Simulation of an 1857-like Mw 7.9 San Andreas Fault Earthquake and the Response of Tall Steel Moment Frame Buildings in Southern California – A Prototype Study

In 1857, an earthquake of magnitude 7.9 occurred on the San Andreas fault, starting at Parkfield and rupturing in a southeasterly direction for more than 360 km. Such a unilateral rupture produces significant directivity toward the San Fernando and Los Angeles basins. The strong shaking in the basins due to this earthquake would have had significant long-period content (2-8 s), and the objective of this study is to quantify the impact of such an earthquake on two 18-story steel moment frame building models, hypothetically located at 636 sites on a 3.5 km grid in southern California. End-to-end simulations include modeling the source and rupture of a fault at one end, numerically propagating the seismic waves through the earth structure, simulating the damage to engineered structures and estimating the economic impact at the other end using high-performance computing. In this prototype study, we use an inferred finite source model of the magnitude 7.9, 2002 Denali fault earthquake in Alaska, and map it onto the San Andreas fault with the rupture originating at Parkfield and propagating southward over a distance of 290 km. Using the spectral element seismic wave propagation code, SPECFEM3D, we simulate an 1857-like earthquake on the San Andreas fault and compute ground motions at the 636 analysis sites. Using the nonlinear structural analysis program, FRAME3D, we subsequently analyze 3-D structural models of an existing tall steel building designed using the 1982 Uniform Building Code (UBC), as well as one designed according to the 1997 UBC, subjected to the computed ground motion at each of these sites. We summarize the performance of these structural models on contour maps of peak interstory drift. We then perform an economic loss analysis for the two buildings at each site, using the Matlab Damage and Loss Analysis (MDLA) toolbox developed to implement the PEER loss-estimation methodology. The toolbox includes damage prediction and repair cost estimation for structural and non-structural components and allows for the computation of the mean and variance of building repair costs conditional on engineering demand parameters (i.e. inter-story drift ratios and peak floor accelerations). Here, we modify it to treat steel-frame high-rises, including aspects such as mechanical, electrical and plumbing systems, traction elevators, and the possibility of irreparable structural damage. We then generate contour plots of conditional mean losses for the San Fernando and the Los Angeles basins for the pre-Northridge and modern code-designed buildings, allowing for comparison of the economic effects of the updated code for the scenario event. In principle, by simulating multiple seismic events, consistent with the probabilistic seismic hazard for a building site, the same basic approach could be used to quantify the uncertain losses from future earthquakes

An absorbing boundary formulation for the stratified, linearized, ideal MHD equations based on an unsplit, convolutional perfectly matched layer

Perfectly matched layers are a very efficient and accurate way to absorb waves in media. We present a stable convolutional unsplit perfectly matched formulation designed for the linearized stratified Euler equations. However, the technique as applied to the Magneto-hydrodynamic (MHD) equations requires the use of a sponge, which, despite placing the perfectly matched status in question, is still highly efficient at absorbing outgoing waves. We study solutions of the equations in the backdrop of models of linearized wave propagation in the Sun. We test the numerical stability of the schemes by integrating the equations over a large number of wave periods.Comment: 8 pages, 7 figures, accepted, A &

Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded media

To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the finite volume method, etc. All these methods have various advantages and drawbacks. The amplification of seismic waves in surface soil layers is mainly due to the velocity contrast between these layers and, possibly, to topographic effects around crests and hills. The influence of the geometry of alluvial basins on the amplification process is also know to be large. Nevertheless, strong heterogeneities and complex geometries are not easy to take into account with all numerical methods. 2D/3D models are needed in many situations and the efficiency/accuracy of the numerical methods in such cases is in question. Furthermore, the radiation conditions at infinity are not easy to handle with finite differences or finite/spectral elements whereas it is explicitely accounted in the Boundary Element Method. Various absorbing layer methods (e.g. F-PML, M-PML) were recently proposed to attenuate the spurious wave reflections especially in some difficult cases such as shallow numerical models or grazing incidences. Finally, strong earthquakes involve nonlinear effects in surficial soil layers. To model strong ground motion, it is thus necessary to consider the nonlinear dynamic behaviour of soils and simultaneously investigate seismic wave propagation in complex 2D/3D geological structures! Recent advances in numerical formulations and constitutive models in such complex situations are presented and discussed in this paper. A crucial issue is the availability of the field/laboratory data to feed and validate such models.Comment: of International Journal Geomechanics (2010) 1-1

2D full-waveform modeling of seismic waves in layered karstic media

We have developed a new propagator-matrix scheme to simulate seismic-wave propagation and scattering in a multilayered medium containing karstic voids. The propagator matrices can be found using the boundary element method. The model can have irregular boundaries, including arbitrary free-surface topography. Any number of karsts can be included in the model, and each karst can be of arbitrary geometric shape. We have used the Burton-Miller formulation to tackle the numerical instability caused by the fictitious resonance due to the finite size of a karstic void. Our method was implemented in the frequency-space domain, so frequency-dependent Q can be readily incorporated. We have validated our calculation by comparing it with the analytical solution for a cylindrical void and to the spectral element method for a more complex model. This new modeling capability is useful in many important applications in seismic inverse theory, such as imaging karsts, caves, sinkholes, and clandestine tunnels

A field expansions method for scattering by periodic multilayered media

The interaction of acoustic and electromagnetic waves with periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the robust and high-order numerical simulation of a model for the interaction of pressure waves generated within the earth incident upon layers of sediment near the surface. Herein described is a boundary perturbation method for the numerical simulation of scattering returns from irregularly shaped periodic layered media. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than finite difference and finite element simulations), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of boundary integral/element methods. The approach is a generalization to multiple layers of Bruno and Reitich’s “Method of Field Expansions” for dielectric structures with two layers. By simply considering the entire structure simultaneously, rather than solving in individual layers separately, the full field can be recovered in time proportional to the number of interfaces. As with the original field expansions method, this approach is extremely efficient and spectrally accurate

An efficient multi-time step FEM–SFEM iterative coupling procedure for elastic–acoustic interaction problems

An iterative coupling methodology between the Finite Element Method (FEM) and the Spectral Finite Element Method (SFEM) for the modeling of coupled elastic-acoustic problems in the time domain is presented here. Since the iterative coupling procedure allows the use of a nonconforming mesh at the interface between the subdomains, the difference in the element sizes concerning the FEM and SFEM is handled in a straightforward and efficient manner, thereby retaining all the advantages of the SFEM. By means of the HHT time integration method, controllable numerical damping can be introduced in one of the subdomains, increasing the robustness of the method and improving the accuracy of the results; besides, independent time-step sizes can be considered within each subdomain, resulting in a more efficient algorithm. In this work, a modification in the subcycling procedure is proposed, ensuring not only an efficient and accurate methodology but also avoiding the computation of a relaxation parameter. Numerical simulations are presented in order to illustrate the accuracy and potential of the proposed methodology.CAPES, UFJF, UFSJ, FAPEMIG and CNP

Seismic slip on an upper-plate normal fault during a large subduction megathrust rupture

Quantification of stress accumulation and release during subduction zone seismic cycles requires an understanding of the distribution of fault slip during earthquakes. Reconstructions of slip are typically constrained to a single, known fault plane. Yet, slip has been shown to occur on multiple faults within the subducting plate1 owing to stress triggering2, resulting in phenomena such as earthquake doublets3. However, rapid stress triggering from the plate interface to faults in the overriding plate has not been documented. Here we analyse seismic data from the magnitude 7.1 Araucania earthquake that occurred in the Chilean subduction zone in 2011. We find that the earthquake, which was reported as a single event in global moment tensor solutions4, 5, was instead composed of two ruptures on two separate faults. Within 12?s a thrust earthquake on the plate interface triggered a second large rupture on a normal fault 30?km away in the overriding plate. This configuration of partitioned rupture is consistent with normal-faulting mechanisms in the ensuing aftershock sequence. We conclude that plate interface rupture can trigger almost instantaneous slip in the overriding plate of a subduction zone. This shallow upper-plate rupture may be masked from teleseismic data, posing a challenge for real-time tsunami warning systems

Significant release of shear energy of the North Korean nuclear test on February 12, 2013

On February 12, 2013 the Democratic People\u27s Republic of Korea (DPRK) carried out an announced nuclear test, which was the third after tests conducted in 2006 and 2009. An important task in discriminating a man-made explosion and a natural tectonic earthquake is the analysis of seismic waveforms. To determine the isotropic and non-isotropic characteristics of the detonation source, I invert long-period seismic data for the full seismic moment tensor to match the observed seismic signals by synthetic waveforms based on a 3D earth model. Here, I show that the inversion of long-period seismic data of the 2013 test reveals a clear explosive (isotropic) component combined with a significant release of shear energy by the double-couple part of the moment tensor. While the isotropic part of the nuclear test in 2009 was similar to that in 2013, the double-couple part was lower by a factor of 0.55 compared to the explosion in 2013. Moreover, the ratio of the isotropic seismic moments of the 2013 and 2009 nuclear tests is 1.4±0.1 and lower than published estimations of the yield ratio, which indicates the importance of considering the release of shear energy. The determined orientation of the double-couple fault plane is parallel to the dominating geologic fault structures NNE-SSW to NE-SW, but the calculated normal faulting mechanism does not correspond to the general tectonic strike-slip regime. Thus, explanations for the enhanced release of shear energy might be induced dip-slip motion pre-stressed by the previous test or near source damaging effects due to a changed containment of the nuclear explosion