a tomographic reconstruction technique (SIRT). The individual Q values along each ray path are then used as Q starting values for a nonlinear iterative Marquardt‐Levenberg inversion of Mo and fc and a “new” Q value. Subsequently, the “new” Q values are used to reconstruct the next Q model which again provides starting values for the “next” nonlinear inversion of Mo, fc, and Q. This process is repeated until the “goodness of fit measure” indicates no further improvement of the results. The method has been tested on a set of approximately 2800 P wave spectra (0.9 < M < 2.0) from the recordings of 635 microearth‐quakes from the Kaoiki seismic zone in Hawaii (Big Island) which were recorded at up to six stations. The hypocenters are distributed within a volume of approximately 18×l8×l5km (depth). The Q model uncertainties have been estimated on the basis of several different tests: Self‐consistency, constraining the comer frequencies, and additionally splitting the data set. The standard deviation of the final Q model which used a grid size of 1.5×1.5×2.0 km (depth) was less than 3% for the depth range 0–5 km, less than 5% between 5 and 7 km, and 7% between 7 and 9 km. The simulation of strong attenuation effects close to the surface shows that site effects may cause a corruption of the resulting Q model at shallow depths. For the given data set and depths below 3–5 km, the method is believed to be able to resolve the model dependent attenuation structure on a scale down to 1–2 km with a resolution of a few percent.

Spectral characteristics of the 1986 September 13 Kalamata (southern Greece) earthquake

SUMMARY The seismic source parameters seismic moment M,, source dimension r, fault length 1, average displacement (u), shear-stress drop Aa, radiated energy Es, and apparent stress n( a) are calculated for the Kalamata (southern Greece) earthquake of 1986 September 13. These source parameters are obtained by using teleseismic P and SH-wave spectra and making use of three independent spectral parameters, the long period spectral level a,, the corner frequency f,, and the parameter E which controls the high-frequency decay of the displacement spectrum. The calculated far-field spectra are based on the direct phases of Pand S-waves and they have been corrected for the instrumental response and for an average radiation pattern assuming normal faulting mechanism. The striking feature of the obtained results is the low stress drop value of about 6-7 bar which is in deviation from the average value (30 bar) for interplate earthquakes. A seismic moment of 1.9 x and 2.2 x loz4 dyne - cm, a fault length of about 22 and 11 km, and an average displacement.of 15 and 9 cm are obtained on the basis of P- and S-waves, respectively.

The 1982 enola, Arkansas, swarm and scaling of ground motion in the eastern United States

Abstract The north-central Arkansas swarm, which began in January of 1982 and was still active as of December 1983, has produced over 30,000 events. Three of these events had duration magnitudes greater than 4.0. Fifty-three locatable events, in the magnitude range 3.8 and below, were recorded during the 2 1/2 weeks our 10 digital seismographs were in place. The hypocentral locations are confined to a tight cluster, with a radius of approximately 1 km. Depths range between 4 and 7 km. Focal mechanisms determined for 10 of the events show a combination of strike slip and normal faulting. Source parameters—seismic moment, source radius, and stress drop—were calculated for 48 of the events. The seismic moments range from 10 18 to 10 21 dyne-cm while the stress drops range from 0.2 to 60 bars. Acceleration spectra are band-limited at the high end at 30 Hz. The stress drops increase with seismic moment up to 10 20 dyne-cm but appear to be constant at greater moment values. The Arkansas source parameters are similar to other body-wave source parameters determined from near-source investigations of earthquakes in Eastern and Central North America (e.g., New Brunswick and South Carolina) and in California (e.g., Mammoth Lakes, Oroville, and Anza), but differ substantially from Lg -wave source parameters estimated for earthquakes in the Eastern and Central United States.

A graphical representation of seismic source parameters

The seismic source parameters seismic moment M0, source dimension r, shear-stress drop Δσ, effective shear stress σeff, radiated energy Es, and apparent stress can all be expressed in terms of three spectral parameters that specify the far-field shear displacement of J. N. Brune's 1970 seismic source model: Ω0 (the long-period spectral level), f0 (the spectral corner frequency), and ε, which controls the high-frequency (f > f0) decay of spectral amplitudes. All the above source parameters can be easily extracted from a log-log plot of Ω0 versus f0 (ε when <1 entering as a parameter), but only three of them are independent. The apparent stress is proportional to the effective shear stress, not the average shear stress. The Ω0-f0 diagram is especially convenient for comparisons within a chosen suite of seismic and/or explosive sources. The equation on which the Gutenberg-Richter energy-magnitude (EGR-ML) relation was originally based is cast into an approximate spectral form; EGR can then be easily compared with Es on the Ω0-f0 diagram for an earthquake of any ML. Within the framework of the (Ω0, f0, ε) relations, it is a simple matter to construct an earthquake magnitude scale directly related to the radiated energy Es.