S13E-01 13:40h
Developing a Methodology for Measuring Stress Transients at Seismogenic Depth
The dependence of crack properties on stress means that crustal seismic velocity exhibits stress dependence. This dependence constitutes, in principle, a powerful means of studying transient changes in stress at seismogenic depth. While its scientific potential has been known for decades, time-dependent seismic imaging has not (yet) become a reliable means of measuring subsurface stress changes. This is because of 1) insufficient delay-time precision necessary to detect small changes in stress, and 2) the difficulty in establishing a reliable in-situ calibration between stress and seismic velocity. These two problems are coupled because the best sources of calibration, solid-earth tides and barometric pressure, produce weak stress perturbations of order $10{^2}-10{^3}$ Pa that require precision in the measurement of the fractional velocity change $dlnv$ of order $10^{-6}$, based on laboratory experiments. We have initiated a series of three experiments to demonstrate the detectability of these stress-calibration signals in progressively more tectonically relevant settings. Initial tests have been completed on the smallest scale, with two boreholes 17 m deep and 3 meters apart. We have used a piezoelectric source (0.1ms source pulse repeated every 100ms) and a string of 24 hydrophones to record P waves with a dominant frequency of 10KHz. Recording was conducted for 160 hours. The massive stacking of ~36,000 high-SNR traces/hr leads to delay-time precision of 6ns (hour sampling) corresponding to $dlnv$ precision of $3 x 10{^{-6}}$. We find that barometric pressure fluctuations are easily observed in the delay time data with a SNR of 1000. Also, while lower in amplitude, diurnal and semidiurnal solid-earth-tidal components are also observed. We have also conducted preliminary tests at the Richmond Field Facility, which permits cross-borehole recordings at a distance of 30 m, and depths to 70 m, using the same equipment. The dominant frequency in this case was 1KHz. While only very short time segments have thus far been analyzed, the preliminary data show that we are able to attain the same high precision ($dlnv$ of order $10{^{-6}}$) as in the first experiment. A third experiment is planned using the 7-level 3-compoment geophone string in the SAFOD Pilot hole at Parkfield,CA, that spans the depth range 850m - 1100 m. Making use of a specially designed 18-element piezoelectric source deployed in a relatively shallow source hole (100m) on the same pad as the Pilot Hole, we plan to shoot along a near-vertical trajectory to these geophones to again detect the presence of tidal and barometric fluctuations in the seismic wavefield. We expect to obtain stress-induced temporal changes in interval properties (between the shallowest and deepest levels) which, if confirmed, would demonstrate the ability to measure KPa-level stress variations at near-seismogenic depth.
S13E-02 13:55h
What do Seismicity Streaks and Holes Reveal About the Distribution of Seismic and Aseismic Slip?
Many studies have shown that faults have "holes," i.e., regions of an otherwise active fault that are devoid of microseismicity, both in the aftershock sequences of large earthquakes (e.g., Mendoza and Hartzell, 1988) and during the interseismic interval (e.g., Oppenheimer et al., 1990). Seismicity holes also appear between more recently discovered "streaks" of seismicity on the Calaveras, Hayward, and San Andreas faults in California. Ellsworth et al. (2000) have made a convincing case that two streaks on the San Andreas fault near Parkfield delimit a stuck patch that has been partially ruptured by several magnitude 4+ events in the early 1990's. We examine these same features using precise earthquake relocations for the Calaveras fault. The Calaveras fault has a number of streaks and holes in its seismicity distribution and with the geometry of locked vs. slipping regions more difficult to discern than it is on the San Andreas fault at Parkfield. Our working hypothesis is that the streaks illuminate the transition from creeping to locked portions of the fault. We can test this by examining medium magnitude (M 3.5) earthquakes, which we expect to rupture inward from the streaks into areas devoid of microearthquakes, i.e. areas that were previously locked. Double difference relocations show medium sized earthquakes within these streaks, but clipping makes it difficult to determine earthquake locations as accurately for these events. To overcome this problem, we use a first-break master-event cross correlation method to improve hypocentral locations of these larger earthquakes that represent where these moderate magnitude events initiate. Analysis of accelerometer and short-period seismometer records provides finite faulting information, which will allow us to constrain the propagation direction relative to these hypocenters.
S13E-03 14:10h
Self-Similar Earthquake Nucleation on Rate-and-State Faults
We obtain self-similar solutions (two-dimensional and quasi-static) for the acceleration to instability of a fixed-length patch on a fault obeying rate-and-state friction. The solution is applicable in the limit $V\theta/D_c$$\gg$$1$, so that the evolution of the state variable is well-approximated by $\dot{\theta}$=$V\theta/D_c$. For simulations on an infinite fault with $a/b$$<$$\sim$0.5, the nucleation zone spontaneously evolves to the size and velocity distribution of the self-similar solution for which the stress intensity factor $K$=0, for which the nucleation length $L_\nu$=$1.3774G^*D_c/b\sigma$, independent of $a$, where $G^*$ is the elastic stiffness. For $a/b$$<$$0.3781$, $V\theta$ increases with time and the large $V\theta/D_c$ solution remains applicable until elastodynamics comes into play. For larger $a/b$, $V\theta$ at the crack center diminishes to a quasi-constant value modestly larger than 1, and the nucleation zone ultimately appears similar to an expanding slip-weakening crack with constant slip-weakening rate but time-varying peak and residual stresses. The nucleation length in these cases (defined as the minimum of the time-dependent size of the nucleation zone) generally increases with $a/b$ but is very sensitive to the boundary and initial conditions. For sufficiently large values of $V\theta/D_c$ upon localization, the nucleation zone can undergo velocity increases of many orders of magnitude before the self-similar solution becomes inapplicable; this is why this solution dominates the simulations of Dieterich [1992] even for $a/b$\sim$0.9. For $a/b$$<$0.3781, smaller nucleation zones are capable of reaching instability; these correspond to self-similar solutions with $[\dot{V\theta}]$\ge$0 and $K$$>$0, so they could be applicable to faults shorter than $L_\nu$. The smallest viable nucleation zone $L_{min}$ increases in size with increasing $a/b$ and equals $L_\nu$ at $a/b$=0.3781. For $a$=0, which in the limit $V\theta/D_c$\gg$1 corresponds to slip-weakening behavior, $L_{min}$ equals the universal nucleation length of $0.579G^*D_c/b\sigma$ found for slip-weakening behavior by Uenishi and Rice [2003] (the slip-weakening rate is $b\sigma/D_c$). The family of self-similar solutions can thus be viewed as linking the observation of Dieterich [1992] that $L_\nu$ scales as $b^{-1}$ (the $K$=0 solution), with the expectation from stability analyses that $L_{min}$ scales as $(b-a)^{-1}$ (the $K$$>$0 solutions for which $[\dot{V\theta}]$=0).
S13E-04 14:25h
Three-Dimensional Rupture Instability of a Slip-Weakening Fault Under Heterogeneous Loading
In previous studies [Rice and Uenishi, {\it EOS}, 2002; Uenishi and Rice, {\it JGR}, 2003], we considered slip initiation and rupture instability on two-dimensional faults that follow a slip-weakening relation and are subjected to a loading stress that is locally peaked spatially, the level of which changes quasi-statically in time. We showed that for the case in which the fault strength weakens linearly with slip, there exists a universal length of the slipping region at instability, independent of any length scales entering into the description of the shape of the loading stress distribution. Here, we study slip development and its (in)stability for three-dimensional planar faults that follow the linear slip-weakening relation. We employ an energy approach to give a Rayleigh-Ritz approximation for the dependence of size of the rupture zone and maximum slip on the level and shape of the loading stress distribution. The zone is assumed elliptical, $x^2/a^2 + z^2/b^2 \le 1$, with unknown axes $a, b$, where the fault coincides with the $x$-$z$ plane ($y = 0$). A loading stress $\tau_p + Rt - \kappa (x^2 + m^2 z^2) / 2$ is assumed on that plane; $\kappa$ and $m$ are positive constants and $Rt$ is the stress change from that for which the peak in the loading stress distribution equals the strength $\tau_p$. Results show this loading induces a rupture zone whose aspect ratio $a(t)/b(t)$ changes with time $t$ except for the cases of circular cracks ($m = a/b = 1$) for the opening (tensile) mode and $m = a/b \approx 1 / (1 - \nu)$ for the sliding mode (unidirectional shear in the $x$-direction). Here, $\nu$ is Poisson's ratio. These values of $m$ minimize the area of critical rupture zone at instability ($\pi a_c b_c$), and for the opening mode, the corresponding critical diameter is $2a_c = 2b_c \approx 1.960 \mu/[W(1 - \nu)]$, with $\mu$ being shear modulus and $W$ linear slip-weakening slope. For the sliding mode, the critical rupture size is written in terms of $\mu$, $\nu$ and $W$ (and the complete elliptic integrals of the first and second kinds). When, for example, $\nu = 0.25$, those critical lengths are $2a_c \approx 2.598\mu/W$ and $2b_c \approx 1.951 \mu/W$. Comparison of these results with the two-dimensional ones ($1.158 \mu/[W(1 - \nu)]$ for modes I and II; $1.158 \mu/W$ for mode III) shows that the critical lengths are of the same order for all cases, implying that the actual critical length associated with seismic nucleation may be of the order of up to few meters, as suggested by Uenishi and Rice [{\it JGR}, 2003].
S13E-05 14:40h
Scaling Relation of Seismic Nucleation Estimated from Slow Initial Phase
Synthetic seismogram expected from the slip dependent friction law isthe slow initial phase; convex downward seismograms seen in aroundfirst P-arrivals of velocity seismograms. The scaling law expectedfrom the slip dependent friction law was suggested, but it has notbeen confirmed with the slow initial phase. In this study, we showthat the scaling law expected from the slip dependent friction law isvalid with the slow initial phase.At first, we obtained moment rate functions by deconvolution with causalattenuation operators. Next, we estimated stress drop and seismicmoment released during unstable, accelerating phase in slip dependentrelationship, and obtained them for 28 earthquakes of which moment rangeis $1 \times 10^{10} \mbox{Nm}$ to $1 \times 10^{13} \mbox{Nm}$.Finally, we evaluated fault dimension of unstable, accelerating phase;the critical size $2L_c$ of the nucleation zone and the critical slipdisplacement $D_c$ with theoretical relation by Ohnaka (2000). Both thecritical size $2L_c$ of the nucleation zone and the critical slipdisplacement $D_c$ are proportional to power of 1/3 of seismic moment,and it can explain the theoretical formula proposed by Ohnaka (2000).Our results suggest that the rupture process of earthquakes is subjectto the slip dependent law because the relationship between the criticalsize $2L_c$ of the nucleation zone and the critical slip displacement$D_c$ and the seismic moment is consistent with scaling law expectedfrom the slip dependent law. The results of this study obtained withthe slow initial phase is consistent with the results with the seismicnucleation phase by Ellsworth and Beroza (1995). This means that theslow initial phase and the seismic nucleation phase is the samephenomenon in the macro scale. However, the results with the seismicnucleation phase are relatively more perturbed than that with the slowinitial phase. This difference can be interpreted as quality or varietyof data. Nevertheless, it is possible that the seismic nucleation phaseis produced by inhomogeneous distribution of asperities on a faultplane.
S13E-06 14:55h
Earthquake Magnitude Estimation Prior to Rupture Termination
An estimate of earthquake moment magnitude is possible within 5 seconds of earthquake initiation for events of every magnitude, including those events which rupture for several 10's of seconds. The magnitude estimate is calculated based on the empirical relationship between the predominant period of the P-wave and moment magnitude. The predominant period is calculated from the frequency content of the data on a moving average basis for the first five seconds after the trigger. The empirically observed relationship is based upon a data set consisting of more than one hundred events with moment magnitude 3.5 - 8.3, thirty events have a moment magnitude of 6.0 or greater. The magnitude estimates for several well known large magnitude events, including Chi Chi (Taiwan, 1999), Hokkaido (Japan, 2003) and Denali (Alaska, 2002), are all calculated within 5 seconds of the P-wave trigger. These events lasted for tens of seconds and the fault rupture extended 10's - 100's of kilometers, yet in each case, the magnitude can be calculated long before the rupture has propagated over the entire surface of the faults. Additionally, for large magnitude events, such as the Chi Chi earthquake mentioned above, less than 5% of the seismic moment is released within the 5 seconds required to measure the predominant period.
S13E-07 15:10h
Energy Budget of Small Earthquakes from a Dense Seismic Array: Results from Western Nagano, Japan
We analyze micro-earthquake recordings from a dense array of 45 surface and 3 borehole seismometers located in an area of 16x12 $km^2$ in the Western Nagano region of central Japan. The borehole stations have high signal-to-noise ratios up to frequencies of 200-300Hz; and most of the surface stations also have good signal-to-noise ratios up to extremely high frequencies (150-200Hz). The high redundancy provided by the exceptional instrumental coverage in this region provides an opportunity to determine robust measurements of the radiated seismic energy and to explore sources of uncertainty in its measurement. We calculate the seismic energy for 24 micro-earthquakes ($M_{w}$ 0.9-3.8) using the spectral ratio approach (i.e., based on the EGF method). For a given event, the variation in energy estimates between stations is less than a factor of 3 and most of this variation can be explained by variation in corner frequency and spectral shape (roughness of spectra) between stations. For the dataset we examined, the energy to moment ratios vary between 1x$10^{-5}$ and 2x$10^{-4}$, similar to that observed for much larger events, and we do not observe any change in the scaling of this ratio with earthquake size in our data set. Stress drops determined from corner frequencies indicate that the radiation efficiency for our events are always larger than 0.5, similar to values found for other earthquakes of widely varying size.
S13E-08 15:25h
Another Look at the Source of the 1906 San Francisco Earthquake
We have taken another look at the source model of the 1906 San Francisco earthquake. Our study is motivated by the large and unresolved discrepancy between geodetic and seismic models of that event. The seismic model [Wald et al., 1993] of the earthquake has rupture that is only about two thirds of the total rupture length as determined geodetically [Thatcher et al., 1997]. Observations of recent large, continental strike-slip earthquakes [e.g., Bouchon and Vallee, 2003] suggests that rupture during these earthquakes may have exceeded the local shear wave velocity. It is reasonable to expect that the source behavior of the 1906 earthquake would be similar to these recent large strike-slip earthquakes, which motivates us to consider the possibility that the rupture velocity in the 1906 earthquake was supershear. Moreover, theoretical models of in-plane rupture suggest that supershear rupture might be expected to occur in this geometry. Our preliminary results suggest that supershear rupture does help to resolve the discrepancy between the seismic and geodetic models of the 1906 earthquake. We are revisiting the analysis of both the geodetic and seismic observations to test this hypothesis.