David J. Wald

NEAR‐SOURCE GROUND MOTION AND ITS EFFECTS ON FLEXIBLE BUILDINGS

Occurrence of large earthquakes close to cities in California is inevitable. The resulting ground shaking will subject buildings in the near-source region to large, rapid displacement pulses which are not represented in design codes. The simulated M w 7.0 earthquake on a blind-thrust fault used in this study produces peak ground displacement and velocity of 200 cm and 180 cm/sec, respectively. Over an area of several hundred square kilometers in the near-source region, flexible frame and base-isolated buildings would experience severe nonlinear behavior including the possibility of collapse at some locations. The susceptibility of welded connections to fracture significantly increases the collapse potential of steel-frame buildings under strong ground motions of the type resulting from the M w 7.0 simulation. Because collapse of a building depends on many factors which are poorly understood, the results presented here regarding collapse should be interpreted carefully.

Relationships between Peak Ground Acceleration, Peak Ground Velocity, and Modified Mercalli Intensity in California

We have developed regression relationships between Modified Mercalli Intensity (I mm ) and peak ground acceleration (PGA) and velocity (PGV) by comparing horizontal peak ground motions to observed intensities for eight significant California earthquakes. For the limited range of Modified Mercalli intensities (I mm ), we find that for peak acceleration with V ≤ I mm ≤ VIII, I mm = 3.66 log(PGA) − 1.66, and for peak velocity with V ≤ I mm ≤ IX, I mm = 3.47 log(PGV) + 2.35. From comparison with observed intensity maps, we find that a combined regression based on peak velocity for intensity > VII and on peak acceleration for intensity < VII is most suitable for reproducing observed I mm patterns, consistent with high intensities being related to damage (proportional to ground velocity) and with lower intensities determined by felt accounts (most sensitive to higher-frequency ground acceleration). These new I mm relationships are significantly different from the Trifunac and Brady (1975) correlations, which have been used extensively in loss estimation.

TriNet "ShakeMaps": Rapid generation of peak ground motion and intensity maps for earthquakes in southern California

Rapid (3-5 minutes) generation of maps of instrumental ground-motion and shaking intensity is accomplished through advances in real-time seismographic data acquisition combined with newly developed relationships between recorded ground-motion parameters and expected shaking intensity values. Estimation of shaking over the entire regional extent of southern California is obtained by the spatial interpolation of the measured ground motions with geologically based frequency and amplitude-dependent site corrections. Production of the maps is automatic, triggered by any significant earthquake in southern California. Maps are now made available within several minutes of the earthquake for public and scientific consumption via the World Wide Web; they will be made available with dedicated communications for emergency response agencies and critical users.

Source Description of the 1999 Hector Mine, California, Earthquake, Part I: Wavelet Domain Inversion Theory and Resolution Analysis

We present a new procedure for the determination of rupture complexity from a joint inversion of static and seismic data. Our fault parameterization involves multiple fault segments, variable local slip, rake angle, rise time, and rupture velocity. To separate the spatial and temporal slip history, we introduce a wavelet transform that proves effective at studying the time and frequency characteristics of the seismic waveforms. Both data and synthetic seismograms are transformed into wavelets, which are then separated into several groups based on their frequency content. For each group, we use error functions to compare the wavelet amplitude variation with time between data and synthetic seismograms. The function can be an L1 + L2 norm or a correlative function based on the amplitude and scale of wavelet functions. The objective function is defined as the weighted sum of these functions. Subsequently, we developed a finite-fault inversion routine in the wavelet domain. A simulated annealing algorithm is used to determine the finite-fault model that minimizes the objective function described in terms of wavelet coefficients. With this approach, we can simultaneously invert for the slip amplitude, slip direction, rise time, and rupture velocity efficiently. Extensive experiments conducted on synthetic data are used to assess the ability to recover rupture slip details. We, also explore slip-model stability for different choices of layered Earth models assuming the geometry encountered in the 1999 Hector Mine, California, earthquake.

Topographic Slope as a Proxy for Seismic Site Conditions and Amplification

We describe a technique to derive first-order site-condition maps di- rectly from topographic data. For calibration, we use global 30 arc sec topographic data and VS 30 measurements (here VS 30 refers to the average shear-velocity down to 30 m) aggregated from several studies in the United States, as well as in Taiwan, Italy, and Australia. VS 30 values are correlated against topographic slope to develop two sets of parameters for deriving VS 30 : one for active tectonic regions where to- pographic relief is high, and one for stable shields where topography ismoresubdued. By taking the gradient of the topography and choosing ranges of slope that maximize the correlation with shallow shear-velocity observations, we can recover, to first order, many of the spatially varying features of site-condition maps developed for California. Our site-condition map for the low-relief Mississippi Embayment also predicts the bulk of the VS 30 observations in that region despite rather low slope ranges. We find that maps derived from the slope of the topography are often well cor- related with other independently derived, regional-scale site-condition maps, but the latter maps vary in quality and continuity, and subsequently, also in their ability to match observed V S 30 measurements contained therein. Alternatively, the slope-based method provides a simple approach to uniform site-condition mapping. After validating this approach in regions with numerous V S 30 observations, we subsequently estimate and map site conditions for the entire continental United States using the respective slope correlations.

Response of High-Rise and Base-Isolated Buildings to a Hypothetical Mw 7.0 Blind Thrust Earthquake

High-rise flexible-frame buildings are commonly considered to be resistant to shaking from the largest earthquakes. In addition, base isolation has become increasingly popular for critical buildings that should still function after an earthquake. How will these two types of buildings perform if a large earthquake occurs beneath a metropolitan area? To answer this question, we simulated the near-source ground motions of a Mw 7.0 thrust earthquake and then mathematically modeled the response of a 20-story steel-frame building and a 3-story base-isolated building. The synthesized ground motions were characterized by large displacement pulses (up to 2 meters) and large ground velocities. These ground motions caused large deformation and possible collapse of the frame building, and they required exceptional measures in the design of the base-isolated building if it was to remain functional.

Slip history and dynamic implications of the 1999 Chi‐Chi, Taiwan, earthquake

We investigate the rupture process of the 1999 Chi-Chi, Taiwan, earthquake using extensive near-source observations, including three-component velocity waveforms at 36 strong motion stations and 119 GPS measurements. A three-plane fault geometry derived from our previous inversion using only static data [ Ji et al., 2001 ] is applied. The slip amplitude, rake angle, rupture initiation time, and risetime function are inverted simultaneously with a recently developed finite fault inverse method that combines a wavelet transform approach with a simulated annealing algorithm [ Ji et al., 2002b ]. The inversion results are validated by the forward prediction of an independent data set, the teleseismic P and SH ground velocities, with notable agreement. The results show that the total seismic moment release of this earthquake is 2.7 × 10^20 N m and that most of the slip occurred in a triangular-shaped asperity involving two fault segments, which is consistent with our previous static inversion. The rupture front propagates with an average rupture velocity of ∼2.0 km s^(−1), and the average slip duration (risetime) is 7.2 s. Several interesting observations related to the temporal evolution of the Chi-Chi earthquake are also investigated, including (1) the strong effect of the sinuous fault plane of the Chelungpu fault on spatial and temporal variations in slip history, (2) the intersection of fault 1 and fault 2 not being a strong impediment to the rupture propagation, and (3) the observation that the peak slip velocity near the surface is, in general, higher than on the deeper portion of the fault plane, as predicted by dynamic modeling.

Resolution analysis of finite fault source inversion using one‐ and three‐dimensional Green's functions: 1. Strong motions

We develop a methodology to perform finite fault source inversions from strong motion data using Greens functions (GFs) calculated for a three-dimensional (3-D) velocity structure. The 3-D GFs are calculated numerically by inserting body forces at each of the strong motion sites and then recording the resulting strains along the target fault surface. Using reciprocity, these GFs can be recombined to represent the ground motion at each site for any (heterogeneous) slip distribution on the fault. The reciprocal formulation significantly reduces the required number of 3-D finite difference computations to at most 3NS, where NS is the number of strong motion sites used in the inversion. Using controlled numerical resolution tests, we have examined the relative importance of accurate GFs for finite fault source inversions which rely on near-source ground motions. These experiments use both 1-D and 3-D GFs in inversions for hypothetical rupture models in order (1) to analyze the ability of the 3-D methodology to resolve trade-offs between complex source phenomena and 3-D path effects, (2) to address the sensitivity of the inversion results to uncertainties in the 3-D velocity structure, and (3) to test the adequacy of the 1-D GF method when propagation effects are known to be three-dimensional. We find that given “data” from a prescribed 3-D Earth structure, the use of well-calibrated 3-D GFs in the inversion provides very good resolution of the assumed slip distribution, thus adequately separating source and 3-D propagation effects. In contrast, using a set of inexact 3-D GFs or a set of hybrid 1-D GFs allows only partial recovery of the slip distribution. These findings suggest that in regions of complex geology the use of well-calibrated 3-D GFs has the potential for increased resolution of the rupture process relative to 1-D GFs. However, realizing this full potential requires that the 3-D velocity model and associated GFs should be carefully validated against the true 3-D Earth structure before performing the inverse problem with actual data.

Resolution analysis of finite fault source inversion using one- and three-dimensional Green's functions 2. : combining seismic and geodetic data

Using numerical tests for a prescribed heterogeneous earthquake slip distribution, we examine the importance of accurate Greens functions (GF) for finite fault source inversions which rely on coseismic GPS displacements and leveling line uplift alone and in combination with near-source strong ground motions. The static displacements, while sensitive to the three-dimensional (3-D) structure, are less so than seismic waveforms and thus are an important contribution, particularly when used in conjunction with waveform inversions. For numerical tests of an earthquake source and data distribution modeled after the 1994 Northridge earthquake, a joint geodetic and seismic inversion allows for reasonable recovery of the heterogeneous slip distribution on the fault. In contrast, inaccurate 3-D GFs or multiple 1-D GFs allow only partial recovery of the slip distribution given strong motion data alone. Likewise, using just the GPS and leveling line data requires significant smoothing for inversion stability, and hence, only a blurred vision of the prescribed slip is recovered. Although the half-space approximation for computing the surface static deformation field is no longer justifiable based on the high level of accuracy for current GPS data acquisition and the computed differences between 3-D and half-space surface displacements, a layered 1-D approximation to 3-D Earth structure provides adequate representation of the surface displacement field. However, even with the half-space approximation, geodetic data can provide additional slip resolution in the joint seismic and geodetic inversion provided a priori fault location and geometry are correct. Nevertheless, the sensitivity of the static displacements to the Earth structure begs caution for interpretation of surface displacements, particularly those recorded at monuments located in or near basin environments.

A Revised Ground-Motion and Intensity Interpolation Scheme for ShakeMap

Wedescribe aweighted-average approach for incorporating varioustypes of data (observed peak ground motions and intensities and estimates from ground- motion prediction equations) into theShakeMap ground motion and intensity mapping framework.ThisapproachrepresentsafundamentalrevisionofourexistingShakeMap methodology. In addition, the increased availability of near-real-time macroseismic intensitydata,thedevelopmentofnewrelationshipsbetweenintensityandpeakground motions, and new relationships to directly predict intensity from earthquake source information have facilitated the inclusion of intensity measurements directly into ShakeMap computations. Our approach allows for the combination of (1) direct observations (ground-motion measurements or reported intensities), (2) observations converted from intensity to ground motion (or vice versa), and (3) estimated ground motionsandintensities frompredictionequationsornumerical models.Critically,each oftheaforementioneddatatypesmustincludeanestimateofitsuncertainties,including those caused by scaling the influence of observations to surrounding grid points and those associated with estimates given an unknown fault geometry. The ShakeMap ground-motion and intensity estimates are an uncertainty-weighted combination of these various data and estimates. A natural by-product of this interpolation process is an estimate of total uncertainty at each point on the map, which can be vital for comprehensive inventory loss calculations. We perform a number of tests to validate this new methodology and find that it produces a substantial improvement in the accuracy of ground-motion predictions over empirical prediction equations alone.