skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Evidence For Departure in Self-Similarity: A New Spectral Ratio Method Using Narrowband Coda Envelopes

Abstract

This study is motivated by renewed interest within the seismic source community to resolve the long-standing question on energy scaling of earthquakes, specifically, 'Do earthquakes scale self-similarly or are large earthquakes dynamically different than small ones?' This question is important from a seismic hazard prediction point of view, as well as for understanding basic rupture dynamics for earthquakes. Estimating the total radiated energy (ER) from earthquakes requires significant broadband corrections for path and site effects. Moreover, source radiation pattern and directivity corrections can be equally significant and also must be accounted for. Regional studies have used a number of different methods, each with their own advantages and disadvantages. These methods include: integration of squared shear wave moment-rate spectra, direct integration of broadband velocity-squared waveforms, empirical Green's function deconvolution, and spectral ratio techniques. The later two approaches have gained popularity because adjacent or co-located events recorded at common stations have shared path and site effects, which therefore cancel. In spite of this, a number of such studies find very large amplitude variance across a network of stations. In this paper we test the extent to which narrowband coda envelopes can improve upon the traditional spectral ratio using direct phases, allowing amore » better comparison with theoretical models to investigate similarity. The motivation for using the coda is its stability relative to direct waves and its unique property of spatially homogenizing its energy. The local and regional coda is virtually insensitive to lateral crustal heterogeneity and source radiation pattern, and the use of the coda might allow for more stable amplitude ratios to better constrain source differences between event pairs. We first compared amplitude ratio performance between local and near-regional S and coda waves in the San Francisco Bay region for moderate-sized events, then applied the coda spectral ratio method to the 1999 Hector Mine mainshock and some of its larger aftershocks. We find: (1) Average amplitude ratio standard deviations using coda are {approx}0.05 to 0.12, roughly a factor of 3 smaller than direct S-waves for 0.2 < f < 15.0 Hz; (2) Coda spectral ratios for the M{sub w} 7.1 Hector Mine earthquake and its aftershocks show a clear departure from self-similarity, consistent with other studies using the same datasets; (3) Event-pairs (Green's function and target events) can be separated by as much as {approx}25 km for coda amplitudes without any appreciable degradation, in sharp contrast to direct waves.« less

Authors:
; ;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1018795
Report Number(s):
UCRL-JRNL-229275
Journal ID: ISSN 0094-8276; GPRLAJ; TRN: US201114%%337
DOE Contract Number:
W-7405-ENG-48
Resource Type:
Journal Article
Resource Relation:
Journal Name: Geophysical Research Letters, vol. 34, n/a, June 8, 2007, LL11303 1-5; Journal Volume: 34
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; AFTERSHOCKS; AMPLITUDES; EARTHQUAKES; FORECASTING; PERFORMANCE; RADIATIONS; RUPTURES; S WAVES; SAN FRANCISCO BAY; SEISMIC SOURCES; SHEAR; SPECTRA; STABILITY; TARGETS; WAVE FORMS

Citation Formats

Mayeda, K, Malagnini, L, and Walter, W R. Evidence For Departure in Self-Similarity: A New Spectral Ratio Method Using Narrowband Coda Envelopes. United States: N. p., 2007. Web.
Mayeda, K, Malagnini, L, & Walter, W R. Evidence For Departure in Self-Similarity: A New Spectral Ratio Method Using Narrowband Coda Envelopes. United States.
Mayeda, K, Malagnini, L, and Walter, W R. Fri . "Evidence For Departure in Self-Similarity: A New Spectral Ratio Method Using Narrowband Coda Envelopes". United States. doi:. https://www.osti.gov/servlets/purl/1018795.
@article{osti_1018795,
title = {Evidence For Departure in Self-Similarity: A New Spectral Ratio Method Using Narrowband Coda Envelopes},
author = {Mayeda, K and Malagnini, L and Walter, W R},
abstractNote = {This study is motivated by renewed interest within the seismic source community to resolve the long-standing question on energy scaling of earthquakes, specifically, 'Do earthquakes scale self-similarly or are large earthquakes dynamically different than small ones?' This question is important from a seismic hazard prediction point of view, as well as for understanding basic rupture dynamics for earthquakes. Estimating the total radiated energy (ER) from earthquakes requires significant broadband corrections for path and site effects. Moreover, source radiation pattern and directivity corrections can be equally significant and also must be accounted for. Regional studies have used a number of different methods, each with their own advantages and disadvantages. These methods include: integration of squared shear wave moment-rate spectra, direct integration of broadband velocity-squared waveforms, empirical Green's function deconvolution, and spectral ratio techniques. The later two approaches have gained popularity because adjacent or co-located events recorded at common stations have shared path and site effects, which therefore cancel. In spite of this, a number of such studies find very large amplitude variance across a network of stations. In this paper we test the extent to which narrowband coda envelopes can improve upon the traditional spectral ratio using direct phases, allowing a better comparison with theoretical models to investigate similarity. The motivation for using the coda is its stability relative to direct waves and its unique property of spatially homogenizing its energy. The local and regional coda is virtually insensitive to lateral crustal heterogeneity and source radiation pattern, and the use of the coda might allow for more stable amplitude ratios to better constrain source differences between event pairs. We first compared amplitude ratio performance between local and near-regional S and coda waves in the San Francisco Bay region for moderate-sized events, then applied the coda spectral ratio method to the 1999 Hector Mine mainshock and some of its larger aftershocks. We find: (1) Average amplitude ratio standard deviations using coda are {approx}0.05 to 0.12, roughly a factor of 3 smaller than direct S-waves for 0.2 < f < 15.0 Hz; (2) Coda spectral ratios for the M{sub w} 7.1 Hector Mine earthquake and its aftershocks show a clear departure from self-similarity, consistent with other studies using the same datasets; (3) Event-pairs (Green's function and target events) can be separated by as much as {approx}25 km for coda amplitudes without any appreciable degradation, in sharp contrast to direct waves.},
doi = {},
journal = {Geophysical Research Letters, vol. 34, n/a, June 8, 2007, LL11303 1-5},
number = ,
volume = 34,
place = {United States},
year = {Fri Mar 16 00:00:00 EDT 2007},
month = {Fri Mar 16 00:00:00 EDT 2007}
}
  • Because many regional seismic discriminants are functions of magnitude, it is important to obtain a stable measurement especially for smaller events that will likely have very limited station coverage. We have collected and analyzed regional broad band waveforms from stations in the middle east region for the purpose of calibrating a stable regional magnitude scale that can be applied to events that are too small to detect teleseismically. Our approach is to obtain frequency-dependent empirical Greens function coda envelopes for narrow frequency bands that can be used to correct for gross path effects. We make the assumption that the moment-ratemore » spectra are generally flat below{approximately}2 Hz for these events smaller than Mw{approximately}3.5. In a least squares sense, we obtain frequency-dependent corrections to the Lg coda measurements to fit the scalar moment estimates. These frequency-dependent corrections remove the effects of the S-to-Lg coda transfer function, thus correcting back to the S-wave source spectra. Due to the averaging nature of Lg coda waves we are then able to obtain a stable single-station estimate of the source spectra.To avoid regional biases we tie our coda envelope amplitude measurements to seismic moments obtained from long period 1-D waveform modeling for moderate sized earthquakes (A4w-3.5.- 4.5). Most importantly, we can now apply the same corrections to significantly smaller events that cannot be observed teleseismically. Our empirical approach takes into account scattering,absorption, and waveguide losses as well as frequency-dependent site effects.Moreover, the use of the coda envelope mitigates the undesirable effects of source anisotropy, random site interference, path variability, and directivity that plague direct wave measurements. This approach was successfully applied to other regions where it was observed that the coda-derived Mw estimates showed significantly smaller dependence on lateral path variation and source radiation anisotropy than the more conventional approaches such as mb(Pg),mb(Lg),and teleseismic mb.« less
  • Scattering by heterogeneities is an important factor controlling shapes oF seismograms. Analyzing horizontal component seismograms in the band 1.0-8 Hz of local earthquakes in western Japan, the author found that coda energy concentration just after the S wave arrival is more than expected for any multiple isotropic scattering model in uniform infinite medium. This behavior was seen even for deep earthquakes and became stronger with increase of frequency. To try to interpret this observation, nonisotropy is introduced into the multiple scattering model. The observed envelopes are compared with the model in order to estimate the amount of nonisotropy in scattering.more » Coda wave envelopes are synthesized using the Monte Carlo method for the nonisotropic scattering media. Two types of angular dependent scattering are considered as models of the nonisotropy with relation to the perturbation of seismic wave velocity in the lithosphere: perturbed media with exponential and Gaussian autocorrelation functions. It is found that forward scattering is dominant and the strength of sideways scattering is at least 10 times larger than that of backward scattering. The amount of the nonisotropic scattering means that correlation distance is estimated to be larger than several hundred meters in the case of Gaussian random media. 31 refs., 17 figs.« less
  • A Monte Carlo departure from nucleate boiling ratio (DNBR) limit analysis has been performed with a six-channel thermal-hydraulics code model as the tool for DNBR calculations. Compared is the use of the few-channel, fast-running code models with the use of a response surface model as the DNBR calculator. The latter had been used to date for Monte Carlo analyses. The principles of Monte Carlo DNBR limit determination are reviewed to provide the necessary background information.
  • Partial melting at the grain boundaries of mantle rock is a source of attenuation often invoked in the interpretation of teleseismic data. However, related experimental studies are extremely difficult and hence are scarce. We have used a convenient metallurgical system to model a rock sample with a layer of fluid at grain boundaries: the analog of the rock samples is a cylinder of fine-grained, pure aluminum (diameter is 6 cm; height is 6 cm), and the analog of the fluid is provided by a thin layer of aluminum-gallium eutectic at the grain boundaries. The metal gallium, liquid at room temperature,more » diffuses extremely rapidly into the grain boundaries of aluminum where it forms a soft eutectic that melts at 28[degrees]C. The total amount of gallium in the sample represents about 0.2 wt%. Ultrasonic (1 MHz) pulses were transmitted through the sample by a transducer, and the full waveform of the reflected and scattered signals, including the coda, were recorded. Analyses of the decay parameter of the coda envelope yield values of Q[sup [minus]1]. Preliminary results show that the thin film of aluminum-gallium eutectic at the grain boundaries noticeably increases attenuation. For pure aluminum at room temperature, Q[sup [minus]1] = 0.095 [times] 10[sup [minus]3]; after invasion of gallium into the grain boundaries, the value measured at 26[degrees]C (in solid state) was Q[sup [minus]1] = 0.62 [times] 10[sup [minus]3]; at 28[degrees]C, when the autectic became liquid, Q[sup [minus]1] = 1.01 [times] 10[sup [minus]3], an order of magnitude higher than for pure aluminum. 26 refs., 6 figs.« less
  • We develop a new methodology to determine apparent attenuation for the regional seismic phases Pn, Pg, Sn, and Lg using coda-derived source spectra. The local-to-regional coda methodology (Mayeda, 1993; Mayeda and Walter, 1996; Mayeda et al., 2003) is a very stable way to obtain source spectra from sparse networks using as few as one station, even if direct waves are clipped. We develop a two-step process to isolate the frequency-dependent Q. First, we correct the observed direct wave amplitudes for an assumed geometrical spreading. Next, an apparent Q, combining path and site attenuation, is determined from the difference between themore » spreading-corrected amplitude and the independently determined source spectra derived from the coda methodology. We apply the technique to 50 earthquakes with magnitudes greater than 4.0 in central Italy as recorded by MEDNET broadband stations around the Mediterranean at local-to-regional distances. This is an ideal test region due to its high attenuation, complex propagation, and availability of many moderate sized earthquakes. We find that a power law attenuation of the form Q(f) = Q{sub 0}f{sup Y} fit all the phases quite well over the 0.5 to 8 Hz band. At most stations, the measured apparent Q values are quite repeatable from event to event. Finding the attenuation function in this manner guarantees a close match between inferred source spectra from direct waves and coda techniques. This is important if coda and direct wave amplitudes are to produce consistent seismic results.« less