Mark D. Fisk

Source Spectral Modeling of Regional P/S Discriminants at Nuclear Test Sites in China and the Former Soviet Union

Theoretical understanding of regional P/S discriminants has been a long- standing research topic with important implications for nuclear explosion monitoring. The observation that discrimination is poor at low frequencies, but becomes significant at higher frequencies, usually at about 3 to 4 Hz, particularly needs understanding. To gain insight, source and attenuation models are used to predict spectra of regional seismic phases ( Pn, Sn , and Lg ) for nuclear explosions and selected earthquakes near the Lop Nor, Semipalatinsk (Balapan and Degelen Mountain), and Novaya Zemlya test sites in China and the former Soviet Union. A modified Brune (1970) model (a la Walter and Taylor, 2002) is used to predict P - and S -source terms for earthquakes. A Mueller/Murphy (1971) model is used for explosions, including a new conjecture that the S waves may be modeled by the same functional form as for P waves, but with corner frequency reduced by the ratio of near-source shear and compressional velocities, vs ( S )/ vs ( P ). Results indicate that the frequency dependence of Pn / Sn and Pn / Lg discrimination performance at all of these hard-rock test sites is primarily due to differences in the corner frequencies of P and S waves for explosions, qualitatively consistent with observations by Xie and Patton (1999) for Lop Nor. P / S discrimination emerges at the explosion S -wave corner frequency and does not improve above the P -wave corner frequency. Scaling of the explosion S -wave corner frequency with elastic radius as vs ( S )/ Re at all of these test sites suggests that major contributions to S -wave generation from explosions may be occurring at the same distance scale (i.e., the elastic radius) as P waves from explosions. The explicit physical mechanism of this near-source S -wave generation is still being investigated. Implications regarding application of regional P / S discriminants are discussed.

Calculation of Broadband Time Histories of Ground Motion, Part II: Kinematic and Dynamic Modeling Using Theoretical Green's Functions and Comparison with the 1994 Northridge Earthquake

In the evolution of methods for calculating synthetic time histories of ground motion for postulated earthquakes, kinematic source models have dominated to date because of their ease of application. Dynamic models, however, which incorporate a physical relationship between important faulting parameters of stress drop, slip, rupture velocity, and rise time, are becoming more accessible. This article compares a class of kinematic models based on the summation of a fractal distribution of subevent sizes with a dynamic model based on the slip-weakening friction law. Kinematic modeling is done for the frequency band 0.2 to 10.0. Hz, dynamic models are calculated from 0.2 to 2.0. Hz. The strong motion data set for the 1994 Northridge earthquake is used to evaluate and compare the synthetic time histories. Source models are propagated to the far field by convolution with 1D and 3D theoretical Green’s functions. In addition, the kinematic model is used to evaluate the importance of propagation path effects: velocity structure, scattering, and nonlinearity. At present, the kinematic model gives a better broadband fit to the Northridge ground motion than the simple slip-weakening dynamic model. In general, the dynamic model overpredicts rise times and produces insufficient shorter-period energy. Within the context of the slip-weakening model, the Northridge ground motion requires a short slip-weakening distance, on the order of 0.15 m or less. A more complex dynamic model including rate weakening or one that allows shorter rise times near the hypocenter may fit the data better.

Accurate Locations of Nuclear Explosions at the Lop Nor Test Site Using Alignment of Seismograms and IKONOS Satellite Imagery

Locations are estimated of 11 underground nuclear explosions conducted between 26 May 1990 and 29 July 1996 at the Lop Nor test site in western China. To perform the analysis, seismic recordings were obtained from the Center for Monitoring Research (CMR), U.S. National Data Center, and Incorporated Research Institutions for Seismology (IRIS) Data Management Center. Using recordings with adequate signal-to-noise ratios, P -wave arrivals are picked manually by aligning waveforms of the events at common stations. This provides very precise relative phase timings (i.e., with relative errors typically much less than 0.1 sec). Based on analysis of commercial IKONOS satellite imagery, the locations of three explosions are fixed and used as master events. The other events are located relative to the nearest master event after correcting their travel times by the travel-time residuals (relative to IASP91) of the master events. Location estimates of the 25 September 1992 and 29 July 1996 nuclear tests are within about 100 m of each other. The 90%-confidence error ellipse for the 29 July 1996 event has a semimajor axis of less than 0.3 km. The results indicate that these two tests were likely conducted in the same tunnel. Location estimates of nine explosions conducted at the eastern zone of the Lop Nor test site are within 140 to 490 meters of vertical boreholes and infrastructure to support nuclear testing observed in IKONOS imagery. The location estimates of the eleven Chinese explosions are all considered to be well within one km of the true detonation points and, hence, are categorized as GT1 events (as defined by Yang et al. , 2000a). These solutions allow seismic travel times to be calibrated accurately for the Lop Nor region at seismographic stations of the International Monitoring System (IMS). Manuscript received 23 October 2001.

Corner Frequency Scaling of Regional Seismic Phases for Underground Nuclear Explosions at the Nevada Test Site

Model fits are used to estimate source spectral corner frequencies of regional seismic phases Pn , Pg , and Lg from underground nuclear explosions (unes) at the Nevada Test Site (nts), based on recordings by Lawrence Livermore National Laboratory (llnl) nts Network stations. The spectra are corrected for instrument response, distance, and station effects, and then network averaged. Explicit information regarding geophysical working-point properties, depth of burial, and some announced yields for nts explosions (Springer et al. , 2002) is utilized for the spectral modeling. Scaling of Pn , Pg , and Lg corner frequencies with source yield is examined for sets of explosions at Yucca Flat, Pahute Mesa, and Rainier Mesa with similar material properties (medium type, density, velocities, and gas porosity). The unes are limited to those in media with gas porosity of 10% or less so that a source spectral model with a rolloff of f −2 is applicable. Model comparisons are also examined for regional P / Lg discriminants. A key result is that Lg corner frequencies for ntsunes exhibit similar scaling with source size as for P waves, but shifted lower, analogous to observations by Fisk (2006) for the Lop Nor, Semipalatinsk, and Novaya Zemlya test sites. This appears to corroborate an important effect, that is, that major contributions to S -wave generation by explosions occur near the source with a similar length scale, comparable to the elastic radius, as for P waves from explosions. Although the explicit physical mechanism is not yet understood, the implications are important regarding where and perhaps how S waves are predominantly generated by explosions. A related, key result is that the increasing separation of P / Lg at higher frequencies between nts explosions and earthquakes has a consistent model-based explanation, as at other nuclear test sites, in terms of the difference between explosion P and S corner frequencies.

Regional Seismic-Event Characterization Using a Bayesian Formulation of Simple Kriging

An approach is presented to calibrate and use regional P - S amplitude ratios to improve seismic-event characterization capabilities with regard to monitoring the Comprehensive Nuclear-Test-Ban Treaty. Data for presumed earthquakes are used to estimate distance corrections for Pn - Sn and Pn - Lg ratios in the 6–8-Hz pass-band for tectonic and stable-region types. The regional phase-amplitude ratios are further corrected for path variations using simple kriging. Simple kriging is derived using a Bayesian approach. A correction surface is determined for each type of amplitude ratio at each station as an optimal linear combination of existing amplitude-ratio data at the station, giving greater weight to calibration data nearer to the correction location. A corresponding uncertainty surface is also estimated in terms of the residual variance of the data and a calibration variance. For well-calibrated locations, the correction converges to the mean of nearby data, and the uncertainty converges to the residual variance. For locations far from calibration data, the correction surface converges to the worldwide average, with larger uncertainty. With these correction and uncertainty surfaces, corrected values of Pn / Smax (6–8 Hz) are obtained and used to define a hypothesis test that fixes the significance level with respect to misclassifying explosions. The criterion is applied to 140 explosions at known nuclear-test sites and to 4173 Reviewed Event Bulletin (REB) events above mb 3.5 (presumed to be mostly earthquakes) with regional recordings between 3° and 17°, Pn signal-to-noise ratio (SNR) >2.0, and Sn or Lg SNR >1.3. At a 0.005 significance level, none of the 140 explosions at any of the known nuclear-test sites are screened out, whereas about 78% of the REB events are screened out. Correcting regional P - S ratios for spatial variations improves the screening performance by about 25% over just correcting for distance. The screening results are fairly insensitive to estimates of parameters (correlation length, calibration variance, and residual variance) that are used, along with data, to compute the correction and uncertainty surfaces at each station.

Experimental Seismic Event-screening Criteria at the Prototype International Data Center

Abstract — Experimental seismic event-screening capabilities are described, based on the difference of body-and surface-wave magnitudes (denoted as Ms:mb) and event depth. These capabilities have been implemented and tested at the prototype International Data Center (PIDC), based on recommendations by the IDC Technical Experts on Event Screening in June 1998. Screening scores are presented that indicate numerically the degree to which an event meets, or does not meet, the Ms:mb and depth screening criteria. Seismic events are also categorized as onshore, offshore, or mixed, based on their 90% location error ellipses and an onshore/offshore grid with five-minute resolution, although this analysis is not used at this time to screen out events.¶Results are presented of applications to almost 42,000 events with mb ≥ 3.5 in the PIDC Standard Event Bulletin (SEB) and to 121 underground nuclear explosions (UNEs) at the U.S. Nevada Test Site (NTS), the Semipalatinsk and Novaya Zemlya test sites in the Former Soviet Union, the Lop Nor test site in China, and the Indian, Pakistan, and French Polynesian test sites. The screening criteria appear to be quite conservative. None of the known UNEs are screened out, while about 41 percent of the presumed earthquakes in the SEB with mb ≥ 3.5 are screened out. UNEs at the Lop Nor, Indian, and Pakistan test sites on 8 June 1996, 11 May 1998, and 28 May 1998, respectively, have among the lowest Ms:mb scores of all events in the SEB.¶To assess the validity of the depth screening results, comparisons are presented of SEB depth solutions to those in other bulletins that are presumed to be reliable and independent. Using over 1600 events, the comparisons indicate that the SEB depth confidence intervals are consistent with or shallower than over 99.8 percent of the corresponding depth estimates in the other bulletins. Concluding remarks are provided regarding the performance of the experimental event-screening criteria, and plans for future improvements, based on recent recommendations by the IDC Technical Experts on Event Screening in May 1999.

A bootstrap generalized likelihood ratio test in discriminant analysis

Abstract A generalized likelihood ratio test is developed for classification in two populations when one needs to control one of the probabilities of misclassification. The proposed classification procedure is constructed by applying the parametric bootstrap to the generalized likelihood ratio. There are known methods for controlling this misclassification probability for the case where normal distributions with the same covariance matrix are assumed. Our approach, however, can be applied to not only this case but to the case of normal distributions with different covariance matrices and the case of a mixture of discrete and continuous variables. The results given here do not depend on normality but can, in fact, be applied to any distribution for which the maximum likelihood estimates exist. We do, however, restrict our simulation of these results to the normal distribution if the variates are all continuous. Three cases are simulated: normal distributions with equal covariance matrix, normal distributions with unequal covariance matrices, and mixture of categorical and normal variables. An application to classifying seismic events is presented.

Constraining Regional Phase Amplitude Models for Eurasia, Part 2: Frequency‐Dependent Attenuation and Site Results

Abstract Fisk and Phillips (2013) motivated the need to constrain trade‐offs among correction parameters for regional phase amplitudes to improve seismic discrimination and magnitude (yield) estimation. Using an empirical Green’s function approach to cancel path and site effects, relative spectra of direct regional phases and coda were fit for many thousands of nearby, similar earthquake pairs of different moments, to estimate reliable source corner frequencies and relative moments. Detailed comparisons demonstrated the benefit of using independent measurements of coda and direct phases to provide a large set of corroborated source terms for earthquakes throughout Eurasia. The spectra were subsequently corrected for source terms to estimate more reliable Q , geometric spreading rates, and site effects. Regression analysis was used to estimate geometric spreading rates and to establish a very consistent set of absolute moments. Here, frequency‐dependent Q and site terms are examined for , Sn , , and Pn spectra. Comparisons to independent Q estimates from amplitude tomography exhibit good agreement for many paths. Large discrepancies are shown for higher frequencies, in low Q regions, and/or at the edges of the tomography grid, which significantly impact P / S discrimination. Our frequency‐dependent site terms are compared with independent estimates from coda tomography, showing good agreement (even for and Pn , at many stations) but also some substantial differences.