Scaling properties of the spatio–temporal distribution of earthquakes: a multifractal approach applied to a Californian catalogue

We study the spatio–temporal scaling properties of the NCSN California catalogue for the period 1975–1995 (about 137 000 events) using a multifractal approach. The study is based on a new method of declustering earthquake catalogues based on looking for independent events. This technique makes use of the properties of the multifractal distribution of the inter-event times. A comparison test between our method and the Gardner and Knopoff (GK hereafter) approach reveals that our method produces a catalogue of independent events (monofractal Poissonian catalogue), while the GK declustered catalogue remains multifractal. The main difference lies in the assumption that the events can be considered to be correlated at large distances. The spatial properties of the declustered catalogue reveal a distribution of epicentres that is more complex than the distribution for the complete catalogue. We suggest that such results are very similar to the scaling properties of fully developed turbulence.     

Application of conditional geostatistical simulation to calculate the probability of occurrence of earthquakes belonging to a seismic series

Geostatistics offers various techniques of estimation and simulation that have been satisfactorily applied in solving geological problems. In this sense, conditional geostatistical simulation is applied to calculate the probability of occurrence of an earthquake with a lower than or equal magnitude to one determined during a seismic series. It is possible to calculate the energy of the next most probable earthquake from a specific time, given knowledge of the structure existing among earthquakes occurring prior to a specific moment.     

Using earthquakes to assess lichen growth rates

Botanists make yearly measurements of lichen sizes that describe highly variable radial expansion of young, and old, Rhizocarpon subgenus Rhizocarpon that is a function of thallus size and age. Such non‐uniform growth would negate use of lichens to date geomorphic events, such as landslides and moraines, of the past 1000 years. Fortunately, many crustose lichens tend toward circular shapes, which can be achieved only when overall uniform radial growth prevails. Largest lichen measurements on rockfall blocks that accumulate incrementally as hillslope talus in earthquake‐prone California plot as distinct peaks in frequency distributions. Rockfall surface‐exposure times are known to the day for historical earthquakes and to the year where mass movements damage trees. Lichenometry consistently dates regionally synchronous rockfall events with an accuracy and precision of ±5 years. Only historical records and tree‐ring dating of earthquakes are better. The four crustose lichens used here have constant long‐term growth rates, ranging from 9.5 to 23.1 mm per century. Growth rates do not vary with altitude or climate in a 900 km long mountainous study region in California, USA. Linear growth regressions, when projected to the present, constrain estimates of colonization time and possible styles of initial lichen growth.     

Ductile shear zones: some aspects of constant slip velocity and constant shear stress models

Summary The thermomechanical differential equations governing deformation in viscous shear zones have been solved for both constant velocity and constant stress boundary conditions. The solutions show that the inertial term in these equations can be neglected everywhere.
The starting condition of the constant velocity model has been shown to be a constant velocity gradient and not a Heaviside function. The temperature anomaly produced by shear heating at the centre of the shear zone is shown to increase gradually and continuously with time, not reaching an asymptotic value. Conclusions for the constant velocity boundary condition are otherwise generally similar to those presented by Yuen et al , and agree with Fleitout & Froidevaux. The temperatures reached by constant velocity shears are sufficient for partial melting.
Constant stress boundary condition shear zone models show an initially broad shear zone with uniform shear velocity gradient. Depending on the level of applied shear stress and ambient temperature, localized intense shear heating may develop followed by thermal runaway. At lower ambient temperatures relatively high stresses are required to produce thermal runaway.
The broadening of the constant velocity shear zone proceeds more rapidly with increased ambient temperature. This can be used to show that shear zones broaden with depth. The merging of parallel shear zone pairs has been investigated and shear zones separated by distances of less than 10km coalesce to form a single shear zone within 3 Myr. Only shear zones separated by 50km or more remain distinct over periods of tens of millions of years.     

A test of the precursory accelerating moment release model on some recent New Zealand earthquakes

The proposal that the moment release rate increases in a systematic way in a large region around a forthcoming large earthquake is tested using three recent, large New Zealand events. The three events, 1993–1995, magnitudes 6.7–7.0, occurred in varied tectonic settings. For all three events, a circular precursory region can be found such that the moment release rate of the included seismicity is modelled significantly better by the proposed accelerating model than by a linear moment release model, although in one case the result is dubious. The 'best' such regions have radii from 122 to 167 km, roughly in accord with previous observations world-wide, but are offset by 50–60 km from the associated main shock epicentre. A grid-search procedure is used to test whether these three earthquakes could have been forecast using the accelerating moment release model. For two of the earthquakes the result is positive in terms of location, but the main shock times are only loosely constrained.     

Modelling the compliance of crustal rock—II. Response to temporal changes before earthquakes

There have been several claims that seismic shear waves respond to changes in stress before earthquakes. The companion paper develops a stress-sensitive model (APE) for the behaviour of low-porosity low-permeability crystalline rocks containing pervasive distributions of fluid-filled intergranular microcracks, and this paper uses APE to model the behaviour before earthquakes. Modelling with APE shows that the microgeometry and statistics of distributions of such fluid-filled microcracks respond almost immediately to changes in stress, and that the behaviour can be monitored by analysing seismic shear-wave splitting. The physical reasons for the coupling between shear-wave splitting and differential stress are discussed.
In this paper, we extend the model by using percolation theory to show that large crack densities are limited at the grain-scale level by the percolation threshold at which interacting crack clusters lead to pronounced increases in rock-matrix permeability. In the simplest formulation, the modelling is dimensionless and almost entirely constrained without free parameters. Nevertheless, APE modelling of the evolution of fluid-saturated rocks under stress reproduces the observed fracture criticality and the narrow range of shear-wave azimuthal anisotropy in crustal rocks. It also reproduces the behaviour of temporal variations in shear-wave splitting observed before and after the 1986, M = 6, North Palm Springs earthquake, Southern California, and several other smaller earthquakes.
The agreement of APE modelling with a wide range of observations confirms that fluid-saturated crystalline rocks are stress-sensitive and respond to changes in stress by critical fluid-rock interactions at the microscale level. This means that the effects of changes in stress and other parameters can be numerically modelled and monitored by appropriate observations of seismic shear waves.     

Large-magnitude Central American earthquakes, 1898–1994

We have collected and re-examined macroseismic information for large Central American earthquakes since the beginning of the period of instrumental recording about one hundred years ago, and combined this with a reassessment of early instrumental information to produce a catalogue of 51 events that, we believe includes ail those with magnitudes ( Ms ) greater than 7.0. We have reassessed surface-wave magnitudes by consulting station bulletins and we have derived a correction that gives an equivalent Ms for events of intermediate depth. We have also developed a regional relationship between Ms and seismic moment, which enables us to estimate the seismic slip rate across the Middle American Trench. Our best estimates give an average slip rate several times smaller than suggested convergence rates, but with the seismic slip in the central segment of the trench almost an order of magnitude smaller than that in the segments on either side. The low seismic slip rate may indicate aseismic crustal deformation     

Modelling of short-interval silent slip events in deeper subduction interfaces considering the frictional properties at the unstable–stable transition regime

Recent high-resolution observations of crustal movements have revealed silent slip events (SSEs) with propagation velocities of around 10–15 km d⁻¹ and with intervals of 3–14 months along the deeper parts of the Cascadia and Nankai subduction zones. This study develops 2-D and 3-D models of these short-interval SSEs considering the frictional behaviour that was confirmed experimentally by Shimamoto for the unstable–stable transition regime. To represent this frictional behaviour, a small cut-off velocity to an evolution effect is introduced in a rate- and state-dependent friction law. When the cut-off velocity to the evolution effect is significantly smaller than that to a direct effect, steady-state friction exhibits velocity weakening at low slip velocities and velocity strengthening at high slip velocities. At the deeper Cascadia and Nankai subduction interfaces, the pore pressure is inferred to be high because of the dehydration of materials in the descending plate. Under conditions where the pore-fluid pressure is nearly equal to the lithostatic pressure and the critical weakening displacement is very small, short-interval SSEs with propagation velocities and slip velocities of 4–8 km d⁻¹ and  2 − 4 × 10⁻⁷  m s⁻¹, respectively, can be reproduced. The propagation velocity of short-interval SSEs is in proportion to the slip velocity. The results also show that during the nucleation process of large earthquakes, the occurrence of short-interval SSEs becomes irregular because of the accelerated slips that occur at the bottom of the seismogenic zone. Our results suggest that monitoring of short-interval SSEs might be useful for forecasting the main earthquakes.