Probability distribution of the Murty‐Loomis tsunami magnitude

Abstract

In 1980, Murty and Loomis proposed a new, objective tsunami magnitude scale based on total tsunami energy. A list of 178 tsunamigenic earthquakes during the period 1815 to 1974 was given along with estimated tsunami magnitudes. In this study, we derived the probability distribution function of tsunami magnitudes based on the assumptions that (1) the occurrences of tsunamigenic earthquakes are a Poisson process, and (2) tsunami energy is a polynomial function of tsunami recurrence time. Using the data given by Murty and Loomis, the parameters of the distribution function are estimated. Comparison with the data shows that the derived distribution is a good representation of the distribution of the Murty‐Loomis tsunami magnitude.     

Regionalization of unit hydrograph parameters: 1. Comparison of regression analysis techniques

Hydrologic regionalization is a useful tool that allows for the transfer of hydrological information from gaged sites to ungaged sites. This study developed regional regression equations that relate the two parameters in Nash's IUH model to the basin characteristics for 42 major watersheds in Taiwan. In the process of developing the regional equations, different regression procedures including the conventional univariate regression, multivariate regression, and seemingly unrelated regression were used. Multivariate regression and seeming unrelated regression were applied because there exists a rather strong correlation between the Nash's IUH parameters. Furthermore, a validation study was conducted to examine the predictability of regional equations derived by different regression procedures. The study indicates that hydrologic regionalization involving several dependent variables should consider their correlations in the process of establishing the regional equations. The consideration of such correlation will enhance the predictability of resulting regional equations as compared with the ones from the conventional univariate regression procedure.     

On response of structures to random waves

The solution to the non-linear, stochastic, ordinary differential equation governing the dynamic response of offshore structures to random waves, hitherto achieved by the statistical equivalent linearization method, is approached in a different manner. It is shown that the correlation function of the response is governed by a non-linear integral equation which can be solved successively. To the first order of approximation, the solution coincides with that of the statistical equivalent linearization method. This equation is solved up to the second order.     

Determination of unit hydrographs by multiple storm analysis

This paper discusses the derivation of a unit hydrograph by multiple storm analysis using least squares methods. Variations of least squares method was generalized using the framework of weighted ridge analysis. The paper also shows two theorems to support using multi-storm analysis to derive UH. In addition, an issue was addressed on the scaling effect in the conventional multi-storm analysis which could create potential bias toward large storms in deriving a multi-storm UH. For that, a simple scaling procedure was proposed to reduce such potential bias problem. Numerical investigations were conducted to examine the performance of the scaling procedure by comparing with the conventional multi-storm analysis (without scaling) and the HEC-1 weighing procedures. Based on various performance criteria using a total of 39 storms from three watersheds, the proposed scaling procedure was found to produce a quite desirable UH.     

Application of extended Kalman filter to back analysis of the natural stress state accounting for measuring uncertainties

In this work, we present a numerical procedure for determining the nature stress state in the rock mass around a tunnel. A finite element method is applied for analyzing the direct problems of tunneling during the back analysis of parameter estimation, in which a no‐tension elastic–plastic model is used to simulate the elastic–tensile and elastic–plastic‐tensile failure states which often occur in the cases of underground excavation in heavily jointed rock masses. By considering the natural stress state as random parameters of the tunneling system, the Kalman filter method is employed for feedback analysis to modify the parameter values in a statistical context, which uses the prior information in the process of estimation and employs a set of displacements obtained from field measurements. To verify the effectiveness of the proposed method of inverse analysis, the developed numerical procedure is applied to a synthetic example of deep tunnels in yielding rock masses. The relative importance of the a priori and updating information is investigated, as is the importance of their uncertainty. The results show great potential of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Extensional Structures in the Ophiolites from Cuba and China: New Constraints to Slowly‐Spreading Ancient Oceanic Lithosphere

A group of low‐angle normal faults developed in banded gabbro of Moa Ophiolite, Cuba. The dark gabbro was cut into puddings by several normal faults, while light gabbro was just swelling in layer thickness. In Hongliuhe ophiolite at eastern segment of South Tien Shan Suture Zone in China, the extensional deformation concentrates on fine cumulus gabbro which is typically mylonitized. Abundant structural features were discovered in HLH ophiolite such as S‐C foliation, C’ foliation, extensional crenulation cleavage, small toughness normal fault, low‐angle normal faults and high‐angle normal faults. According to the above tectonic phenomenon from the ophiolite belts in Cuba and China, we will get the conclusion: the maximum principal compressive stress (b1) is vertical to cumulus bedding, and the maximum tensile stress (b3) is paralleling to cumulus bedding. Considering of the above evidence, the extensional tectonic event should developed at mid‐ocean ridge. Due to seafloor spreading, the maximum tensile stress is paralleling to cumulus layer, and extensional tectonic is kept in cumulus gabbro. In this way, normal faults developed in dark gabbro, while brittle‐ductile extensional developed in light gabbro. A large number of domes, folds paralleling to ocean ridge and detachment faults represented by low angle normal fault were discovered near ocean ridge in Indian Ocean and Atlantic Ocean. In this way, materials from deep oceanic lithosphere (e.g. gabbro, mantle peridotite) outcrop at the crust surface of ocean basin. The above evidences from China and Cuba are consistent with extensional tectonic and metamorphic core complex from slowly and super‐slowly spreading Indian Ocean and Atlantic Oceanic lithosphere based on ODP. Therefore, extensional deformation in the ophiolite belt is of significant meaning for clarifying the formation process and mechanism of ancient oceanic basin.     

Occurrence of Alaskan-type mafic-ultramafic intrusions in the North Qilian Mountains, northwest China: Evidence of Cambrian arc magmatism on the Qilian Block

Field relationships, mineralogy and petrology, whole‐rock chemistry, and age of the Zhamashi mafic–ultramafic intrusion in the North Qilian Mountains, northwest China, have been studied in the present work. The Zhamashi intrusive body consists of ultramafic, gabbroic, and dioritic rocks in a crudely concentrically zoned structure. The ultramafic rocks are layered cumulates with rock types varying continuously from dunite through wehrlite and olivine clinopyroxenite to clinopyroxenite. The gabbroic and dioritic rocks are also layered or massive cumulates with rock types varying continuously from noritic gabbro through hornblende gabbro to diorite. The ultramafic and adjoining gabbroic rocks are discontinuous in lithology and discordant in structure across the interface. The interface is steep, sharp, and fractured. Contact metamorphic zones are well developed between the Zhamashi intrusive body and the country rock. The concentrically zoned structure of the intrusive body and the intrusion into the continental crust are the two main pieces of evidence for considering that the Zhamashi intrusion is Alaskan‐type. The mineral chemistry of the chromian spinels (Cr‐spinels) and clinopyroxenes, and the variation trend of the whole‐rock compositional plot in the (Na₂O + K₂O)–FeO–MgO (AFM) diagram are also supportive of this consideration. The age of the Zhamashi intrusive body, determined with sensitive high mass‐resolution ion microprobe on the zircon grains, is 513.0 ± 4.5 Ma. Parental magma of the Zhamashi intrusion is compositionally close to the primitive magma produced by partial melting of the mantle peridotite. It was differentiated by fractional crystallization at low total pressure and under H₂O‐rich conditions in an arc environment to form all the major rock types. The concentrically zoned structure of the Zhamashi intrusive body was constructed in two stages: formation of a stratiform‐type layered sequence, followed by diapiric re‐emplacement. The occurrence of the Alaskan‐type intrusion suggests an active continental margin and Cambrian arc magmatism for the northern margin of the Qilian Block.