We mapped the minimum magnitude of complete reporting, M c , for Alaska, the western United States, and for the JUNEC earthquake catalog of Japan. Mc was estimated based on its departure from the linear frequency-magnitude relation of the 250 closest earthquakes to grid nodes, spaced 10 km apart. In all catalogs studied, Mc was strongly heterogeneous. In offshore areas the Mc was typically one unit of magnitude higher than onshore. On land also, Mc can vary by one order of magnitude over distance less than 50 km. We recommend that seismicity studies that depend on complete sets of small earthquakes should be limited to areas with similar Mc, or the minimum magnitude for the analysis has to be raised to the highest com- mon value of Mc. We believe that the data quality, as reflected by the Mc level, should be used to define the spatial extent of seismicity studies where Mc plays a role. The method we use calculates the goodness of fit between a power law fit to the data and the observed frequency-magnitude distribution as a function of a lower cutoff of the magnitude data. Mc is defined as the magnitude at which 90% of the data can be modeled by a power law fit. Mc in the 1990s is approximately 1.2 0.4 in most parts of California, 1.8 0.4 in most of Alaska (Aleutians and Panhandle excluded), and at a higher level in the JUNEC catalog for Japan. Various sources, such as ex- plosions and earthquake families beneath volcanoes, can lead to distributions that cannot be fit well by power laws. For the Hokkaido region we demonstrate how neglecting the spatial variability of M c can lead to erroneous assumptions about deviations from self-similarity of earthquake scaling.

http://basin.earth.ncu.edu.tw/download/courses/seminar_MSc/2009/0225-2_Minimum%20Magnitude%20of%20Completeness%20in%20Earthquake%20Catalogs-%20Examples%20from%20Alaska,%20the%20Western%20United%20States,%20and%20Japan.pdf

Minimum Magnitude of Completeness in Earthquake Catalogs: Examples from Alaska, the Western United States, and Japan

Most of our understanding of the Earth's interior has been derived from measurements from global seismic networks, although no network has ever been truly “global” because some 71% of the Earth's surface is underwater. The resulting gaps in coverage produce a biased and incomplete image of the Earth. Work has begun toward establishing permanent observatories on the deep seafloor, although the technical difficulties remain severe. Will these stations be useful, and where and how shall they be established? Data from seafloor observatories will be of poorer quality than continental site data because the sea surface is an important and local source of broadband noise. This noise is derived from wind and waves through direct forcing at long periods and by nonlinear coupling to elastic waves at short periods. Our understanding of the generation and propagation of seismic noise and of wind and wave climatology can be used to predict the temporal and geographical variability of the noise spectrum and to assess likely sites for permanent seafloor observatories. High noise levels near 1 Hz may raise detection limits for short-period, teleseismic arrivals above mb = 7.5, limiting the usefulness of many seafloor sites. Noise levels in deep boreholes will be 10 dB quieter than those at the seafloor, but sensors buried short distances below the seafloor may also provide comparable noise levels and fidelity. The retrieval of data from permanent seafloor observatories remains an unsolved problem, but long-term temporary arrays of ocean bottom seismometers are now being used in regional scale experiments using earthquakes as sources. Such experiments are likely to be less successful in the Pacific basin than in either the Indian Ocean or North Atlantic Ocean because of higher noise levels.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97RG02287

Broadband seismology and noise under the ocean

SUMMARY

The sizes of three major or great historical earthquakes are reassessed using the isoseismal-area-regression tools developed in Parts I and II of this study of stable continental region (SCR) seismicity. The earthquakes are 1811 New Madrid, central United States, and its following sequence; 1886 Charleston, coastal South Carolina; and 1755 Lisbon, oceanic intraplate off the continental shelf of Portugal. The analysis confirms the large size of these events and for the first time places constraints on the uncertainty of their seismic moment release. Because of the exceptionally low seismic-wave attenuation of eastern North America (ENA), a separate North American regression of seismic moment on isoseismal area was developed. Additionally, the unknown western extents of the New Madrid isoseismal areas were calibrated with the patterns of the M 6.3-6.6 1843 and 1895 earthquakes. Application of Part II analysis procedures with these corrections yields New Madrid size estimates, expressed as moment magnitude, of M 8.1±0.31 for the 1811 December 16, M 7.8±0.33 for the 1812 January 23, and M 8.0±0.33 for the 1812 February 7 principal events. The Charleston earthquake's magnitude decreases from M≳7.4 to M 7.3±0.26 after compensation for the effect of coastal plain sediments on its inner isoseismals. Intensity regressions for Lisbon are calibrated against the isoseismal pattern of the nearly co-located M 7.8 1969 St Vincent earthquake, which in this case increases the predicted size of Lisbon from M 8.4 to M 8.7±0.39. These size estimates are supported by data from independent phenomena: extent and severity of liquefaction, the maximum distance of induced landslides, and for Lisbon, tsunami wave amplitudes. Estimated source parameters are controlled by crustal or lithospheric temperature, which governs the depth extent of brittle faulting. Using estimated continental and oceanic geotherms, viable fault lengths are 30–80 km for Charleston, 120–180 km for 1811 New Madrid, and 180–280 km for Lisbon for average displacements of 2–4 m, 8–11 m, and 10–14 m, respectively, and for average static stress and strain drops. At the estimated seismic moments of this study, the 1811 New Madrid and the 1755 Lisbon events are, respectively, the largest known SCR and oceanic lithosphere earthquakes.

Seismic moment assessment of earthquakes in stable continental regions—III. New Madrid 1811–1812, Charleston 1886 and Lisbon 1755

A simple plane wave model is adequate to explain many surface versus borehole seismometer data sets. Using such a model, we present a series of examples which demonstrate the effects of the free-surface, near-surface velocity gradients, and low impedance surface layers on the amplitudes of upcoming body waves. In some cases, these amplitudes are predictable from simple free-surface and impedance contrast expressions. However, in other cases these expressions are an unreliable guide to the complete response, and the full plane wave calculation must be performed. Large surface amplifications are possible, even without focusing due to lateral heterogeneities or nonlinear effects. Both surface and borehole seismometer site responses are almost always frequency-dependent. 

Ocean bottom versus borehole seismic data from the 1983 Ngendei Seismic Experiment in the southwest Pacific are consistent with both a simple plane wave model and a more complete synthetic seismogram calculation. The borehole seismic response to upcoming P waves is reduced at high frequencies because of interference between the upgoing P wave and downgoing P and SV waves reflected from the sediment-basement interface. However, because of much lower borehole noise levels, the borehole seismometer enjoys a P -wave signal-to-noise advantage of 3 to 7 dB over nearby ocean bottom instruments.

Surface and near-surface effects on seismic waves—theory and borehole seismometer results

We describe an empirical calibration method for obtaining stable seismic source moment-rate spectra derived from regional coda envelopes using broadband stations. The results of applying this method yield source spectra that are more stable than any other direct-phase measure to date. The procedure accounts for all propagation, site, and S -to-coda transfer function effects. The resultant coda-derived moment-rate spectra are then used to provide traditional band-limited magnitudes (e.g., M L , m b ), as well as an unbiased, unsaturated magnitude (moment magnitude, M w ) that is tied to a physical measure of earthquake size (i.e., seismic moment). We validate our results by comparing our coda-derived moment estimates with those obtained from long-period waveform modeling. Most importantly, we demonstrate that the interstation magnitude scatter is significantly reduced when using long-window-length coda (i.e., M w (coda) and m b (coda)). However, when we use short-window coda measurements of 5 sec in length taken after twice the direct-wave travel time, the scatter remains large, comparable to direct waves. Once calibrated, the coda-derived source spectra provide stable, unbiased magnitude estimates for events that are too small either to be reliably waveform modeled or to be seen at far-regional and teleseismic distances. This property is ideal for sparse local or regional networks. We found that our source amplitude estimates were nearly insensitive to the expected source radiation pattern and exhibited roughly a factor of 3-5 less interstation scatter when compared against coda duration and conventional direct-phase measurements (e.g., P g , L g ). We also found that the coda stability, as measured by the interstation scatter for common events, reached a minimum value beyond a certain critical measurement window length. For example, at 6-8 Hz, the interstation standard deviation was less than 0.08 provided the coda measurement was at least ∼80 sec in duration, whereas at 1.5-2.0 Hz, the critical window length was ∼100 sec. For all frequency bands, as the coda window becomes shorter, the standard deviation increases, asymptotically approaching the direct-wave scatter. In this article we describe in detail the calibration methodology and address concerns related to choosing optimal measurement window lengths, estimating error, testing empirical path corrections, and tying coda amplitudes to an absolute scale. In order to demonstrate the usefulness and transportability of our method, we chose the Dead Sea Rift as our study area.

Stable and Transportable Regional Magnitudes Based on Coda-Derived Moment-Rate Spectra

Frequency-dependent regional wave attenuation is estimated for continental paths to the NORESS array in Norway. Regional Lg and Pn spectra from 186 events at ranges between 200 and 1400 km and local magnitudes between 1.1 and 4.8 are inverted for both seismic moment and apparent attenuation. The Lg spectra were inverted between 1 and 7 Hz, and the Pn spectra were inverted between 1 and 15 Hz. The method uses both the spectral and spatial decay of observed signal amplitudes to separate source and path contributions. The assumptions include the geometric spreading rate and the source spectrum to be uniquely defined by its long-period level. Most events considered have local magnitudes less than 3.0, so the source corner frequencies are near or beyond the upper limit of the inverted bandwidth. The Q results, particularly for Lg, are therefore not very sensitive to the details of our source parameterization. The inversion parameters are source moment (for each event), a constant relating corner frequency and moment for the entire data set, and two parameters describing a power law frequency dependence of Q in the region. For fixed source and spreading assumptions the inversion defines clear trade-offs among model parameters. These trade-offs are resolved by adding the constraint that the separately derived source parameters for Lg and Pn are consistent. The “preferred” estimates for the apparent attenuation are QLg(f) = 560f0.26 and QPn(f) = 325f0.48. These Q values correspond to assumed geometric spreading rates of r−0.5 for Lg and r−1.3 for Pn. For fixed Lg spreading, the Pn spreading rate is constrained by requiring that the relative Lg amplitude for earthquakes and explosions of the same moment be consistent with well-supported results from previous empirical studies. The relationship between the inverted seismic moment values and local magnitude is generally consistent with values from near-field studies. Since magnitude does not enter the inversion, this result lends considerable support to the derived Q models. Whatever the physical interpretation of the results, they certainly provide an accurate parameterization of observed amplitude spectra in this region. This is valuable for representing wave propagation in the region, and it provides important data for assessing the event monitoring capabilities of small regional networks.

Simultaneous inversion of regional wave spectra for attenuation and seismic moment in Scandinavia

The oceanic lithosphere is an extremely efficient waveguide for high-frequency seismic energy. In particular, the propagation of the regional to teleseismic oceanic Pn and Sn phases is largely controlled by properties of the oceanic plates. The shallow velocity gradient in the sub-Moho lithosphere results in a nearly linear travel time curve for these oceanic phases and an onset velocity near the material velocity of the uppermost mantle. The confinement of Pn/Sn to the lithosphere imposes a constraint on the maximum range that a normally refracted wave can be observed. The rapid disappearance of Sn and the discontinuous drop in Pn/Sn group velocity beyond a critical distance, dependent upon the local thickness of the lithosphere, are interpreted as a shadowing effect of the low Q asthenosphere. Wave number integration was used to compute complete synthetic seismograms for a model of oceanic lithosphere. The results were compared to data collected during the 1983 Ngendei Seismic Experiment in the southwest Pacific. The Pn/Sn coda is successfully modeled as a sum of leaky organ-pipe modes in the sediment layer and oceanic water column. While scattering is present to some degree, it is not required to explain the long duration and complicated nature of the Pn/Sn wave trains. The presence of extremely high frequencies in Pn/Sn phases and the greater efficiency of Sn than Pn propagation are interpreted in terms of an absorption band rheology. A shorter high-frequency relaxation time for P waves than for S waves results in a rheology with the property that Qα > Qβ at low frequency while Qβ > Qα at high frequency, consistent with the teleseismic Pn/Sn observations. The absorption band model is to viewed as only an approximation to the true frequency dependence of Q in the oceanic lithosphere for which analytic expressions for the material dispersion have been developed.

Synthetic Pn and Sn phases and the frequency dependence of Q of oceanic lithosphere

The detection threshold of a network including NORESS-type arrays in the Soviet Union is estimated using the frequency-dependent attenuation of Pn and Lg observed at NORESS to normalize the threshold of individual stations. The normalization begins with a parameterization of the magnitude and range dependence of the NORESS Pn and Lg spectra in terms of seismic moment and apparent attenuation. A relationship between these spectral amplitudes and the time-domain amplitudes used in signal detection at NORESS is then determined. This allows an estimate of NORESS detection capability from the spectral parameterization and a prediction of the Pn detection capability for regions with different wave propagation characteristics. A comparable prediction is not possible for Lg because of dispersion and the non-stationarity of pre-Lg noise. Instead, an empirical relationship for Lg detectability based on observed temporal amplitudes is determined. To validate the results for NORESS, predictions based on our model are compared with observed detection statistics and with results obtained by Ringdal (1986), who compared detections at NORESS to bulletins produced by local seismic networks. The simulations represent the detection capability of a network of NORESS-type arrays, 20 within and 13 outside the Soviet Union. The 90% ML threshold for detecting three Pn phases for events in the Soviet Union is estimated to be between 2.4 and 2.7 if the frequency-dependent attenuation and noise throughout the network are the same as those observed at NORESS. This threshold is reduced by 0.1 ML if Pn Q is 50% higher in the Soviet Union than estimated for Scandinavia, and is increased by 0.2–0.3 ML if Pn Q is 50% lower. The ML thresholds are reduced by 0.2–0.3 if the detection criteria include Lg as well as Pn phases. While these simulations are carefully normalized by the actual detection capability of a prototype station for test ban treaty monitoring, observations of attenuation and noise inside the Soviet Union are needed to determine how they actually differ from those at NORESS. Also, it must be noted that the NORESS detection capability estimates (and therefore the simulations) are for average conditions and there are regular variations that must be considered when estimating treaty monitoring capability.

Seismic detection capability at NORESS and implications for the detection threshold of a hypothetical network in the Soviet Union

: This report describes a computer program called NetSim that calculates simulations of detection and location capability of seismic networks that include regional stations and arrays. These simulations are used to assess seismic network capability to monitor existing and proposed nuclear explosion test limitation treaties. The main advantage of NetSim compared to similar computer programs (e.g., NETWORTH and SNAP/D) is the incorporation of frequency dependence in the source model, noise estimates (for both primarily and secondary phases), attenuation estimates, and array gain estimates. This is important for simulating the monitoring capability of regional networks, since the dominant signal frequency of regional phases often varies substantially with epicentral distance. The report provides functional descriptions of the NetSim detection and location modules and sample runs for frequency-independent and frequency-dependent input parameters. The accuracy of location uncertainties computed using two methods that attempt to account for the effect of undetected phases is also investigated. These are the probability-weighted approach used in SNAP/D and a Monte Carlo approach that mimics the way location uncertainties vary in practice. Keywords: Computer programs; Modules(Electronics); Input/ Output data; Computer program verification; Seismic data.

NETSIM: A Computer Program for Simulating Detection and Location Capability of Regional Seismic Networks

The amplitudes of water waves generated by shallow explosive sources and recorded by a subbottom seismometer provide constraints on velocity and attenuation parameters of oceanic sediments and upper oceanic crust. Analysis of data collected during the 1983 Ngendei Seismic Experiment in the southwest Pacific Ocean illustrates this method. The data were recorded by a triaxial geophone emplaced 54 m into the basaltic basement. Synthetic seismograms are computed using wave number integration for several crustal models to determine the sensitivity of water wave amplitudes to specific parameters of the sediments and oceanic crust. The synthetic seismograms fit the recorded data to better than a factor of 2 for frequencies as high as 15 Hz and ranges out to 30 km. The amplitude of the direct water wave beyond critical incidence (“direct wave root”) indicates that the sediment P wave velocity is near 1.8 km/s. Modeling of the attenuation of shear wave reverberations in the sediments indicates that sediment Qβ is between 30 and 50. Modulations in water wave amplitude as a function of receiver offset are related to the velocity of the upper oceanic crust. The distances at which amplitude maxima occur indicate that the shear wave velocity of the upper crust at the Ngendei site is 2.4±0.1 km/s. This is an important result since reliable estimates of the shear wave velocity of upper oceanic crust are rare. The distances at which amplitude minima occur are used to constrain the compressional wave velocity of the uppermost crust. However, the modulations do not resolve the compressional wave velocity of the crust as well as the shear wave velocity. The relative amplitudes of successive water waves indicate that the reflection coefficient at the sediment-basement interface is 0.66. This further constrains the compressional wave velocity of the upper crust. Using estimates of the sediment properties and crustal shear wave velocity, the compressional wave velocity of the upper crust at the Ngendei site is estimated from this reflection coefficient to be 4.3–4.4 km/s. A method for estimating the velocity gradient in the upper kilometer of the crust from the interference of water waves with upgoing crustal refractions is presented. Application of the method to these data indicate that the shear wave velocity gradient is about 1.0 s−1, which is indistinguishable from the previous determination by Shearer and Orcutt (1986) using a quite different methodology. The velocity of the upper crust at the Ngendei site is consistent with velocities reported for other regions of similar crustal age (>100 m.y.) and is much greater than velocities typically found for young oceanic crust (<5 m.y.). This lends support to current theories regarding the evolution of the uppermost oceanic crust that attribute higher velocities in older crust to the closing of cracks and pores.

Thomas J. Sereno

Papers

Simultaneous inversion of regional wave spectra for attenuation and seismic moment in Scandinavia

Synthetic Pn and Sn phases and the frequency dependence of Q of oceanic lithosphere

Seismic detection capability at NORESS and implications for the detection threshold of a hypothetical network in the Soviet Union

NETSIM: A Computer Program for Simulating Detection and Location Capability of Regional Seismic Networks

Numerical modeling of water waves recorded by a subbottom seismometer in the southwest Pacific