The use of modern statistical theories in the assessment of earthquake hazard, with application to quiet regions of eastern North America

It is generally accepted that both deterministic and statistical approaches are useful for the characterization of earthquake hazard. Although the most reliable estimates of seismic hazard can only be based on an improved understanding of the earthquake mechanism, efficient utilization of the appropriate methods provided by recent statistical theories is also important in seismic risk analysis. This is especially true in regions where the connection between seismicity and geologic structure is tenuous at best. We are particularly interested in developing better statistical treatments of data for regions with little known seismic activity. To this end, we have applied three statistical methods to the historical record of seismicity in relatively quiet regions of eastern North America. These are: (1) the threshold method for tail inference, a new theory for modeling earthquakes with sizes above a given threshold, (2) the ‘bootstrap’ technique in which the characteristics of an unknown population are simulated by replacing the true population by an estimated one, and (3) a technique to estimate the number of earthquakes below a given size, in order to compensate for the under-reporting of small earthquakes in most catalogs. A combination of these techniques has been used to estimate the probabilities of future large earthquakes for the regions studied. Because of limitations imposed by existing catalogs, the size estimate used has been maximum intensity.     

ELF propagation parameters for uniform models of the Earth–ionosphere waveguide

Uniform models for the Earth–ionosphere cavity are considered with particular attention to the physical properties of the ionosphere for the extremely low frequency (ELF) range. Two consistent features have long been recognized for the range: the presence of two distinct altitude layers of maximum energy dissipation within the lower ionosphere, and a “knee”-like change in the vertical conductivity profile representing a transition in dominance from ion-dominated to electron-dominated conductivity. A simplified two-exponential version of the Greifinger and Greifinger (1978) technique widely used in ELF work identifies two slopes in the conductivity profile and, providing accurate results in the ELF communication band (45–75 Hz), simulates too flat a frequency dependence of the quality factor within the Schumann resonance frequency range (5–40 Hz). The problem is traced to the upward migration, with frequency increasing, of the lower dissipation layer through the “knee” region resulting in a pronounced decrease of the effective scale height for conductivity. To overcome this shortcoming of the two-exponential approximation and still retain valuable model analyticity, a more general approach (but still based on the Greifinger and Greifinger formalism) is presented in the form of a “knee” model whose predictions for the modal frequencies, the wave phase velocities and the quality factors reasonably represent observations in the Schumann resonance frequency range.     

African monsoon variability during the previous interglacial maximum

Little is known about centennial- to millennial-scale climate variability during interglacial times, other than the Holocene. We here present high-resolution evidence from anoxic (unbioturbated) sediments in the eastern Mediterranean Sea that demonstrates a sustained ∼800-yr climate disturbance in the monsoonal latitudes during the Eemian interglacial maximum (∼125 ka BP). Results imply that before and after this event, the Intertropical Convergence Zone (ITCZ) penetrated sufficiently beyond the central Saharan watershed (∼21°N) during the summer monsoon to fuel flooding into the Mediterranean along the wider North African margin, through fossil river/wadi systems that to date have been considered only within a Holocene context. Relaxation in the ITCZ penetration during the intra-Eemian event curtailed this flux, but flow from the Nile - with its vast catchment area - was not affected. Previous work suggests a concomitant Eurasian cooling event, with intensified impact of the higher-latitude climate on the Mediterranean basin. The combined signals are very similar to those described for the Holocene cooling event around 8 ka BP. The apparent type of concurrent changes in the monsoon and higher-latitude climate may reflect a fundamental mechanism for variability in the transfer of energy (latent heat) between the tropics and higher latitudes.     

From stable dipolar towards reversing numerical dynamos

We are using a three-dimensional convection-driven numerical dynamo model without hyperdiffusivity to study the characteristic structure and time variability of the magnetic field in dependence of the Rayleigh number (Ra) for values up to 40 times supercritical. We also compare a variety of ways to drive the convection and basically find two dynamo regimes. At low Ra, the magnetic field at the surface of the model is dominated by the non-reversing axial dipole component. At high Ra, the dipole part becomes small in comparison to higher multipole components. At transitional values of Ra, the dynamo vacillates between the dipole-dominated and the multipolar regime, which includes excursions and reversals of the dipole axis. We discuss, in particular, one model of chemically driven convection, where for a suitable value of Ra, the mean dipole moment and the temporal evolution of the magnetic field resemble the known properties of the Earth’s field from paleomagnetic data.     

Distribution of Mantle Up-welling Determined from Plate Motions: A Case for Large-scale Bénard Convection

—?The number and geometric distribution of putative mantle up-welling centers and the associated convection cell boundaries are determined from the lithospheric plate motions as given by the 14 Euler poles of the observational NUVEL model. For an assumed distribution of up-welling centers (called “cell-cores”) the corresponding cell boundaries are constructed by a Voronoi division of the spherical surface; the resulting polygons are called “Bénard cells.” By assuming the flow-kinematics within a cell, the viscous coupling between the flow and the plates is estimated, and the Euler poles for the plates are computed under the assumption of zero-net-torque. The positions of the cell-cores are optimized for the HS2-NUVEL1 Euler poles by a method of successive approximation (“subplex”); convergence to one of many local minima occurred typically after ～20,000 iterations. Cell-cores associated with the fourteen HS2-NUVEL1 Euler poles converge to a relatively small number of locations (8 to 10, depending on interpretation), irrespective of the number of convection cells submitted for optimized distribution (from 6 to 50). These locations are correlated with low seismic propagation velocities in tomography, uniformly occur within hotspot provinces, and may specifically be associated with the Hawaiian, Iceland, Reunion/Kerguelen (Indian Ocean), Easter Island, Melanesia/Society Islands (South Pacific), Azores/Cape Verde/Canary Islands, Tristan da Cunha (South Atlantic), Balleny Islands, and possibly Yellowstone hotspots. It is shown that arbitrary Euler poles cannot occur in association with mantle Bénard convection, irrespective of the number and the distribution of convection cells. Nevertheless, eight of the observational Euler poles – including the five that are accurately determined in HS2-NUVEL1 (Australia, Cocos, Juan de Fuca, Pacific, and Philippine) – are “Bénard-valid” (i.e., can be explained by our Bénard model). Five of the remaining six observational poles must be relocated within their error-ellipses to become Bénard-valid; the Eurasia pole alone appears to be in error by ～115°, and may actually lie near 40°N, 154°E. The collective results strongly suggest Bénard-like mantle convection cells, and that basal shear tractions are the primary factor in determining the directions of the plate motions as given by the Euler poles. The magnitudes of the computed Euler vectors show, however, that basal shear cannot be the exclusive driving force of plate tectonics, and suggest force contributions (of comparable magnitude for perhaps half of the plates) from the lithosphere itself, specifically subducting slab-pull and (continental) collision drag, which are provisionally evaluated. The relationship of the putative mantle Bénard polygons to dynamic chaos and turbulent flow is discussed.     

Modelling of meteorological conditions at an urban scale for the PUMA winter campaign

For the winter 2000 campaign of the Pollution of Urban Midlands Atmosphere project, observation and numerical modelling of meteorological conditions over the West Midlands conurbation, UK, was undertaken. Modelling was performed using the regional atmospheric meteorological system (RAMS). This paper presents a comparison of modelled and observed wind and temperature for 25 and 26 January 2000. The RAMS model uses two nested grids with a mesh size of 2 km for the inner grid which is embedded in the outer grid with a mesh size of 8 km. Statistical evaluation of the model results against the observational data of wind speed, direction and temperature at 10 m was conducted. In general, the modelling results are in a reasonable agreement with observation. The statistical evaluation suggests that model performance is poorer for the inner grid than the outer grid as the model uncertainties (mainly mean bias) transfer from the outer to inner one. The low indices of agreement of temperature and wind are mainly associated with the systematic root-mean-square-difference values. For temperature, the systematic bias may also be affected by representation of cloud amount by the model. For wind, the model tends to have a poor performance for calm conditions, as under a stable anti-cyclonic situation local wind patterns associated with topography may develop, although the topography of the region is relatively flat. The results for the inner grid reveal some subtle spatial patterns at a scale smaller than 10 km near hills and valleys with differences in elevation of a few hundred metres.     

A rifted inside corner massif on the Mid-Atlantic Ridge at 5°S

The structure of the Mid-Atlantic Ridge at 5°S was investigated during a recent cruise with the FS Meteor. A major dextral transform fault (hereafter the 5°S FZ) offsets the ridge left-laterally by 80 km. Just south of the transform and to the west of the median valley, the inside corner (IC – the region bounded by the ridge and the active transform) is marked by a major massif, characterized by a corrugated upper surface. Fossil IC massifs can also be identified further to the west. Unusually, a massif almost as high as the IC massif also characterizes the outside corner (OC) south of the inactive fracture zone and to the east of the median valley. This OC massif has axis-parallel dimensions identical to the IC massif and both are bounded on their sides closest to the spreading axis by abrupt, steep slopes. An axial volcanic ridge is well developed in the median valley both south of the IC/OC massifs and in an abandoned rift valley to the east of the OC massif, but is absent along the new ridge-axis segment between the IC and OC massifs. Wide-angle seismic data show that between the massifs, the crust of the median valley thins markedly towards the FZ. These observations are consistent with the formation of the OC massif by the rifting of an IC core complex and the development of a new spreading centre between the IC and OC massifs. The split IC massif presents an opportunity to study the internal structure of the footwall of a detachment fault, from the corrugated fault surface to deeper beneath the fault, without recourse to drilling. Preliminary dredging recovered gabbros from the scarp slope of the rifted IC massif, and serpentinites and gabbros from the intersection of this scarp with the corrugated surface. This is compatible with a concentration of serpentinites along the detachment surface, even where the massif internally is largely plutonic in nature.     

Melting of β-quartz up to 2.0 GPa and thermodynamic optimization of the silica liquidus up to 6.0 GPa

Melting relations of β-quartz were experimentally determined at 1.0 GPa (1900±20 °C), 1.5 GPa (2033±20 °C), and 2.0 GPa (2145±20 °C) using a new high-pressure assembly in a piston–cylinder apparatus and substantial differences were found with data previously reported. The new melting data of β-quartz were combined and optimized with all available thermodynamic, volumetric, and phase equilibria data for β-cristobalite, β-quartz and coesite to produce a P–T liquidus diagram for silica valid up to 6.0 GPa. Using the new optimized thermodynamic parameters, the invariant point β-cristobalite+β-quartz+liquid and β-quartz+coesite+liquid were determined to lie at 1687±17 °C and 0.457 GPa, and 2425±25 °C and 5.00 GPa, respectively.     

Synthetic Seismograms and Wide-angle Seismic Attributes from the Gaussian Beam and Reflectivity Methods for Models with Interfaces and Velocity Gradients

— The effects of interfaces and velocity gradients on wide-angle seismic attributes are investigated using synthetic seismograms. The seismic attributes considered include envelope amplitude, pulse instantaneous frequency, and arrival time of selected phases. For models with interfaces and homogeneous layers, head waves can propagate which have lower amplitudes, as well as frequency content, compared to the direct arrivals. For media with interfaces and velocity gradients, higher amplitude diving waves and interference waves can also occur. The Gaussian beam and reflectivity methods are used to compute synthetic seismograms for simple models with interfaces and gradients. From the results of these methods, seismic attributes are obtained and compared. It was found that both methods were able to simulate wide-angle seismic attributes for the simple models considered. The advantage of using the Gaussian beam method for seismic modeling and inversion is that it is fast and also asymptotically valid for laterally varying media.     

Modelling Seismic Waves Around Underground Openings in Fractured Rock

—?The potential for large excavation-induced seismic events may be recognised, even if the timing of an event may be inherently unpredictable. In this case, modelling the wave propagation from a potential event could allow the dynamic motions around an excavation to be projected, and for areas of danger to be anticipated. However, the above and other potential applications require accurate models of wave interaction with the openings, as well as with the fractured rock which surrounds such excavations. This paper considers real recorded waveforms and how well these waveforms are modelled by explicit mechanical models of the source, the medium and the excavation. Models of experiments at three different scales of the problem are presented: small and large amplitude waveforms recorded around a deep-level mining tunnel in a synthetic rockburst experiment; waveforms from laboratory experiments of waves through plates of steel representing fractures; waveforms from active pulses in an acoustic emission experiment in a small volume of fractured rock at the surface of an underground excavation. The results show that elastic wave propagation around an excavation was a first approximation for small amplitude waves, but was less successful for modelling large amplitude waves and more fractured rock. Fractures in the models were represented explicitly with displacement discontinuities. Waveforms through known fracture geometries were particularly well-reproduced, and indicate the importance of fracture stiffness, the in situ stress state, and stress-dependence of the fractures in such models. Overall, the models are sufficiently successful at representing recorded behaviour, to be encouraging for the goal of representing accurate wave motions around excavations.