A stochastic modelling of earthquake frequencies

Summary. The frequency of earthquake occurrence in a given region can be formulated as

where n ( t ) is the number of earthquakes per unit time, and r, k and α are constants. Empirically determined values of α range from 0.67 to 1.0. This is a generalization of the modified Omori formula for aftershocks, the latter being an approximation of the former for n > k. This formula adequately describes the initial increasing and later decreasing activity of earthquakes during the Matsushiro and Wakayama swarms as well as aftershocks of large earthquakes.
When a random external force is added to this system as a driving mechanism, the equation above becomes

where v = l n ( n/k ) and R ( t ) is the random Gaussian noise. Repetitive seismic patterns with bursts, which are commonly observed in real earthquake sequences, are predicted from this formulation under stationary conditions. These formulations appear to be quite promising in helping to understand macroscopic features of the microearthquake activity.     

An externally forced barotropic circulation model for the New York Bight

The sea level and the barotropic, frictional circulation response for the New York Bight are used to demonstrate the effects of external sea-level forcing, bathymetry, and variable friction. The governing equation is the steady, integrated vorticity equation and is computed by finite differencing over a curvilinear grid conforming to the 10- and 100-m isobaths and extending for 250 km alongshore. The boundary conditions are based on the hypothesis that the dynamics of the shelf are driven by the external sea-level gradient and the coastal no-flux condition; and consequently the conditions at the lateral boundaries are dependent thereon. Therefore, the external sea-level slope must be independently specified, and the lateral boundary conditions must be dependently generated. The diabathic component of the external sea slope forces the calm wind circulation by its effect on the transport through the upstream boundary; and the parabathic component has also an important modifying effect by forcing a shelf convergent transport. The parabathic sea slope at the coast is independent of its offshore value, being instead a direct product of the coastal boundary condition.The bottom friction is expressed as related to the sea level through a bottom length parameter and a veer angle, both of which are taken to increase shoreward. An additional bottom stress component, related to the surface stress, is determined for bottom depths less than the Ekman depth. Such bottom stress variability produces significant alterations in the nearshore flow field, over the constant bottom stress formulation, by reducing it and causing it to veer downgradient and downwind in the nearshore.The model is forced by different wind directions and the results are discussed. The circulations generally conform to the observed mean flow patterns, but with several smaller-scale features. The strong bathymetric feature of the Hudson Shelf Valley causes a polarized up- and downvalley flow for winds with an eastward or westward component, respectively. Under mean westerly winds, there is a divergence in the shelf valley flow at about the 60-m isobath. The Apex gyre existing off the western tip of Long Island becomes more extensive for winds changing from northeast to southwest. Mean flow reversals (to the northeast) occur off both Long Island and New Jersey for wind directions changing counterclockwise from northwest to southeast and from west to east, respectively. Southeastward transport over the outer New Jersey shelf tends to be enhanced by wind and external sea-level conditions; and the transport over the New Jersey midshelf, particularly in the lee of the shelf valley, tends to be weak and variable also under these mean conditions.     

Faint comet searching

Comets are usually discovered to a magnitude limit of B_lim～19 at best. This can be improved by one magnitude with a blank-search technique that is described here. To find a new comet, the required search area near opposition is ～600 square degrees at B_lim～20.0. Three faint comets were found this way; they are inconspicuous and would not have been discovered in any other manner. It therefore appears that the presently known statistics must be incomplete at the faint end due to incompleteness of the discovery observations. Another, future, method to find such inconspicuous comets is with electronically scanning cameras and computerized reduction. If such a CCD scannerscope were to have a ～1.8-m aperture, it could discover at least 40 comets per year.     

Rate constants of dissolution derived from the measurements of mass balance in hydrological catchments

The experimental rate constant of dissolution of oligoclase, 1.7 × 10 ^{? 2} mol · m^?2 · s^?1 (Busenberg and Clemency, 1976), is compared with rate constants, 5.2 × 10^?15 to 6.8 × 10^?13 mol · m^?2· s^?1, derived from mass-balance measurements of sodium in hydrological catchments. The wide range of the field-based rate constants mainly reflects the uncertainty in the evaluation of the specific wetted surface of rock in aquifer. The most probable order of magnitude of the field rate constant is 10^?14 mol · m^?2· s^?1. The difference between the experimental and field rate constant is only partly caused by lower temperature and lowerP_CO2 in the aquifer. The main reason for the discrepancy is the diverse history of the mineral surfaces undergoing reaction.It is suggested that the feldspar surfaces in an aquifer are old, compared to those of feldspars utilized in laboratory experiments. They have fewer defects and are smooth. The fresh surfaces of feldspars studied in the laboratory consist of many kinks and ledges and small-area terraces which dissolve faster.The differences in rate constants derived from field data on several specific catchments indicate that the anthropogenic processes which have operated during this century in Central Europe speed up the rate of dissolution by a factor of three. Modern agricultural practices speed up the rate by a factor of five.     

The Rehabilitation of Monitoring Wells Clogged by Calcite Precipitation and Drilling Mud

Based on aquifer performance tests, 13 out of 15 wells situated at the Mixed Waste Disposal (MWD) area located at the Savannah River site. South Carolina, exhibited high skin factors and low well efficiencies indicative of severely damaged wells. The use of damaged wells in aquifer testing can lead to inaccurate determinations of aquifer properties, and such wells are unusable in future remediation programs. Moreover, damaged wells can go dry during purging, thus compromising sample collection. Pump tests, chemical analyses, and biological investigations revealed that the poor well performance at MWD was attributable to calcite precipitation on the well screen and drilling mud in the filter pack. The calcite problem resulted from improper well installation, and the drilling mud in the filter pack was due to inadequate well development.
Experimental rehabilitation procedures employed on two wells, MWD 5A and 1A, included acidification, swabbing, introduction of surfactants, and surging. Treatment of the wells substantially improved well yields, skin factors, and well efficiencies. Moreover, well rehabilitation was determined to be a reasonable alternative to drilling new wells at the MWD wellfield.     

Recent environmental changes in a naturally acidic rocky lake in southern Finland, as reflected in its sediment geochemistry and biostratigraphy

Paleolimnological methods are combined with statistical multivariate analyses (PCA and CCA) to study the effects of local environmental disturbances and changes in loading of atmospheric origin on water acidity and the physiochemical properties of the sediment in a small, naturally acidic rocky lake in southern Finland. The pH of the lake as calculated from the diatom flora increased by 0.9 pH units as a consequence of a forest fire in the catchment area at the turn of the last century, and the changes in the diatom assemblages point to an increase in dys(eu)trophy and turbulence. In terms of element influx (in µg cm^-2 yr^-1), the effects of the fire are seen in a slight increase in the accumulation of lithophilous elements. Diatom-inferred pH values decline upwards in the sediment, but do not regain the level recorded before the fire. This is attributed to reactions between Fe³⁺ and S, which has partly accumulated from the air as SO^2-, producing internal alkalinity. Accumulation rates of many elements increase markedly after the 1960s, an effect for Al, Mg, Na, P and Zn may be connected mainly with the enhanced accumulation of dry matter, whereas the accumulation of K, Ni, Pb, Ti and V in surface sediment are obviously related to atmospheric loading. Measured accumulation rates of Cd and Cu are lower than the calculated values especially in the surface sediment, possibly because of diagenetic changes. Accumulation of Ca and Mn decreases towards the surface on account of acidification of anthropogenic origin.     

Dynamics of sedimentation in a tide-dominated backbarrier salt marsh, Norfolk, UK

Progressive burial of artificial markers over a 5-year period is used to determine the rate and pattern of vertical accretion within a large backbarrier salt marsh on the UK east coast. Over this period, annual accretion varies spatially from 1 to 8 mm yr⁻¹. The arithmetic mean rate for the whole marsh is 3.9 mm yr⁻¹. Spatial variability in accretion is a joint function of (1) elevation-dependent inundation frequency and (2) progressive sediment removal from water masses advected across channel margins. Accretion is, therefore, inadequately represented by simple averaging of point measurements. Numerical integration of the ‘accretion surface’ results in a spatial average rate of around 3 mm yr⁻¹, well below the arithmetic mean rate.

Short-term sediment trap deployments show that local and long-range meteorological effects, and remobilisation of sediment deposited within tidal creeks, often mask the expected link between tidal height and sedimentation rate. Retention of sediment on plant surfaces is minimal, with direct settling accounting for approximately 95% of total deposition.

Time-extrapolation of weekly sediment trap data, and comparison with the 5-year marker horizon burial, shows that processes associated with ordinary tides can account for long-term accretion over most of the marsh. However, the highest surfaces receive appreciable sediment input only during aperiodic storm events.