Multifractal analysis of the spatial distribution of earthquakes in southern Italy

We evaluate the complete spectrum of the generalized fractal dimension of the spatial pattern of microearthquakes in Southern Italy, revealing a multifractal distribution structure. Our analysis is focused on the dependence of the multifractal distribution on the size of the selected area and the kind of seismicity in the area. As the size of the window varies, we observe that the capacity, information and correlation dimensions vary significantly, while both d _∞ and d _−infin; remain unchanged within their errors limits. We interpret this result in terms of the observation that our data are mainly clustered around a linear fault (the Sisifo fault). When we restrict the selected windows around the fault, clustering around a line (the fault) is highlighted. The capacity dimension changes from about 1.8 to about 1.4 and the correlation dimension decreases because we observe in detail the clustering of the seismicity along the fault, which approximates the maximum intense clustering of the whole data set. Although our results are strongly influenced by the fact that the data are dominated by the epicentres located on the fault, we can conclude that multifractal analysis can be a very useful tool to discriminate the seismicity linked to a particular fault in a given area.     

Distribution and morphology of sinkholes triggered by flooding following Tropical Storm Alberto at Albany, Georgia, USA

Flooding of the Flint River in July 1994 triggered the collapse of at least 312 sinkholes in the karstic Dougherty Plain at Albany, Georgia. We examined the distribution and morphology of these new sinkholes to evaluate the mode of formation, to characterize early stages of the evolution of sinkhole form, and to estimate the lowering of the surface associated with the development of new sinkholes.Eighty-eight percent of sinkholes occur inside the limits of flooding, especially in areas of sandy overburden, and they often follow joint-controlled linear trends. Sinkhole dimensions are log-normally distributed with median values of circumference = 5.7 m, length = 1.8 m, width = 1.6 m, and depth = 0.7 m; asymmetry (L:W) = 1.2. Cross-sectional forms range from narrow cylinders to large bowls, with many sinkholes having undercut sides.Flooding triggered the formation of sinkholes by saturating and liquefying overburden, which caused soil arches to collapse and flow into cavities in bedrock. The prevalence of sinkholes near the periphery of flooding suggests that drainage and loss of buoyant support as flood waters subsided may also have contributed to failure. A volume ratio index is used to quantify the three dimensional geometric form of sinkholes. Initially, small cylindrical shafts open over a bedrock joint, followed by progressive slumping that leads to widening and increases in volume to a final bowl form. Estimates of the aggregate volume of overburden transported underground in flooded areas range from 7,990 to 11,130 m3. Averaged over flooded areas, this accounts for 0.26 to 0.37 mm/km² lowering of the surface. Based on a 500 year recurrence interval for the flood event, values for lowering of the surface range from 0.52 to 0.74 mm per 1,000 years. These values are an order of magnitude less than estimates of carbonate dissolution and suggest that transport of overburden underground is limited by triggering events.     

Cation ordering of orthopyroxenes from the Skaergaard Intrusion: implications for the subsolidus cooling rates and permeabilities

 We have determined the quenched cation ordering states of five orthopyroxene crystals collected from the marginal border group and the lower zone a and b of the Skaergaard intrusion, and modeled these data to retrieve their closure temperatures (T _c) of Fe–Mg ordering and cooling rates. According to existing thermal models for the Skaergaard pluton, conductive cooling dominated the high and low temperature regimes, which were separated by an intermediate temperature regime in which the cooling was controlled primarily by convective fluid circulation. The cooling rates retrieved from the quenched cation ordering states of the orthopyroxene crystals strictly apply to temperatures around the closure temperatures of the ordering states, ∼340–400^° C, which fall at the transition from convective to the lower temperature conductive cooling. The cooling rates obtained from the cation ordering states of orthopyroxene vary from ∼1 to 270 K/ka. These results agree well with a thermal model calculated using an assumed average permeability of 10^-12 cm² for the pluton, but not completely with a model calculated on the basis of an average permeability of 10^-13 cm², although both values produced shifts of δ¹⁸O that are comparable to those observed in the pluton. Received: 27 February 1995/Accepted: 20 July 1995     

Stability analysis of rock wedges with multiple sliding surfaces

Summary Although wedge and plane sliding stability analyses are well established in the geotechnical literature, certain geologic environments produce blocks which cannot be adequately modelled as either wedges or plane slides. An example is blocks forming in cylindrically folded sedimentary rocks, where the surface of sliding is neither a single plane nor a double plane but is curved. This type of block may be idealized as a prismatic block with multiple sliding planes, all with parallel lines of intersection. If the sliding planes number three or more, the distribution of normal forces, and hence the factor of safety, is indeterminate. A new analytical model for sliding stability analysis is described in which the distribution of normal forces on the contact planes is chosen to minimize the potential energy of the system. The classic wedge and plane solutions are shown to be special cases of this more general model, which allows determination of the safety factor for any shape of prismatic contact surface. An example from Tennessee concerning a block with a curved sliding surface is described and the factor of safety compared with the standard wedge analysis. It is shown that with three or more contact planes, the safety factor may be significantly lower than that calculated from the wedge model, which provides an upper limit on stability.     

Hazard mapping based on macroseismic data considering the influence of geological conditions

The object of this study is to consider directly the influence of regional geological conditions on the assessment of seismic hazard. It is assumed that macroseismic data at individual locations contain, in an average way, the influence of geological conditions.A Data Base referring to 199 historical (5) and instrumental (194, in the 1947–1993 period) events with macroseismic information in 1195 locations of Portugal was built. For any given seismic event, whenever macroseismic information was available at a location (town, village, etc.), an EMS-92 intensity value was estimated. To each one of those locations a geological unit, representing the most common type of soil, was assigned, based on the Geological Portuguese Map at a scale 1:500 000; the geological units were grouped into three categories: soft, intermediate and hard soils.The Data Base was used to determine the attenuation laws in terms of macroseismic intensity for the three different geological site conditions, using multiple linear regression analysis. The reasonability of the laws was tested by (i) checking residual distributions and (ii) comparing the map of isoseismals of important earthquakes with the isoseismals generated by the attenuation curves derived for each one of the three different soil classes, taking into consideration the soil class of each site. The main results of attenuation modeling are: high dispersion on macroseismic intensity data; all the models predict intensity values, for short hypocentral distances, lower than the ones observed; and for some important analyzed earthquakes and for the observed range of distances, the models confirm the expectancy that macroseismic intensity increases from hard to soft soil.The approach to obtain the hazard assessment at each location consisted in the use of the attenuation law specifically derived for the class of soil of that particular location. This method, which considers the influence of the regional geology, was illustrated with the mapping of hazard for the country for several return periods. Comparison with previous maps not taking into consideration the regional geological conditions emphasizes the importance of this new parameter. It can be concluded that (i) soil segmentation is clearly the cause for hazard increase in the region to the north of Lisbon, especially at sites with soft and intermediate soils as the ones in lower Tagus valley; the maximum increase on hazard is, in any case, less than one degree; (ii) when geological conditions are disregarded in the attenuation regression analysis, hazard pattern is similar to the one obtained for the case of hard soil everywhere.     

Melting of albite and dehydration of brucite in H2O–NaCl fluids to 9 kbars and 700–900°C: implications for partial melting and water activities during high pressure metamorphism

 The melting reaction: albite_(solid)+ H₂O_(fluid) =albite-H₂O_(melt) has been determined in the presence of H₂O–NaCl fluids at 5 and 9.2 kbar, and results compared with those obtained in presence of H₂O–CO₂ fluids. To a good approximation, albite melts congruently at 9 kbar, indicating that the melting temperature at constant pressure is principally determined by water activity. At 5 kbar, the temperature (T)- mole fraction (X _(H2O) ) melting relations in the two systems are almost coincident. By contrast, H₂O–NaCl mixing at 9 kbar is quite non-ideal; albite melts ∼70 ^°C higher in H₂O–NaCl brines than in H₂O–CO₂ fluids for X _(H2O) =0.8 and ∼100 ^°C higher for X _(H2O) =0.5. The melting temperature of albite in H₂O–NaCl fluids of X _(H2O)=0.8 is ∼100 ^°C higher than in pure water. The P–T curves for albite melting at constant H₂O–NaCl show a temperature minimum at about 5 kbar. Water activities in H₂O–NaCl fluids calculated from these results, from new experimental data on the dehydration of brucite in presence of H₂O–NaCl fluid at 9 kbar, and from previously published experimental data, indicate a large decrease with increasing fluid pressure at pressures up to 10 kbar. Aqueous brines with dissolved chloride salt contents comparable to those of real crustal fluids provide a mechanism for reducing water activities, buffering and limiting crustal melting, and generating anhydrous mineral assemblages during deep crustal metamorphism in the granulite facies and in subduction-related metamorphism. Low water activity in high pressure-temperature metamorphic mineral assemblages is not necessarily a criterion of fluid absence or melting, but may be due to the presence of low a _(H2O) brines. Received: 17 March 1995/Accepted: 9 April 1996     

Benchmarking the thermomechanical behaviour of clays — a progress report — the CEC interclay project

In 1989 a small-scale exercise conducted by the CEC as part of its research programme into the underground storage of radioactive waste highlighted the difficulty of making accurate predictions a priori, of the geomechanical behaviour of clay. Given source data about the Boom clay from the underground research facility at Mol, three organisations independently performed f.e. analyses of two somewhat hypothetical problems. While the results were very broadly in agreement, they were shown to be sensitive to both the type of constitutive model used and the way data was fitted to the model.

Subsequently, the CEC sponsored a more comprehensive benchmark exercise called INTERCLAY II. This involves eleven organisations from various member states of the EC in a project encompassing the three aspects of software development for predictive modelling: verification, validation on the laboratory scale and the treatment of in-situ tests. The paper briefly describes the exercise currently in progress and presents the main results achieved to date concentrating on validation aspects.