Matthew D. Purvance

A Comprehensive Study of the Observed Spectral Decay in Strong-Motion Accelerations Recorded in Guerrero, Mexico

The Fourier spectra of S waves on strong-motion accelerograms fall off rapidly at the highest frequencies. Anderson and Hough (1984) suggested characterizing the high-frequency fall-off as A ( f ) ∼ exp(– πκf ), defining the observed rate of fall-off, κ , as the spectral decay parameter. It has been proposed that variability in κ results from variable near-surface attenuation and that estimates of κ from small- to moderate-magnitude events apply to the largest earthquakes. No systematic investigation into the behavior of κ over a broad magnitude range has been previously undertaken. The Guerrero Accelerograph Array has recorded enough strong-motion data from earthquakes with magnitudes ranging from under 3.0 to 8.0 to achieve a high level of statistical significance. The records are chosen to minimize the influence of the corner frequency on the spectral shape, and the κ values are estimated from the high-frequency slopes alone. This study finds that the terms in the model κ = κ site + κ event reduce the misfit significantly, with the κ site and κ event contributing similarly to the total κ value. Evidence suggests that κ event results primarily from source characteristics as opposed to propagation path effects. The absence of a statistically significant dependence of κ on epicentral distance is observed in the Guerrero region. Measuring κ over the frequency bands from 10 to 30 Hz and 10 to 45 Hz reveals increasing κ event with magnitude. When κ is measured from 25 to 45 Hz, κ event is not correlated with magnitude, although its role in error reduction remains significant. κ event also varies systematically with focal mechanism: of all M ≥5.1 earthquakes with available focal mechanisms, κ event is on average 4.5 msec less in normal-faulting earthquakes than in thrusting events.

Hybrid Broadband Ground-Motion Simulation Using Scattering Green's Functions: Application to Large-Magnitude Events

We calculate near-source broadband (0-10 Hz) seismograms by combin- ing low-frequency three-dimensional (3D) finite-difference seismograms (0-0.5 Hz) computed in a 3D velocity model using site-specific scattering Greens functions for random, isotropic scattering media. The scattering Greens functions are convolved with a slip-rate function to form local scattering operators (scatterograms), which constitute the high-frequency scattered wave field. The low-frequency and high- frequency scatterograms are then combined in the frequency domain to generate broadband waveforms. Our broadband method extends the Mai et al. (2010) approach by incorporating dynamically consistent source-time functions and account- ing for finite-fault effects in the computation of the high-frequency waveforms. We used the proposed method to generate broadband ground motions at 44 sites located 5-100 km from the fault, for Mw 7.7 earthquake scenarios (TeraShake) on the south- ern San Andreas fault, which include north-to-south, south-to-north, and bilateral rupture propagation from kinematic and spontaneous dynamic rupture models. The broadband ground motions computed with the new method are validated by com- paring peak ground acceleration, peak ground velocity, and spectral acceleration with recently proposed ground-motion prediction equations (GMPEs). Our simulated ground motions are consistent with the median ground motions predicted by the GMPEs. In addition, we examine overturning probabilities for 18 precariously balanced rock sites (PBR). Our broadband synthetics for the Mw 7.7 TeraShake sce- narios show no preferred rupture direction on the southern San Andreas fault but are inconsistent with the existence of PBRs at several of the sites analyzed.

Band of precariously balanced rocks between the Elsinore and San Jacinto, California, fault zones: Constraints on ground motion for large earthquakes

A spectacular band of precariously and semiprecariously bal- anced rocks extends from Riverside to near Borrego Valley, Cali- fornia, about halfway between the Elsinore and San Jacinto fault zones. The rocks are distributed in a band a few kilometers wide midway between the San Jacinto and Elsinore fault zones, an in- dication that the distribution is caused by attenuation of strong ground motion from numerous large events along these two fault zones. These rocks have apparently been in place for thousands of years, and thus place important constraints on ground motions from earthquakes. On the basis of field tests and photographic analysis, the estimated quasi-static toppling accelerations for the precariously balanced rocks are ;0.32 6 0.10 g (g 5 gravitational acceleration). The dynamic toppling accelerations are within this range for earthquakes with waveforms similar to those recorded during the Izmit and Denali earthquakes. These constraints are roughly consistent with the median predicted value of ground mo- tion for M7 earthquakes, but somewhat lower than 11s ground motion curves, and much lower than the values from the 2% in 50 yr hazard maps. The evidence from these rocks has importance for some of the assumptions that go into calculating probabilistic seismic hazard assessment, including median and standard devia- tion of ground motion attenuation curves (especially for hard rock, for which few instrumental data are available), the possible exis- tence of random background earthquakes, and the smoothing dis- tance for historical seismicity.

Consistency of Precariously Balanced Rocks with Probabilistic Seismic Hazard Estimates in Southern California

Abstract The overturning fragility of a freestanding block such as a precariously balanced rock (PBR) has been parameterized as a function of a vector of ground-motion intensity measures. Methodologies are outlined to estimate the failure probabilities of such objects given their residence times. For deterministic seismic hazard analyses (DSHAs), a PBR is exposed to the scenario earthquakes that occur during its exposure time providing an estimate of the probability that the PBR survives the ensemble of events. For probabilistic seismic hazard analyses (PSHAs), the PBR overturning fragility is multiplied by the ground-motion occurrence rate from a vector-valued probabilistic seismic hazard analysis (VPSHA), yielding the marginal overturning rate for each ground-motion bin. Summing the marginal rates over all ground-motion bins produces the total overturning rate. For time-independent Poisson-based PSHA estimates, the probability of block failure can be easily calculated as a function of exposure time. This latter method is used to test VPSHA estimates similar to the 2002 U.S. Geological Survey (USGS) National Seismic Hazard Maps via PBR residence times. PBR overturning fragilities are estimated at sites in southern California near the San Andreas fault, between the San Jacinto and Elsinore faults, and near the White Wolf fault. The resulting failure probabilities for several of the PBRs are very high, suggesting that they are inconsistent with the 2002 USGS ground motions. An investigation of the hazard calculated with zero aleatory variability in the ground-motion prediction equations (GMPEs) suggests that the median ground motions or the earthquake rupture rates are too high at certain PBR sites.

Data Needs for Improved Seismic Hazard Analysis

Probabilistic seismic hazard analysis (PSHA) attempts to predict the occurrence rates of various ground motion parameters, and is therefore potentially verifiable. At very low probabilities, features that might bound past ground motions, such as surviving precarious rocks, often seem to be inconsistent with the predictions. The PSHA predictions at small probabilities are very sensitive to the way uncertainties are handled. One challenge is to separate uncertainties into their aleatory and epistemic components, which currently are mingled due to making an ergodic assumption when ground motion prediction equations are developed. At Lovejoy Buttes, California, there are several precarious rocks that have not been toppled by about 10,000 years of earthquakes. This paper shows a formal way to evaluate whether a particular probability distribution for peak acceleration from the largest earthquakes, M∼8 events on the nearby San Andreas fault, is consistent with existence of those rocks. The paper concludes with suggested data needs from strong motion observations, since the solution to these PSHA issues will ultimately be driven by new data.

Estimating two-dimensional static stabilities and geomorphic settings of precariously balanced rocks from unconstrained digital photographs

The need to accurately document the spatiotemporal distribution of earthquake-generated strong ground motions is essential for evaluating the seismic vulnerability of sites of critical infrastructure. Understanding the threshold for maximum earthquake-induced ground motions at such sites provides valuable information to seismologists, earthquake engineers, local agencies, and policymakers when determining ground motion hazards of seismically sensitive infrastructures. In this context, fragile geologic features such as precariously balanced rocks (PBRs) serve as negative evidence for earthquake-induced ground motions and provide important physical constraints on the upper limits of ground motions. The three-dimensional (3D) shape of a PBR is a critical factor in determining its static stability and thus susceptibility to toppling during strong ground shaking events. Furthermore, the geomorphic settings of PBRs provide important controls on PBR exhumation histories that are interpreted from surface exposure dating methods. In this paper, we present PBRslenderness, a MATLAB-based program that evaluates the two-dimensional (2D) static stabilities of PBRs from unconstrained digital photographs. The program’s graphical user interface allows users to interactively digitize a PBR and calculates the 2D geometric parameters that define its static stability. A reproducibility study showed that our 2D calculations compare well against their counterparts that were computed in 3D (R 2 = 0.77–0.98 for 22 samples). A sensitivity study for single-user and multiuser digitization routines further confirmed the reproducibility of PBRslenderness estimates (coefficients of variation c v = 4.3%–6.5% for 100 runs; R 2 = 0.87–0.99 for 20 PBRs). We used PBRslenderness to analyze 261 PBRs in a low-seismicity setting to investigate the local geomorphic controls on PBR stability and preservation. PBRslenderness showed that a PBR’s shape strongly controls its static stability and that there is no relationship between a PBR’s stability and its geomorphic location in a drainage basin. However, the geomorphic settings of PBRs control their preservation potential by restricting their formation to hillslope gradients