S12A-01 INVITED 10:20h
The origin of high frequency radiation in earthquakes and the geometry of faulting
In a seminal paper of 1967 Kei Aki discovered the scaling law of earthquake spectra and showed that, among other things, the high frequency decay was of type omega-squared. This implies that high frequency displacement amplitudes are proportional to a characteristic length of the fault, and radiated energy scales with the cube of the fault dimension, just like seismic moment. Later in the seventies, it was found out that a simple explanation for this frequency dependence of spectra was that high frequencies were generated by stopping phases, waves emitted by changes in speed of the rupture front as it propagates along the fault, but this did not explain the scaling of high frequency waves with fault length. Earthquake energy balance is such that, ignoring attenuation, radiated energy is the change in strain energy minus energy released for overcoming friction. Until recently the latter was considered to be a material property that did not scale with fault size. Yet, in another classical paper Aki and Das estimated in the late 70s that energy release rate also scaled with earthquake size, because earthquakes were often stopped by barriers or changed rupture speed at them. This observation was independently confirmed in the late 90s by Ide and Takeo and Olsen et al who found that energy release rates for Kobe and Landers were in the order of a MJ/m$^2$, implying that Gc necessarily scales with earthquake size, because if this was a material property, small earthquakes would never occur. Using both simple analytical and numerical models developed by Addia-Bedia and Aochi and Madariaga, we examine the consequence of these observations for the scaling of high frequency waves with fault size. We demonstrate using some classical results by Kostrov, Husseiny and Freund that high frequency energy flow measures energy release rate and is generated when ruptures change velocity (both direction and speed) at fault kinks or jogs. Our results explain why super shear ruptures are only observed when faults are relatively flat and smooth, and why complex geometry inhibits fast ruptures.
http://www.geologie.ens.fr/~madariag
S12A-02 10:50h
Properties of fault slip in large earthquakes and its relation to aftershock distribution.
From inversions of broad band body wave data to obtain the fault rupturing process and the moment distribution over the fault for several large earthquakes, together with accurate aftershock locations, we find that: 1. Ruptures generally nucleate in the region of low slip or at the edge of high slip regions, though a few exceptions are found, the most notable being the great 1996 Biak, Indonesia subduction zone earthquake. 2. No universal relation between high and low moment regions and high or low aftershock occurrence, or vice versa, is found. Generally fewer, and usually the smaller, aftershocks occur in the high slip regions. In his work on the characterization of fault barriers, Aki (JGR, 1979) suggested that most aftershocks should occur in the regions of little or no slip, and we found this to be generally true. The 1996 Biak earthquake is an exception. 3. The 1986 and the 1996 Andreanof Islands earthquakes are both believed to be ruptures of regions with little or no slip in the 1957 Rat Island earthquake, but their behavior with respect to the 1957 aftershocks is different (Das and Henry, Rev. Geophys., 2003) showing that even on adjacent portions of the same plate boundary the behavior can be different. 4. In all cases, aftershocks occur on favorably oriented planes of weakness in regions of increased post-seismic stress. 5. Aftershocks are generally, clustered at both ends of faults but examples where aftershocks occur only at one end or where there is no clustering at the ends are found. Aftershock clusters are also found at the edge of unbroken barriers, and regions of rapid transition from high to low slip, within the main fault area. 5. We identify examples of geometrical and inhomogeneous barriers, and sharp and dull stress concentrations. 6. Off-fault aftershocks are found for all earthquakes examined, and sometimes rupture the nodal plane conjugate to the main shock fault plane.
S12A-03 11:05h
An Approximate 3D Elastodynamic Green's Function for an Inhomogeneous Elastic Medium
The seismic rays from a given point source within a constant-gradient elastic isotropic medium (a medium with linear variation of wave velocities) are known to be circular. This feature comes along with the remarkable fact that the associated wave fronts are cylindrical or spherical in two or three-dimensions, respectively. The rays and wavefronts form a bipolar orthogonal system with well known properties. These unique circumstances allowed us to construct analytical approximations for the corresponding elastodynamic Green's functions. The derivation of our analytical approximations starts in 2D with the anti-plane SH line source making a generalization of the homogeneous medium Green's functions that relies on the asymptotic ray theory to establish both travel times and geometrical spreading factors. Our approximation accounts for both near-source effects and low frequencies. Moreover, the said correction is frequency-independent and this allows to obtain the Green's function in time domain. This remarkable result was heuristically extended to the in-plane P-SV line source vector case and was validated with the staggered stress-velocity pseudo spectral method with excellent results. Details are given in Sanchez-Sesma, Madariaga and Irikura (2001). In this paper our discovery is extended to 3D for a unit point force. Thus our approximation for the elastodynamic Green's function in a constant-gradient medium becomes the counterpart of the classical Stokes' problem for a homogeneous, isotropic elastic medium. The adequate behavior of our analytical expressions in 3D is tested by comparing them with results from a fourth order finite difference scheme. Acknowledgements This research have had the support of DGAPA-UNAM, Mexico, under grant IN121202 and CONACYT, Mexico, under project NC-204, by CICYT, Spain, under REN2002-04198-CO2-02/RIES, by the E.U. with FEDER, and the team RNM-194 of Junta de Andalucia, Spain. Reference Sanchez-Sesma, F. J., R. Madariaga and K. Irikura (2001), An approximate elastic 2D Green's functions for a constant gradient medium, Geophys. J. Int., 146, 237-248.
S12A-04 11:20h
Spontaneous rupture dynamics of a planar fault with arbitrary dipping orientation embedded in 3-D elastic half-space
In this study, we proposed the boundary integral equation method (BIEM) with exact Green's function for half-space to model the dynamic rupture propagation on a planar fault embedded in a half-space. Although the conventional BIEM is flexible and efficient in modeling dynamic rupture on complicated fault systems (Aochi et al., 2000, 2002), it has been restricted to extremely simple medium model, i.e., infinite medium. The reason is that the formulation of the BIEM relies heavily on the existence of suitable Green's functions, and only the Green's function for an infinite medium has a simple and closed form. Unfortunately, when the simplest Green's function is used, the influence of free surface cannot be included without taking the free surface into account. However, for many large earthquakes, especially those in which rupture propagated up to the surface (e.g., the 1999, ChiChi earthquake), the effect of free surface may play an important role in the rupture pattern. For the first time, we introduced the exact Green's function for a half-space, which can be expressed as a wave-number integral in frequency domain, into the BIEM, therefore the effect of the free surface is automatically included. The model we considered is an inclined planar fault (the dip angle can vary from 0 to 90 degree) embedded in a half-space, the rupture started from a small patch, and propagated spontaneously. First, we derived the Green's functions and their derivatives with respect to spatial coordinates for a half-space based on bases expand. Starting from the representation theorem in general form, we derived the boundary integral equations (i.e., the stress-slip relations on the fault), and removed the hypersingularities in the BIEs following Fukuyama and Madariaga (1995, 1998). Then a simple discretization scheme (Fukuyama and Madariaga, 1998; Aochi et al., 2000) was applied to the BIEs. Since the Green's function for a half-space doesn't have a simple form, the discretized BIEs involved double integrals. Special attention was paid to decrease the double integrals to single ones, and we finally obtained a series of simplified discrete BIEs. Combined with the slip weakening law, the rupture process can be obtained numerically. We compared the rupture patterns between the two models: a fault embedded in a half-space and that in an infinite space, and found that significant difference when the depth of the fault is small, especially the case in which the fault extends to the free surface. The proposed method can be easily extended into a more complicated model in principal: a fault system embedded in a multilayered half-space, which need further study in the future. However, since more complicated Green's function is adopted, the computation is much more expensive than the case of simple Green's function.
S12A-05 11:35h
The Source Physics of Large Earthquakes - Validating Spontaneous Rupture Methods
Computer simulations of earthquake source rupture physics started more than 20 years ago, and the now classic papers of Andrews [1976], Das and Aki [1977], Mikumo and Miyatake [1978], and Day [1982] are included in every new spontaneous rupture modeler's required reading. Until 10 years ago, only a few researchers were able to numerically simulate spontaneous rupture propagation in 3D and the users of this methodology were primarily theoretical seismologists. In contrast, in current times numerous spontaneous rupture computer codes are being developed by researchers around the world, and the results are starting to be implemented in earthquake hazard assessment, for both seismological and engineering applications. Since most of the problems simulated using this numerical approach have no analytical solutions, it is imperative to compare and validate the various versions of this research tool. To this end, a collaborative project of the Southern California Earthquake Center (funded by the U.S. Geological Survey and the National Science Foundation) is currently underway. Our first 3D simulation exercise occurred in the fall of 2003 and had participants with 8 operational 3D spontaneous rupture codes; the most recent 2004 exercise involves participants with 10 operational codes. We have started with the basic problem of earthquake nucleation and spontaneous rupture propagation on a vertical strike-slip fault in a homogeneous material. We will soon be moving from comparison to validation, by comparing our simulation results with laboratory recordings of seismic motion due to rupture on a vertical strike-slip fault. Future simulation exercises will have increased complexity in fault geometry, material properties, stress conditions, and friction. Our overall objective is a complete understanding of the simulation methods and their ability to faithfully replicate our hypotheses about earthquake rupture physics.
S12A-06 11:50h
Using 3D Wavefield Modeling in Modeling in Interpreting Historical Macroseismic Observations - The Luroy Earthquake of 31 Aug. 1819.
The Luroy earthquake of August 31, 1819 with MS around 6.0 is, by many colleagues, rated as the largest in NW Europe in historical times (pre-1900) and even up to present. Local shaking manifestations were most spectacular with rock and mud avalanches, mast-high waves in nearby Rana fjord and even liquefaction was reported. Most surprisingly, at epicentral distances exceeding 100 km except for Stockholm 800 km away, very few macroseismic observations are available. Another peculiarity was the lack of any significant housing damage even in the Luroy parish itself. In a recent paper, we postulated that the earthquake was of moderate size, reestimated at MS = 5.1, but of shallow depth between 5 - 10 km causing the intense local shaking. In this article, we add a new dimension to the many of Luroy earthquake studies namely simulating the seismic wavefield response of Luroy itself and adjacent areas characterized by steep topographic relief. We use a 3D finite difference scheme and compute ground motion for a point source. We used a shear waves source with a focal depth of 5 km. Water covered areas are replaced by crystalline crust due to the dearth of dense bathymetric data. Main results are that the topography of the Luroy, close to the mountain peak at 685 meter, cause wavefield amplification by a factor of 20 and even stronger. Further away in the Rana fjord and surrounding areas, we also got strong amplification in particular where the relief is sharpest thus explaining triggering of avalanches in a quantitative manner. In other words, macroseismic observations would be biased upward due to the topographic focusing effects and unless properly corrected for also will increase the final earthquake magnitude estimate. We take these results to strongly support our claim that the historic Luroy earthquake was of moderate size of MS = 5.1 and not at MS = 6.0 class as claimed by many colleagues. Finally, downscaling of maximum earthquake magnitude would also lower the seismic risk levels significantly.
S12A-07 12:05h
Evidence for Non-Constant Energy/Moment Scaling
Unlike the well-established techniques of long-period waveform modeling for seismic moment (Mo), reliable measurements of radiated seismic energy (Er) have been elusive. In addition to correcting for source heterogeneity (e.g., directivity and source radiation pattern effects) significant broadband path corrections are required at scale lengths that are poorly resolved in the Earth. At frequencies above ~0.5 Hz, site response corrections become increasingly important, especially for small-to-moderate sized earthquakes. Comparing Er for events distributed over a broad region can make resolving scaling variations impossible. For example, if the region includes a mixture of source types (e.g., high and low stress drop events at a given magnitude) or if the path corrections are overly simplistic, then the study becomes an apples to oranges comparison. Instead, it may be more prudent to look for scaling within earthquake sequences or smaller geographical regions. To avoid the above mentioned problems we did the following: 1) We chose a wide range of event sizes from selected aftershock sequences that were recorded by multiple broadband stations; 2) We applied the coda methodology to estimate the source spectra to minimize any source heterogeneity; 3) We validated our spectra against independent moment estimates from regional moment tensor inversions. Using the large earthquakes sequences Mw 7.4 Izmit, Mw 7.2 Gulf of Aqaba, and Mw 7.2 Hector Mine our findings point to the scaled energy (e=Er/Mo) increasing with increasing moment for 3.7 < Mw < 7.4. As a validation, we posed the following question to ourselves. "What source spectral shape is needed to maintain good agreement with independent moments and have a constant scaled energy?" We tried to transform our spectra by adjusting the site correction terms such that the scaled energy would be constant (e.g., 5.0e-5, 5.5e-5 or 1.0e-4) but at the same time maintaining good agreement with our seismic moments and those derived from waveform modeling. All three cases resulted in very unusual, non-self similar source spectra. We believe that this study properly accounts for many of the problems that are commonly encountered in energy studies and that the use of the coda-derived source spectra provide unparalleled stability.