Statistical model on the surface elevation of waves with breaking

In the surface wind drift layer with constant momentum flux, two sets of the consistent surface eleva- tion expressions with breaking and occurrence conditions for breaking are deduced from the first in- tegrals of the energy and vortex variations and the kinetic and mathematic breaking criterions, then the expression of the surface elevation with wave breaking is established by using the Heaviside function. On the basis of the form of the sea surface elevation with wave breaking and the understanding of small slope sea waves, a triple composite function of real sea waves is presented including the func- tions for the breaking, weak-nonlinear and basic waves. The expression of the triple composite func- tion and the normal distribution of basic waves are the expected theoretical model for surface elevation statistics.     

Comparison of two different solutions to Molodensky’s G1 term

The main purpose of this paper is comparison of two different approaches of solution to the Simple Molodensky’s Problem, the Molodensky’s Approach and the Analytical Continuation Approach, based on numerical computation. Although these approaches have been described theoretically by several authors, e.g. Molodensky et al. (1960), Heiskanen and Moritz (1967), Vaníček (1974), Moritz (1980) and Holota (1991, unpublished results) and theoretical proof of equivalence was given by Heiskanen and Moritz (1967), Moritz (1971), Ecker (1971) and Pellinen (1972, unpublished results), only very few practical experiences about the differences between particular solutions and computational efficiency exist. In this paper we compare the above two mentioned approaches in terms of the G₁-effect on quasigeoid. Both quasigeoid solutions are tested by the independent GPS/levelling approach and are also compared with the previous quasigeoid model of Slovakia where the G₁-term has been approximated using the classical terrain correction. The effect of the G₂-term is also numerically estimated, revealing that it might be significant for the precise quasigeoid determination. Some practical comments and recommendations are given at the end of the paper.     

Optimal design of structures for earthquake loads by a hybrid RBF-BPSO method

The optimal seismic design of structures requires that time history analyses （THA） be carried out repeatedly. This makes the optimal design process inefficient, in particular, if an evolutionary algorithm is used. To reduce the overall time required for structural optimization, two artificial intelligence strategies are employed. In the first strategy, radial basis function （RBF） neural networks are used to predict the time history responses of structures in the optimization flow. In the second strategy, a binary particle swarm optimization （BPSO） is used to find the optimum design. Combining the RBF and BPSO, a hybrid RBF-BPSO optimization method is proposed in this paper, which achieves fast optimization with high computational performance. Two examples are presented and compared to determine the optimal weight of structures under earthquake loadings using both exact and approximate analyses. The numerical results demonstrate the computational advantages and effectiveness of the proposed hybrid RBF-BPSO optimization method for the seismic design of structures.     

Comparison of source parameters estimated in the frequency and time domains for seismic events at the Rudna copper mine,Poland

Source parameters estimated in the frequency domain for 100 selected seismic events from the Rudna copper mine, with moment magnitude ranging from 1.4 to 3.6, were collected to study their scaling relations and to compare them with the parameters estimated in the time domain. The apparent stress and static stress drop, corrected for the limited bandwidth recording, increase slightly in a similar manner with increasing seismic moment. The ratio of apparent stress to static stress drop, a measure of radiation efficiency, is practically constant and its mean value is close to 0.1. For 37 seismic events, with moment magnitude between 1.9 and 3.4, source parameters were estimated in the time domain from relative source time functions, that displayed unilateral rupture propagation, and their rupture velocity could be estimated. It ranges from 0.23 to 0.80 of shear wave velocity and is almost independent of seismic moment. The fault length, estimated from the average source pulse width and rupture velocity, is clearly dependent on seismic moment and is smaller than the source radius estimated from the corner frequency on the average by about 25 percent. There is no correlation between the values of static stress drop estimated in the frequency and time domains, but the time domain stress drop is in general similar to that estimated in the frequency domain. The apparent stress increases with increasing rupture velocity, and the ratio of apparent stress to static stress drop seems also to depend on rupture velocity.     

基于华北区域地震活动性分布的地震危险性评价模型

采用了分布式地震活动性模型. 该模型无需潜在震源区划分,同时简化了地震危险性概率分析方法. 根据破坏性地震目录建立了3个地震活动性模型,利用高斯光滑函数获得了华北区域内的a值分布特征,使用3种典型的衰减模型,分别计算了50年内超越概率10%, 5%和2%的地震动峰值加速度分布. 其分析结果显示了峰值加速度分布特征与我国第四代区划图大体一致,特定地震活动区（太原、 石家庄等地区）的峰值加速度略高于第四代区划图的结果,而这种峰值加速度分布特征与该地区较高的地震活动性特征是一致的. 概率危险性曲线结果表明,唐山、太原和北京等地区的潜在地震危险性比华北区域内其它城市高.      

Axial poloidal electromagnetic core-mantle coupling torque: A re-examination for different conductivity and satellite supported geomagnetic field models

We investigate the temporal behaviour of the axial component of the electromagnetic core-mantle coupling torque that is associated with the poloidal part of the geomagnetic field observable at the Earth surface. For its computation, we use different models of the geomagnetic field, expanded into spherical harmonics (Wardinski and Holme, 2006; Sabaka et al., 2004), and the mantle conductivity. The geomagnetic field, which we have to know at the core-mantle boundary for the associated computations, will be inferred from the field at the Earth surface by the non-harmonic field continuation through a conducting mantle shell. The aims of this investigation are (i) to check how sensitive is the computation of the torque with respect to the different geomagnetic field models, (ii) to check its dependence on the spherical harmonic degree n, and (iii) to determine the difference between the mechanical torque derived from the observed length-of-day variations (atmospheric influence subtracted) and the poloidal electromagnetic torque in dependence on the assumed conductivity. To use the non-harmonic field continuation for the torque calculation and to obtain an insight into the influence of the different geomagnetic field models on the EM torques are the major aspects of this paper. grm@gfz-potsdam.de     

Integral inversion of SST data of type GRACE

Satellite missions CHAMP and GRACE dedicated to global mapping of the Earth’s gravity field yield accurate satellite-to-satellite tracking (SST) data used for recovery of global geopotential models usually in a form of a finite set of Stokes’s coefficients. The US-German Gravity Recovery And Climate Experiment (GRACE) yields SST data in both the high-low and low-low mode. Observed satellite positions and changes in the intersatellite range can be inverted through the Newtonian equation of motion into values of the unknown geopotential. The geopotential is usually approximated in observation equations by a truncated harmonic series with unknown coefficients. An alternative approach based on integral inversion of the SST data of type GRACE into discrete values of the geopotential at a geocentric sphere is discussed in this article. In this approach, observation equations have a form of Green’s surface integrals with scalar-valued integral kernels. Despite their higher complexity, the kernel functions exhibit features typical for other integral kernels used in geodesy for inversion of gravity field data. The two approaches are discussed and compared based on their relative advantages and intended applications. The combination of heterogeneous gravity data through integral equations is also outlined in the article. panovak@kma.zcu.cz     

Shear waves at a corrugated interface between anisotropic elastic and visco-elastic solid half-spaces

Rayleigh’s method of approximation is employed to find out the reflection and transmission coefficients due to an incident plane SH wave at a corrugated interface between a laterally and vertically inhomogeneous anisotropic elastic solid half-space and a laterally and vertically inhomogeneous isotropic visco-elastic solid half-space. The lateral and vertical inhomogeneities are described by the exponential variations of elastic parameters. The formulae of reflection and transmission coefficients are derived in closed form for the first-order approximation of the corrugation. The effects of the corrugation of the interface, the inhomogeneity, the anisotropy, the visco-elasticity and the frequency of the incident wave on these coefficients are studied analytically and numerically for a specific model containing a periodic interface. The results of earlier workers have been reduced as particular cases from the present formulation.     

Stochastic modelling of soil moisture dynamics in a grassland of Qilian Mountain at point scale

Stochastic modeling of soil moisture dynamics is crucial to the quantitative understanding of plant responses to water stresses,hydrological control of nutrient cycling processes,water competition among plants,and some other ecological dynamics,and thus has become a hotspot in ecohydrology at present.In this paper,we based on the continuously monitored data of soil moisture during 2002―2005 and daily precipitation date of 1992―2006,and tried to make a probabilistic analysis of soil moisture dynamics at point scale in a grassland of Qilian Mountain by integrating the stochastic model improved by Laio and the Monte Carlo method.The results show that the inter-annual variations for the soil moisture patterns at different depths are very significant,and that the coefficient of variance(CV) of surface soil moisture(20 cm) is almost continually kept at about 0.23 whether in the rich or poor rainy years.Interestingly,it has been found that the maximal CV of soil moisture has not always appeared at the surface layer.Comparison of the analytically derived soil moisture probability density function(PDF) with the statistical distribution of the observed soil moisture data suggests that the stochastic model can reasonably describe and predict the soil moisture dynamics of the grassland in Qilian Mountain at point scale.By extracting the statistical information of the historical precipitation data in 1994―2006,and inputting them into the stochastic model,we analytically derived the long-term soil moisture PDF without considering the inter-annual climate fluctuations,and then numerically derived the one when considering the inter-annual fluctuation effects in combination with a Monte-Carlo procedure.It was found that,though the peak position of the probability density distribution significantly moved towards drought when considering the disturbance forces,and its width was narrowed,accordingly its peak value was increased,no significant bimodality was observed in the soil moisture dynamics under the given intensity of random fluctuation disturbance.     

Spheroidal oscillations of the Earth stimulated by the Sumatra-Andaman earthquake with CDSN data

The 0S2~0S54 spheroidal modes of Earth’s free oscillations, triggered by the great Sumatra-Andaman earthquake of 26 December 2004 are retrieved from VHZ data recorded by seven upgraded stations of China Digital Seismograph Network (CDSN). We compare these spheroidal modes with theoretical free oscillation spectra calculated from the Preliminary Reference Earth Model (PREM) and find a coincidence between their periods. Spectral splitting phenomenon is observed obviously in 0S2, 0S3, 0S4, 2S1 and 1S2 free oscillation modes. What is most noticeable is that the oscillation mode 2S1 is reported for the second time (the first time by Rosat et al) without any data stacking. We simulated the split singlet of 0S2 mode on seven CDSN stations based on general focal mechanism and seismic moment of the earthquake. The result shows that seismic moment of the earthquake can reach 1023 N.m. We also find that the recording of Earth’s free oscillations carries abundant information of source mechanism and earthquake location, which is applicable to the detailed study of source rupture parameters.