Howard J. Patton

Regional Magnitude Scaling, Transportability, and Ms:mb Discrimination at Small Magnitudes

Abstract — Data sets of mb(Pn) and mb(Lg) measurements are presented for three continental regions in order to investigate scaling relationships with moment magnitude Mw and event discrimination at small magnitudes. Compilations of published measurements are provided for eastern North American and central Asian earthquakes, and new measurements are reported for earthquakes located in western United States. Statistical tests on Mw:mb relationships show that the mb(Lg) scale of Nuttli (1973) is transportable between tectonic regions, and a single, unified Mw:mb(Lg) relationship satisfies observations for Mw∼4.2–6.5 in all regions. A unified relationship is also developed for nuclear explosions detonated at the Nevada Test Site and test sites of the former Soviet Union. Regional mb for explosions scale at higher rates than for earthquakes, and of significance is the finding that mb(Pn) for explosions scales at a higher rate than mb(Lg). A model is proposed where differences in scaling rates are related to effects of spectral overshoot and near-field Rg scattering on the generation of Pn and Lg waves by explosions. For earthquakes, mb(Pn) and mb(Lg) scale similarly, showing rates near 1.0 or 2/3 · log10Mo (seismic moment).¶Mw:mb(Lg) scaling results are converted to unified Ms:mb(Lg) relationships using scaling laws between log Mo and Ms. For earthquakes with Ms greater than 3.0, the scaling rate is 0.69 · Ms, which is the same as it is for nuclear explosions if Ms is proportional to 1.12 · log Mo, as determined by NTS observations. Thus, earthquake and explosion populations are parallel and separated by 0.68 mb units for large events. For small events (Ms < 3.0), populations may converge or diverge depending on the tectonic region in which earthquakes occur and the scaling rate of explosions at small yields. Earthquakes scale as 0.64 and 0.75 on Ms:mb(Lg) plots for stable and tectonic regions, respectively. While the scaling rate for explosions is ∼0.69, this value is uncertain due to paucity of Mo observations at small yields. Measurements of [mb(P) − mb(Lg)] for earthquakes in the western United States have an average value of −0.33 ± .03 mb units, in good agreement with Nuttlis estimate of mb bias for NTS. This result suggests that Nuttlis method for estimating test site bias can be extended to earthquakes to make estimates of bias on regional scales. In addition, a new approach for quick assessments of regional bias is proposed where Ms:mb(P) observations are compared with Ms:mb(Lg) relationships. Catalog Ms:mb(P) data suggest that mb bias is significant for tectonic regions of southern Asia, averaging about −0.4 mb units.

Improving Regional Seismic Event Location in China

Abstract — In an effort to improve our ability to locate seismic events in China using only regional data, we have developed empirical propagation path corrections and applied such corrections using traditional location routines. Thus far, we have concentrated on corrections to observed P arrival times for crustal events using travel-time observations available from the USGS Earthquake Data Reports, the International Seismic Centre Bulletin, the preliminary International Data Center Reviewed Event Bulletin, and our own travel-time picks from regional data. Location ground truth for events used in this study ranges from 25 km for well-located teleseimic events, down to 2 km for nuclear explosions located using satellite imagery. We also use eight events for which depth is constrained using several waveform methods. We relocate events using the EvLoc algorithm from a region encompassing much of China (latitude 20°–55°N; longitude 65°–115°E). We observe that travel-time residuals exhibit a distance-dependent bias using IASPEI91 as our base model. To remedy this bias, we have developed a new 1-D model for China, which removes a significant portion of the distance bias. For individual stations having sufficient P-wave residual data, we produce a map of the regional travel-time residuals from all well-located teleseismic events. Residuals are used only if they are smaller than 10 s in absolute value and if the seismic event is located with accuracy better than 25 km. From the residual data, correction surfaces are constructed using modified Bayesian kriging. Modified Bayesian kriging offers us the advantage of providing well-behaved interpolants and their errors, but requires that we have adequate error estimates associated with the travel-time residuals from which they are constructed. For our P-wave residual error estimate, we use the sum of measurement and modeling errors, where measurement error is based on signal-to-noise ratios when available, and on the published catalog estimate otherwise. Our modeling error originates from the variance of travel-time residuals for our 1-D China model. We calculate propagation path correction surfaces for 74 stations in and around China, including six stations from the International Monitoring System. The statistical significance of each correction surface is evaluated using a cross-validation technique. We show relocation results for nuclear tests from the Balapan and Lop Nor test sites, and for earthquakes located using interferometric synthetic aperture radar. These examples show that the use of propagation path correction surfaces in regional relocations eliminates distance bias in the residual curves and significantly improves the accuracy and precision of seismic event locations.

Chemical Explosion Experiments to Improve Nuclear Test Monitoring

A series of chemical explosions, called the Source Physics Experiments (SPE), is being conducted under the auspices of the U.S. Department of Energy’s National Nuclear Security Administration (NNSA) to develop a new more physics-based paradigm for nuclear test monitoring. Currently, monitoring relies on semi-empirical models to discriminate explosions from earthquakes and to estimate key parameters such as yield. While these models have been highly successful monitoring established test sites, there is concern that future tests could occur in media and at scale depths of burial outside of our empirical experience. This is highlighted by North Korean tests, which exhibit poor performance of a reliable discriminant, mb:Ms (Selby et al., 2012), possibly due to source emplacement and differences in seismic responses for nascent and established test sites. The goal of SPE is to replace these semi-empirical relationships with numerical techniques grounded in a physical basis and thus applicable to any geologic setting or depth.

Seismic source functions from free-field ground motions recorded on SPE: Implications for source models of small, shallow explosions

Reduced displacement potentials (RDPs) for chemical explosions of the Source Physics Experiments (SPE) in granite at the Nevada Nuclear Security Site are estimated from free-field ground motion recordings. Far-field P wave source functions are proportional to the time derivative of RDPs. Frequency domain comparisons between measured source functions and model predictions show that high-frequency amplitudes roll off as ω− 2, but models fail to predict the observed seismic moment, corner frequency, and spectral overshoot. All three features are fit satisfactorily for the SPE-2 test after cavity radius Rc is reduced by 12%, elastic radius is reduced by 58%, and peak-to-static pressure ratio on the elastic radius is increased by 100%, all with respect to the Mueller-Murphy model modified with the Denny-Johnson Rc scaling law. A large discrepancy is found between the cavity volume inferred from RDPs and the volume estimated from laser scans of the emplacement hole. The measurements imply a scaled Rc of ~5 m/kt1/3, more than a factor of 2 smaller than nuclear explosions. Less than 25% of the seismic moment can be attributed to cavity formation. A breakdown of the incompressibility assumption due to shear dilatancy of the source medium around the cavity is the likely explanation. New formulas are developed for volume changes due to medium bulking (or compaction). A 0.04% decrease of average density inside the elastic radius accounts for the missing volumetric moment. Assuming incompressibility, established Rc scaling laws predicted the moment reasonable well, but it was only fortuitous because dilation of the source medium compensated for the small cavity volume.

Modeling Ms‐Yield Scaling of Nevada Test Site Nuclear Explosions for Constraints on Volumetric Moment due to Source‐Medium Damage

Abstract The precision of M s ‐yield‐scaling results is exploited to place tighter constraints on the volumetric moment due to source‐medium damage than previously estimated for Pahute Mesa explosions on the Nevada Test Site (NTS). Results for two coupling scenarios, one based on P waves to set a lower bound and one based on Rayleigh waves to set an upper bound, bracket the predictions of a model based on moment tensor theory for an explosion monopole and the accompanying damage. This study confirms that the apparent explosion moment M I is a consequence of direct effects of the energy release with a volumetric moment M t due to cavity formation and the effects due to source‐medium damage. The source model predicts that M I = M t ( K +2)/3, where K is a damage index and a value of 1 means no permanent deformation due to damage. Excess moment due to dilation of the source medium ( K >1) is quantified and shown to be a factor increasing the apparent yield ( W ) scaling of M s from 0.80log[ W ] for a pure explosion with cube‐root containment practice and uniform coupling to ∼1.0log[ W ], a scaling commonly accepted by the explosion community. Scaling observations are related to the source model by establishing the equivalence between network M s and the theoretical Rayleigh‐wave radiation for an azimuthal‐independent source component. This equivalence motivates a physical basis for transporting observations to other test sites. Transported M s scaling results for NTS indicate that damage is a more important source of Rayleigh waves for Balapan explosions, most likely due to better energy coupling of upgoing shock waves and stronger free‐surface interactions than for NTS explosions.

Difference Spectrograms: A New Method for Studying S-Wave Generation from Explosions

Abstract A new method for studying the source characteristics of regional phases including explosion-generated S waves is developed and utilizes differences between spectrograms of two closely located explosions recorded at a common station. Relative source effects of a normal-buried explosion with respect to an overburied explosion are isolated in the resultant difference spectrogram because path and receiver site effects cancel. Difference spectrograms provide a global view of the relative frequency content, while the spectral ratio method is specific to the time window selected for Fourier analysis. Difference spectrograms for Nevada test site (NTS) explosions are characterized by the presence of amplitude modulations in Pg coda, in time windows predicted for Sn and Lg , and in long-duration Lg codas. Previous studies have modeled similar features in Lg spectral ratios by invoking the Rg -to- S scattering hypothesis and the notion of Rg imprinting, where the modulations arise due to interference of Rg waves from explosion and induced tensile failure sources. We propose that spectral peaking at low frequencies in Lg spectra is related to resonances in the source medium that affect the excitation and propagation of Rg waves, adding further support to Rg imprinting and the Rg -to- S scattering hypothesis. Difference spectrograms for explosion pairs Rousanne/Techado and Baseball/Borrego are interpreted to have a spectral null related to a pulse of Rg -derived energy from a common scatterer. Using the relative timing of this null, we estimate an Rg velocity (∼0.8 km/sec) and locate a candidate scattering source at the Yucca Basin boundary near Climax Stock. Difference spectrograms provide a wealth of information about the spectral content of regional phases related to source effects, which can be used to gain insights into source generation processes.

Modeling Anomalous Surface-Wave Propagation across the Southern Caspian Basin

The South Caspian Basin contains one of the thickest sedimentary deposits in the world. Intermediate-frequency (0.02–0.04 Hz) fundamental-mode Rayleigh waves propagating across the basin are severely attenuated, but apparent attenuation is significantly less for both low and high frequencies. We have modeled the response of surface waves in a simplified rendition of the South Caspian Basin model of Mangino and Priestley (1998) using a hybrid normal-mode/2D finite-difference approach. To gain insight into the features of the basin that cause the anomalous surface-wave propagation, we have varied parameters of the basin model and computed synthetic record sections to compare with the observed seismograms. We have varied the Moho depth beneath the basin, the shape of the basin boundaries, the thickness and shear-wave Q of the sediments and mantle, and the water depth. Of these parameters, the intermediate-frequency surface waves are most severely affected by the sediment thickness and shear-wave attenuation. All models fail to satisfy observations for frequencies of 0.05 Hz and above, and this failure is attributed to significant 3D wave propagation effects caused by focusing and scattering of surface waves by basin structures.

A Probability of Detection Method for Reducing Short-Period mb−Ms False Alarm Rates

The 20-sec m b− M s discriminant is one of the most reliable and best understood methods for identifying underground nuclear explosions. To extend the discriminant to lower magnitude thresholds at regional distances it is necessary to perform the M s measurement at shorter periods. Although short-period Rayleigh- wave measurements have lower detection thresholds than those at 20 sec, they are more influenced by the effects of earthquake depth that cause overlap of earthquake and explosion populations. We present a technique using a probability of detection model (pxd) to estimate the probability that a surface-wave detection came from an underground explosion. The key to the method is the development of a simple analytic model to predict the maximum expected amplitude probability distribution (upper tail) from an underground explosion of a given body-wave magnitude recorded at a specified distance. The model assumes full coupling and accounts for material effects, attenuation, and amplification from tectonic release. The detection classifier is applicable when there is a signal detection above a specified signal-to-noise cutoff and the detection is of greater amplitude than the maximum expected explosion amplitude. We assume that in general, earthquakes generate larger 6- to 12-sec Rayleigh-wave amplitudes than explosions for a given body-wave magnitude. For a given sensor we define the probability of detection given that the source was an explosion. Using Bayes’ Rule we determine the probability that the signal detection originated from an explosion. The surface-wave probability of detection curve for a given period and the prior probability that an explosion occurred can also be included in the formulation. We compute the conditional probability (represented as a p value) that the detected signal originated from an explosion. No assumptions regarding the non-explosion source are necessary other than the fact that the maximum amplitudes are expected to be greater than those from the explosion under full coupling conditions. Under the specified conditions, the p value will always be a small value indicating a low probability that the detected signal originated from an explosion. The p value can also be thought of as a random variable that can be combined with other discriminants in a multivariate setting. We show results of the signal detection formulation using short- period Rayleigh waves from earthquakes and explosions in Eurasia and compare to the traditional m b− M s at different periods. For a set of earthquakes and explosions recorded at wmq measured at a 6- to 12-sec period, false alarm rates are reduced from 28.3% for m b− M s to 18.6% using the probability of detection model. Using pxd by itself as an earthquake identifier, 78% of all events are assigned a p value resulting in a false alarm rate of 22% that is better than m b− M s alone for this dataset.

Apparent Explosion Moments from Rg Waves Recorded on SPE

Abstract Seismic moments for the first four chemical tests making up phase I of the Source Physics Experiments (SPE) are estimated from 6‐Hz Rg waves recorded along a single radial line of geophones under the assumption that the tests are pure explosions. These apparent explosion moments are compared with moments determined from the reduced displacement potential method applied to free‐field data. Light detection and ranging (lidar) observations, strong ground motions on the free surface in the vicinity of ground zero, and moment tensor inversion results are evidence that the fourth test SPE‐4P is a pure explosion, and the moments show good agreement, 8×10 10   N·m for free‐field data versus 9×10 10   N·m for Rg waves. In stark contrast, apparent moments for the first three tests are smaller than near‐field moments by factors of 3–4. Relative amplitudes for the three tests determined from Rg interferometry using SPE‐4P as an empirical Green’s function indicate that radiation patterns are cylindrically symmetric within a factor of 1.25 (25%). This fact assures that the apparent moments are reliable even though they were measured on just one azimuth. Spallation occurred on the first three tests, and ground‐based lidar detected permanent deformations. As such, the source medium suffered late‐time damage. Destructive interference between Rg waves radiated by explosion and damage sources will reduce amplitudes and explain why apparent moments are smaller than near‐field moments based on compressional energy emitted directly from the source.

Apparent Explosion Moments from Rg Waves Recorded on SPEApparent Explosion Moments from Rg Waves Recorded on SPE

Abstract Seismic moments for the first four chemical tests making up phase I of the Source Physics Experiments (SPE) are estimated from 6‐Hz Rg waves recorded along a single radial line of geophones under the assumption that the tests are pure explosions. These apparent explosion moments are compared with moments determined from the reduced displacement potential method applied to free‐field data. Light detection and ranging (lidar) observations, strong ground motions on the free surface in the vicinity of ground zero, and moment tensor inversion results are evidence that the fourth test SPE‐4P is a pure explosion, and the moments show good agreement, 8×10 10   N·m for free‐field data versus 9×10 10   N·m for Rg waves. In stark contrast, apparent moments for the first three tests are smaller than near‐field moments by factors of 3–4. Relative amplitudes for the three tests determined from Rg interferometry using SPE‐4P as an empirical Green’s function indicate that radiation patterns are cylindrically symmetric within a factor of 1.25 (25%). This fact assures that the apparent moments are reliable even though they were measured on just one azimuth. Spallation occurred on the first three tests, and ground‐based lidar detected permanent deformations. As such, the source medium suffered late‐time damage. Destructive interference between Rg waves radiated by explosion and damage sources will reduce amplitudes and explain why apparent moments are smaller than near‐field moments based on compressional energy emitted directly from the source.