The development of numerical methods for stochastic differential equations has intensified over the past decade. The earliest methods were usually heuristic adaptations of deterministic methods, but were found to have limited accuracy regardless of the order of the original scheme. A stochastic counterpart of the Taylor formula now provides a framework for the systematic investigation of numerical methods for stochastic differential equations. It suggests numerical schemes, which involve multiple stochastic integrals, of higher order of convergence. We shall survey the literature on these and on the earlier schemes in this paper. Our discussion will focus on diffusion processes, but we shall also indicate the extensions needed to handle processes with jump components. In particular, we shall classify the schemes according to strong or weak convergence criteria, depending on whether the approximation of the sample paths or of the probability distribution is of main interest. 相似文献
The October 6/2000 Tottori earthquake that occurred in central Japan was an intermediate size strike-slip event that produced a very large number of near field strong motion recordings. The large amount of recorded data provides a unique opportunity for investigating a source asperity model of the Tottori earthquake that, combined with a hybrid strong motion simulation technique, is able to reproduce the observed broadband frequency near-fault ground motion.
We investigated the optimum source asperity parameters of the Tottori earthquake, by applying a Genetic Algorithm (GA) inversion scheme to optimise the fitting between simulated and observed response spectra and Peak Ground Acceleration (PGA) values. We constrained the initial model of our inversion by using the heterogeneous slip distribution obtained from a kinematic inversion of the source of previous studies. We used all the observed near-fault ground motions (−100 m) from the borehole strong motion network of Japan (KiK-Net), which are little affected by surficial geology (site effects).
The calculation of broadband frequency strong ground motion (0.1–10 Hz) is achieved by applying a hybrid technique that combines a deterministic simulation of the wave propagation for the low frequencies and a semi-stochastic modelling approach for the high frequencies. For the simulation of the high frequencies, we introduce a frequency-dependent radiation pattern model that efficiently removes the dependence of the pattern coefficient on the azimuth and take-off angle as the frequency increases. The good agreement between the observed and simulated broadband ground motions shows that our inversion procedure is successful in estimating the optimum asperity parameters of the Tottori earthquake and provides a good test for the strong ground motion simulation technique.
The ratio of background stress drop to average asperity stress drop from our inversion is nearly 50%, in agreement with the theoretical asperity model of Das and Kostrov [Das, S., Kostrov, B.V., 1986. Fracture of a single asperity on a finite fault: a model for weak earthquakes? Earthquake Source Mechanics, AGU, pp. 91–96.], and an empirical ratio of asperities to rupture area [Seismol. Res. Lett. 70 (1999) 59–80.].
The simulated radiation pattern is very complex for epicentral distances within half the fault length, but it approaches the radiation of a double-couple point source for larger distances.
The rupture velocity and rise time have a significant influence on the Peak Ground Velocity (PGV) distribution around the fault. An increase in rupture velocity produces a similar effect on the ground motion as a reduction in rise time. 相似文献
Over the years a large number of rock samples were collected by the explorationists of Atomic Minerals Directorate for Exploration
and Research (AMD), Department of Atomic Energy from Sambalpur district, Orissa, India. The variation of uranium enrichment
with various types of rock in these samples was studied with an aim to help quick reviewing of toposheets in case of newly
taken up areas, for uranium exploration. The radioelements U, Th and K determined for these samples are plotted in ternary
diagrams for classifying them as being uraniferous or thoriferous with respect to various type of rocks, keeping the total
natural content of radioelements (expressed by eUP3O8) as a parameter.
In this study it is seen that samples of quartzofeldspathic breccia type are enriched in uranium irrespective of their further
sub classification and eU3O8 content. Granites are enriched in thorium when eU3O8 < 100 ppm and are enriched in uranium when eU3O8 > 100 ppm.
A database prepared for this purpose may be useful for reviewing toposheets in future 相似文献
Abstract This paper discusses the relationships between granitic magmatism and gold mineralization and the exhumation history of the Dapinggou gold deposit in northern Altun, NW China based on the geochronological data, including zircon U‐Pb ages, Rb‐Sr isochron age and 40Ar‐39Ar dating and MDD modeling data. The main granitic magmatism age in this area is attained from the ID TIMS U‐Pb geochronology of zircons from the Kuoshibulak granite, the biggest granite in the northern Altun area, which gives a concordant age of 443±5 Ma in the Late Ordovician. Zircon ID TIMS U‐Pb geochronology of the West Dapinggou biotite granite west of the Dapinggou gold deposit gives concordant ages around 485±10 Ma, representing the early stage of Ordovician magmatism. The Rb‐Sr isochron age (487±21 Ma) of 6 quartz inclusion samples from quartz veins in this gold deposit is very close to that of the West Dapinggou granite. MDD modeling of step heating 40Ar‐39Ar data of K‐feldspar from the same West Dapinggou biotite granite gives a rapid cooling history from 300°C to 150°C during 200–185 Ma. According to the age data and the geological setting of this area, we conclude that the Dapinggou gold deposit was formed at the early stage of the Early Paleozoic granitic magmatism in northern Altun, and exhumed in the Early Jurassic due to the normal faulting of the Lapeiquan detachment. The Early Paleozoic magmatism may provide heat source and produce geological fluids, which are very important for gold mineralization. Exhumation in the Mesozoic caused the uplift of the deposit towards the ground surface. 相似文献