Real-Time Estimation of Fault Rupture Extent Using Envelopes of Acceleration

We present a new strategy to estimate the geometry of a rupture on a finite fault in real time for earthquake early warning. We extend the work of Cua and Heaton who developed the virtual seismologist (VS) method (Cua, 2005), which is a Bayesian approach to seismic early warning using envelope attenuation relationships. This article extends the VS method to large earthquakes where fault finiteness is important. We propose a new model to simulate high-frequency motions from earthquakes with large rupture dimension: the envelope of high-frequency ground motion from a large earthquake can be expressed as a root-mean-squared combination of envelope functions from smaller earthquakes. We use simulated envelopes of ground acceleration to estimate the direction and length of a rupture in real time. Using the 1999 Chi-Chi earthquake dataset, we have run simulations with different parameters to discover which parameters best describe the rupture geometry as a function of time. We parameterize the fault geometry with an epicenter, a fault strike, and two along-strike rupture lengths. The simulation results show that the azimuthal angle of the fault line converges to the minimum uniquely, and the estimation agrees with the actual Chi-Chi earthquake fault geometry quite well. The rupture direction can be estimated at 10 s after the event onset, and the final solution is achieved after 20 s. While this methodology seems quite promising for warning systems, it only works well when there is an adequate distribution of near-source stations

Probabilistic prediction of rupture length, slip and seismic ground motions for an ongoing rupture: implications for early warning for large earthquakes

Earthquake EarlyWarning (EEW) predicts future ground shaking based on presently available data. Long ruptures present the best opportunities for EEW since many heavily shaken areas are distant from the earthquake epicentre and may receive long warning times. Predicting the shaking from large earthquakes, however, requires some estimate of the likelihood of the future evolution of an ongoing rupture. An EEW system that anticipates future rupture using the present magnitude (or rupture length) together with the Gutenberg-Richter frequencysize statistics will likely never predict a large earthquake, because of the rare occurrence of ‘extreme events’. However, it seems reasonable to assume that large slip amplitudes increase the probability for evolving into a large earthquake. To investigate the relationship between the slip and the eventual size of an ongoing rupture, we simulate suites of 1-D rupture series from stochastic models of spatially heterogeneous slip. We find that while large slip amplitudes increase the probability for the continuation of a rupture and the possible evolution into a ‘Big One’, the recognition that rupture is occurring on a spatially smooth fault has an even stronger effect.We conclude that anEEWsystem for large earthquakes needs some mechanism for the rapid recognition of the causative fault (e.g., from real-time GPS measurements) and consideration of its ‘smoothness’. An EEW system for large earthquakes on smooth faults, such as the San Andreas Fault, could be implemented in two ways: the system could issue a warning, whenever slip on the fault exceeds a few metres, because the probability for a large earthquake is high and strong shaking is expected to occur in large areas around the fault. A more sophisticated EEW system could use the present slip on the fault to estimate the future slip evolution and final rupture dimensions, and (using this information) could provide probabilistic predictions of seismic ground motions along the evolving rupture. The decision on whether an EEW system should be realized in the first or in the second way (or in a combination of both) is user-specific

Northridge 20 Years After

Urban earthquakes such as the 1994 M 6.7 Northridge earthquake provide unique moments of clarity for those of us working on earthquake hazards. I recall being jolted awake at 4:31 a.m., 17 January 1994, in my Pasadena home. As I hurried to my U.S. Geological Survey (USGS) office on the Caltech campus, I remember wondering what the day would bring. Was the epicentral region sparsely populated, or had we just taken a direct hit to urbanized Los Angeles (LA)? We now know that, although damaging shaking extended into the LA basin, it was the San Fernando Valley that experienced truly violent shaking; five strong-motion accelerometers recorded peak ground velocities (PGV) of more than 1 m=s. Although the attack was over in 15 seconds, it left behind about $20 billion in damage and millions of terrified Angelenos, especially those living in the San Fernando Valley

Static deformations from point forces and force couples located in welded elastic Poissonian half-spaces: Implications for seismic moment tensors

We present analytic expressions for the static deformations produced by point forces and point force couples embedded in two elastic Poissonian half-spaces that are welded on a horizontal interface. We show that the deformations from point forces and from vertically dipping strike-slip point double couples vary continuously (except at the strike-slip source) as the source is moved across the welded interface. We show that the pattern of deformations from vertically dipping (or horizontally dipping) dip-slip point double couples also vary continuously as the source is moved across the welded interface, but the amplitude of the deformations jumps by the ratio of the rigidities. Finally, we show that the pattern of deformation from a point explosion source or from a point double-couple source dipping at angles other than 0° or 90° jumps as the source is moved across the boundary. We demonstrate that integration of point double-couple sources on a plane of finite extent mimics the deformation of slip on a fault plane where the total moment of the double-couples is μAD. We also demonstrate that deformations from a distribution of double couples on a horizontally dipping finite plane just above the interface are indistinguishable from the deformations produced by a similar distribution of double couples located just below the interface but with a total moment that is different by the ratio of the rigidities. This demonstrates that the moment of a dislocation that occurs between two materials is ambiguously defined. We discuss reasons why seismic moment is not a very satisfying way to parameterize the size of an earthquake. We show that potency, defined to be the integral of the slip over the rupture surface, is a more natural size scaling parameter than seismic moment

Long-Period Building Response to Earthquakes in the San Francisco Bay Area

This article reports a study of modeled, long-period building responses to ground-motion simulations of earthquakes in the San Francisco Bay Area. The earthquakes include the 1989 magnitude 6.9 Loma Prieta earthquake, a magnitude 7.8 simulation of the 1906 San Francisco earthquake, and two hypothetical magnitude 7.8 northern San Andreas fault earthquakes with hypocenters north and south of San Francisco. We use the simulated ground motions to excite nonlinear models of 20-story, steel, welded moment-resisting frame (MRF) buildings. We consider MRF buildings designed with two different strengths and modeled with either ductile or brittle welds. Using peak interstory drift ratio (IDR) as a performance measure, the stiffer, higher strength building models outperform the equivalent more flexible, lower strength designs. The hypothetical magnitude 7.8 earthquake with hypocenter north of San Francisco produces the most severe ground motions. In this simulation, the responses of the more flexible, lower strength building model with brittle welds exceed an IDR of 2.5% (that is, threaten life safety) on 54% of the urban area, compared to 4.6% of the urban area for the stiffer, higher strength building with ductile welds. We also use the simulated ground motions to predict the maximum isolator displacement of base-isolated buildings with linear, single-degree-of-freedom (SDOF) models. For two existing 3-sec isolator systems near San Francisco, the design maximum displacement is 0.5 m, and our simulations predict isolator displacements for this type of system in excess of 0.5 m in many urban areas. This article demonstrates that a large, 1906-like earthquake could cause significant damage to long-period buildings in the San Francisco Bay Area

Will Performance-based Earthquake Engineering Break the Power Law?

It seems that the entire community of earthquake professionals was stunned by the number of fatalities (approximately 300,000 dead or missing and presumed dead) in the 2004 Sumatran-Andaman earthquake and tsunami. It took us by surprise and seemed so out of proportion with anything that occurred in the decades prior. It was a rare confluence of circumstances that led to such massive loss. If, through our earthquake studies, we had been able to prevent just 5% of those deaths, then we would have saved more lives than have been lost in all other tsunamis for many decades. One clear lesson stands out from this tragedy: We must do a better job on tsunami hazard mitigation efforts for very large earthquakes (M > 9). While these events are rare, they account for most of the total hazard