Summary. A first-order form of the Euler's equations for rays in an ellipsoidal model of the Earth is obtained. The conditions affecting the velocity law for a monotonic increase, with respect to the arc length, in the angular distance to the epicentre, and in the angle of incidence, are the same in the ellipsoidal and spherical models. It is therefore possible to trace rays and to compute travel times directly in an ellipsoidal earth as in the spherical model. Thus comparison with the rays of the same coordinates in a spherical earth provides an estimate of the various deviations of these rays due to the Earth's flattening, and the corresponding travel-time differences, for mantle P -waves and for shallow earthquakes. All these deviations are functions both of the latitude and of the epicentral distance. The difference in the distance to the Earth's centre at points with the same geocentric latitude on rays in the ellipsoidal and in the spherical model may reach several kilometres. Directly related to the deformation of the isovelocity surfaces, this difference is the only cause of significant perturbation in travel times. Other differences, such as that corresponding to the ray torsion, are of the first order in ellipticity, and may exceed 1 km. They induce only small differences in travel time, less than 0.01s. Thus, we show that the ellipticity correction obtained by Jeffreys (1935) and Bullen (1937) by a perturbational method can be recovered by a direct evaluation of the travel times in an ellipsoidal model of the Earth. Moreover, as stated by Dziewonski & Gilbert (1976), we verify the non-dependence of this correction on the choice of the velocity law. 相似文献
Evolution of sedimentary systems at large temporal and spatial scales cannot be scaled down to laboratory dimensions by conventional hydraulic Froude scaling. Therefore, many researchers question the validity of experiments aiming to simulate this evolution. Yet, it has been shown that laboratory experiments yield stratigraphic responses to allocyclic forcing that are remarkably similar to those in real‐world prototypes, hinting at scale independency with strong dependence on boundary conditions but weak dependence on the actual sediment transport dynamics. This paper addresses the dilemma by contrasting sediment transport rules that apply in the laboratory with those that apply in real‐world geological systems. It is demonstrated that the generation of two‐dimensional stratigraphy in a flume can be simulated numerically by the non‐linear diffusion equation. Sediment transport theory is used to demonstrate that only suspension‐dominated meandering rivers should be simulated with linear diffusion. With increasing grain‐size (coarse sand to gravel) and shallowness of river systems, the prediction of long‐term transport must be simulated by non‐linear, slope‐dependent diffusion to allow for increasing transport rates and thus change in stratigraphic style. To point out these differences in stratigraphic style, three stages in infill of accommodation have been defined here: (i) a start‐up stage, when the system is prograding to base level (e.g. the shelf edge) with no sediment flux beyond the base‐level point; (ii) a fill‐up stage, when the system is further aggrading while progressively more sediment is bypassing base level with the progression of the infill; and (iii) a keep‐up stage, when more than 90% of the input is bypassing the base level and less than 10% is used for filling the accommodation. By plotting the rate of change in flux for various degrees of non‐linearity (varying the exponent in the diffusion equation) it was found that the error between model and real‐world prototype is largest for the suspension‐dominated prototypes, although never more than 30% and only at the beginning of the fill‐up stage. The error reduces to only 10% for the non‐linear sandy‐gravelly and gravelly systems. These results are very encouraging and open up ways to calibrate numerical models of sedimentary system evolution by such experiments. 相似文献
The paper is dedicated to the review of methods of seismic hazard analysis currently in use, analyzing the strengths and weaknesses of different approaches. The review is performed from the perspective of a user of the results of seismic hazard analysis for different applications such as the design of critical and general (non-critical) civil infrastructures, technical and financial risk analysis. A set of criteria is developed for and applied to an objective assessment of the capabilities of different analysis methods. It is demonstrated that traditional probabilistic seismic hazard analysis (PSHA) methods have significant deficiencies, thus limiting their practical applications. These deficiencies have their roots in the use of inadequate probabilistic models and insufficient understanding of modern concepts of risk analysis, as have been revealed in some recent large scale studies. These deficiencies result in the lack of ability of a correct treatment of dependencies between physical parameters and finally, in an incorrect treatment of uncertainties. As a consequence, results of PSHA studies have been found to be unrealistic in comparison with empirical information from the real world. The attempt to compensate these problems by a systematic use of expert elicitation has, so far, not resulted in any improvement of the situation. It is also shown that scenario-earthquakes developed by disaggregation from the results of a traditional PSHA may not be conservative with respect to energy conservation and should not be used for the design of critical infrastructures without validation. Because the assessment of technical as well as of financial risks associated with potential damages of earthquakes need a risk analysis, current method is based on a probabilistic approach with its unsolved deficiencies.
Traditional deterministic or scenario-based seismic hazard analysis methods provide a reliable and in general robust design basis for applications such as the design of critical infrastructures, especially with systematic sensitivity analyses based on validated phenomenological models. Deterministic seismic hazard analysis incorporates uncertainties in the safety factors. These factors are derived from experience as well as from expert judgment. Deterministic methods associated with high safety factors may lead to too conservative results, especially if applied for generally short-lived civil structures. Scenarios used in deterministic seismic hazard analysis have a clear physical basis. They are related to seismic sources discovered by geological, geomorphologic, geodetic and seismological investigations or derived from historical references. Scenario-based methods can be expanded for risk analysis applications with an extended data analysis providing the frequency of seismic events. Such an extension provides a better informed risk model that is suitable for risk-informed decision making. 相似文献