Crustal deformation in great California earthquake cycles

Periodic crustal deformation associated with repeated strike slip earthquakes is computed for the following model: A depth L (less than or similiar to H) extending downward from the Earth's surface at a transform boundary between uniform elastic lithospheric plates of thickness H is locked between earthquakes. It slips an amount consistent with remote plate velocity V sub pl after each lapse of earthquake cycle time T sub cy. Lower portions of the fault zone at the boundary slip continuously so as to maintain constant resistive shear stress. The plates are coupled at their base to a Maxwellian viscoelastic asthenosphere through which steady deep seated mantle motions, compatible with plate velocity, are transmitted to the surface plates. The coupling is described approximately through a generalized Elsasser model. It is argued that the model gives a more realistic physical description of tectonic loading, including the time dependence of deep slip and crustal stress build up throughout the earthquake cycle, than do simpler kinematic models in which loading is represented as imposed uniform dislocation slip on the fault below the locked zone

Fiscal Paradise: Foreign Tax Havens and American Business

The offshore tax haven affiliates of American corporations account for more than a quarter of US foreign investment, an nearly a third of the foreign profits of US firms. This paper analyzes the origins of this tax haven activity and its implications for the US and foreign governments. Based on the behavior of US fins in 1982, it appears that American companies report extraordinarily high profit rates on both their real and their financial investments in tax havens. We calculate from this behavior that the tax rate that maximizes tax revenue for a typical haven is around 6%. The revenue implications for the US are more complicated, since tax havens may ultimately enhance the ability of the US government to tax the foreign earnings of American companies.

Nucleation and early seismic propagation of small and large events in a crustal earthquake model

Earthquake nucleation and early seismic propagation are studied in a two-dimensional strike-slip fault model with depth-variable properties. The fault is governed by the Dieterich-Ruina rate and state friction law. We use an efficient and rigorous numerical procedure for elastodynamic analysis of earthquake sequences on slowly loaded faults developed by Lapusta et al. [2000]. We find that for decreasing values of the characteristic slip distance of the friction law, small events appear at the transition from the locked to creeping behavior toward the bottom of the seismogenic zone. Small and large events have very similar nucleation phases in our simulations. Here, by “nucleation phase” we mean gradually accelerating aseismic slip in a small slowly expanding zone before the breakout of the dynamic, seismically detectable event. Moment acceleration (to which velocity seismograms are proportional) in early stages of seismic propagation exhibits irregular fluctuations, in the form of speedups and slowdowns in the moment release rate, consistently with observations as reported by Ellsworth and Beroza [1995]. Our simulations show that such irregular moment acceleration can, at least in part, be due to the heterogeneous stress distribution imprinted on the fault by the arrest of previous small events and by stress concentrations at the borders of creeping regions and to partial arrest of the rupture in velocity-strengthening fault regions which inhibit seismic slip

Slow Slip Predictions Based on Granit and Gabbro Friction Data Compared to GPS Measurements in Northern Cascadia

For episodic slow slip transients in subduction zones, a large uncertainty in comparing surface deformations predicted by forward modeling based on rate and state friction to GPS measurements lies in our limited knowledge of the frictional properties and fluid pore pressure along shallow subduction faults. In this study, we apply the laboratory rate and state friction data of granite and gabbro gouges under hydrothermal conditions to a Cascadia-like 2-D model to produce spontaneous aseismic transients, and we compare the resulting intertransient and transient surface deformations to GPS observations along the northern Cascadia margin. An inferred region along dip of elevated fluid pressure is constrained by seismological observations where available and by thermal and petrological models for the Cascadia and SW Japan subduction zones. For the assumed friction parameters a and a − b profiles, we search the model parameter space, by varying the level of effective normal stress , characteristic slip distance L in the source areas of transients, and the fault width under , to identify simulation cases that produce transients of total aseismic slip and recurrence interval similar to the observed 20–30 mm and 1–2 years, respectively, in northern Cascadia. Using a simple planar fault geometry and extrapolating the 2-D fault slip to a 3-D distribution, we find that the friction data for gabbro gouge, a better representation of the seafloor, fit GPS observations of transient deformation in northern Cascadia much better than do the granite data, which, for lack of a suitable alternative, have been the basis for most previous modeling.Earth and Planetary SciencesEngineering and Applied Science

Does Shear Heating of Pore Fluid Contribute to Earthquake Nucleation?

Earthquake nucleation requires reduction of frictional strength $\tau = \mu (\sigma - p)$ with slip or slip rate, where $\mu, \sigma_n$, and $p$ are the friction coefficient, normal stress, and fluid pressure, respectively. For rate state $\mu$ at fixed $(\sigma - p)$, instabilities can occur when $d \mu_{ss}/dv0$ are linearly stable at all wavelengths to adiabatic perturbations when v is near a plate rate if the wall rock permeability exceeds a critical value that is orders of magnitude less than inferred. Thus shear heating alone cannot then nucleate unstable slip; frictional weakening is required. However, shear heating can produce inertial instability on velocity strengthening faults following strong stress perturbations. On faults with $d \mu_{ss}/dv<0$, shear heating increases pore pressure faster than is dissipated by Darcy flow at slip speeds of order $1$ mm $s^{−1}$. For faults bounding half-spaces with uniform thermal and hydraulic properties, $\mu \dot{p}$ exceeds $\dot{\mu}(\sigma - p)$ during nucleation for slip speeds in excess of $10^{−2}$ to $10^1$ mm $s^{−1}$, depending on parameters chosen. Thus thermal effects are likely to dominate late in the nucleation process, well before seismic waves are radiated, as well as during fast seismic slip. By the time shear heating effects dominate, inertial slip is imminent $(∼10^{−1} s)$, so that time-to-failure calculations baseed on rate state friction are not biased by thermal pressurization.Earth and Planetary SciencesEngineering and Applied Science

Spontaneous and Triggered Aseismic Deformation Transients in a Subduction Fault Model

Aseismic deformation transients can emerge as a natural outcome of the rate and state friction processes revealed in laboratory fault-sliding experiments. When that constitutive formulation is applied to model subduction earthquake sequences, transients can arise spontaneously for certain effective stress (sigma bar) variations with depth. We show that if interstitial fluids are present and pore pressure is near-lithostatic around and downdip from the frictional stability transition, transients with recurrence intervals of ∼1 year are predicted on the basis of laboratory friction parameters and their temperature (hence depth) variations. The recurrence interval decreases with (sigma bar) and reaches 14 months when (sigma bar) is ∼2–3 MPa. Dimensional analysis and numerical studies show that the fault response primarily depends on a parameter W/h*. Here the high pore pressure zone extends distance W updip from the stability transition, and h* is the stable patch size for steady sliding. Evidence that such fluid conditions may actually be present is independently provided by the occurrence of nonvolcanic tremors as apparent responses to extremely small stress changes and by petrological constraints on expected regions of dehydration for the shallow dipping subduction zones where transients are observed. Transient sequences can also be triggered by a modest, one-time, step-like interseismic stress perturbation on the subduction fault, due to nearby earthquakes, or to pore pressure changes, e.g., during episodes of metamorphic fluid release. Properties of triggered transients and future thrust earthquakes depend on the interseismic time when the perturbation is introduced, its relative location along the subduction fault, and its magnitude.Earth and Planetary SciencesEngineering and Applied Science

Magnetic Response in the Underdoped Cuprates

We examine the dynamical magnetic response of the underdoped cuprates by employing a phenomenological theory of a doped resonant valence bond state where the Fermi surface is truncated into four pockets. This theory predicts a resonant spin response which with increasing energy (0 to 100meV) appears as an hourglass. The very low energy spin response is found at (pi,pi +- delta) and (pi +- delta,pi) and is determined by scattering from the pockets' frontside to the tips of opposite pockets where a van Hove singularity resides. At energies beyond 100 meV, strong scattering is seen from (pi,0) to (pi,pi). This theory thus provides a semi-quantitative description of the spin response seen in both INS and RIXS experiments at all relevant energy scales

Photon Statistics of a Single Atom Laser

We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as β, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for β are 0.01\u3cβ\u3c1.0. We find that for large enough β, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as β is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with β values in the range considered here. As β is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results

Effective Normal Stress Alteration due to Pore Pressure Changes Induced by Dynamic Slip Propagation on a Plane Between Dissimilar Materials

Recent, detailed examinations of fault zones show that walls of faults are often bordered by materials that are different from each other and from the more uniform material farther away. In addition, they show that the ultracataclastic core of mature fault zones, where slip is concentrated, is less permeable to flow across it than the adjoining material of the damage zone. Inhomogeneous slip at the interface between materials with different poroelastic properties and permeabilities causes a change in pore pressure there. Because slip causes compression on one side of the fault wall and extension on the other, the pore pressure on the fault increases substantially when the compressed side is significantly more permeable and decreases when, instead, the extended side is more permeable. This change in pore pressure alters the effective normal stress on the slip plane in a way that is analogous to the normal stress alteration in sliding between elastically dissimilar solids. The magnitude of the effect due to induced pore pressure can be comparable to or larger than that induced by sliding between elastic solids with a dissimilarity of properties consistent with seismic observations. The induced pore pressure effect is increased by increasing contrast in permeability, but the normal stress alteration due to elastic contrast increases rapidly as the rupture velocity approaches the generalized Rayleigh velocity. Because the alteration in effective normal stress due to either effect can be positive or negative, depending on the contrast in properties, the two effects can augment or offset each other.Earth and Planetary SciencesEngineering and Applied Science