二维物性界面深度重磁反演的一种非线性迭代解法──样条函数法

提出一种重磁导演非线性反演的直接解 ,它是基于迭代法求解一个非线性各分方程。当物性界面起伏分布△ｈ满足｜△ｈ｜〈√２－１）ｈ时,积分的补积函数可展成△ｈ的幂级数,考虑△ｈ高次项的影响,应用简单迭代法可将问题化成相应的线性积分方程,并可用Ｂ样条函数求解。在不同磁化方向的△Ｔ和Ｚα异常上和变密度界面引起的重力异常上实现了模拟反演。精度显著高于线性直接解。在南海东沙群岛地区进行了莫霍面的反演计算,效果良     

基于非线性误差模型的参数估计

测量平差与数据处理所涉及到的误差模型大多为非线性模型。对非线性模型作线性化处理必然导致信息的损失和牲的改变。因此,在非线性模型空间内进行测量平差与数据处理是学科发展的必然趋势。在对非线性函数误差模型与非线性随机误差模型作出假定的基础上,本文着重讨论了关系型函数模型与相关型函数模型中参数的估计准则与解算方法。     

Dynamic properties of the Quaternary sedimentary rocks and their influence on seismic site effects. Case study in Bucharest City,Romania

Bucharest is one of the cities most affected by earthquakes in Europe. Situated at 150–170 km distance from Vrancea epicentral zone, Bucharest had suffered many damages due to high energy Vrancea intermediate-depth earthquakes. For example, the 4 March 1977 event produced the collapse of 32 buildings with 8–12 levels, while more than 150 old buildings with 6–9 levels were seriously damaged. The studies done after this earthquake had shown the importance of the surface geological structure upon ground motion parameters. New seismic measurements are performed in Bucharest area aiming at defining better elastic and dynamic properties of the shallow sedimentary rocks. Down-hole seismic measurements were performed in a number of 10 cased boreholes drilled in the Bucharest City area. Processing and interpretation of the data lead to the conclusion that shallow sedimentary rocks can be considered weak in the area, down to 150–200 m depth. Seismic wave velocity values and bulk density values presented in the paper associated with local geology are useful primary data in the seismic microzonation of Bucharest City. They are used as 1D models to derive transfer functions and response spectra for the stack of sedimentary rocks in several parts of Bucharest area, leading to a better knowledge of the local site amplification and associated frequency spectra. In a recent study the H/V spectral ratio using Nakamura’s method was applied on the seismic noise measurements in 22 sites in Bucharest City in order to derive the fundamental period associated with these sites. The values confirm the previous results, showing a dominant resonance in the period range of 1.25–1.75 s. The fundamental periods obtained with Nakamura’s method are in good agreement with those computed on the basis of geological and geotechnical data in boreholes, which show an increase of the fundamental period in the Bucharest area from south to north, in the same direction as the increase of the thickness of the Quaternary deposits above the Fratesti layer which is considered the bedrock in the area.     

A hypoplastic model for site response analysis

Site response analyses must take into account the nonlinear behavior of soils. This is typically achieved using an equivalent linear approach or using numerical analyses with an appropriate constitutive model. In this work a family of hypoplastic models is proposed for use in site response analyses. These nonlinear models use a rate-type tensorial equation and are capable of reproducing plastic deformation of soils for cyclic loading under both drained and undrained conditions. A methodology for the calibration of hypoplastic parameter for dynamic loading is proposed. The hypoplastic constitutive models are implemented in a finite element code and the site response of the Lotung downhole array site is used to validate the use of hypoplastic models for site response analysis. The hypoplastic models reproduce accurately site response at the Lotung site. The advantages and disadvantages of the hypoplastic models compared to other models are discussed.     

Wavelet approximation of earthquake strong ground motion-goodness of fit for a database in terms of predicting nonlinear structural response

Reduced dimensionality representation of strong ground motion records as a superposition of a relatively small number of pulses is studied. Such representation is obtained by the expansion of velocity in orthogonal wavelet series using the Fast Wavelet Transform, and approximation by only the largest energy terms in the series. The Coiflet 5 wavelet family is used, which is orthogonal, smooth and nearly symmetric. The goodness of the approximation is examined for the EQUINFOS for USA Part I database, as representative of a large variety of strong motion records (it consists of 494 three-component records from 106 earthquakes recorded in the western US between 1933 and 1984). The goodness of fit is measured in terms of closeness of predicting several input and output characteristics of a nonlinear oscillator representing a structure: (i) energy of the input ground motion (proportional to integral of velocity squared), (ii) the peak input power, and (iii) the time of collapse of a bi-linear oscillator (considering also collapse due to dynamic instability). The results show very high degree of correlation of these characteristics as estimated from the actual record and from its approximations, even for small number of pulses (relative to the number that would represent the ground velocity exactly). Such reduced representation of strong ground motion is useful for extracting such pulses from strong motion records to study their nature, and for development of new algorithms for the synthesis of artificial earthquake strong motion records.     

Near-source ground motion attenuation relationship for PGA and PSA of the vertical and horizontal components

In this paper, empirical ground-motion models for the vertical and average horizontal components of peak ground-motion and acceleration response spectra from shallow crustal earthquakes are derived using near-source database. These attenuation relationships were derived using a worldwide dataset consisted of corrected and processed accelerograms of 678 strong-motion records recorded with 60 km of the rupture plane of earthquakes between M_w 5.2 and 7.9. Ground motion models are functions of earthquake mechanism, distance from source to site, local average shear wave velocity, nonlinear soil response, sediment depth, depth-to-top of the rupture, hanging wall effects and faulting mechanism.     

Processing Italian damage data to derive typological fragility curves

Typological fragility curves have been derived from post-earthquake survey data on building damage, collected in the areas affected by the most relevant Italian earthquakes of the last three decades. A complex and time consuming codification and reinterpretation work has been done on a set of about 150,000 survey building records, in order to define empirical damage probability matrices for several building typologies, characteristic of the Italian building stock. The obtained data have then been processed by advanced nonlinear regression methods in order to derive typological fragility curves. These curves, organised in five damage levels, provide useful information both for relative comparisons among typologies and for seismic risk analyses at different scales. By combining hazard definitions, fragility curves and inventory data, complete earthquake risk scenario studies can be performed, but even the single convolution of hazard and fragility allows to obtain typological risk maps, both for single damage state definitions and for concise average loss parameters. The very high potential of these results is shown by some applications reported in the paper.     

Long period microtremors, microseisms and earthquake damage: Northridge, CA, earthquake of 17 January 1994

Three studies of site amplification factors, based on the recorded aftershocks, and one study based on strong motion data, are compared one with another and with the observed distribution of damage from the Northridge, CA, earthquake of 17 January 1994 (M_L=6.4). In the epicentral area, when the peak ground velocities are larger than v_m≈15 cm/s, nonlinear response of soil begins to distort the amplification factors determined from small amplitude (linear) wave motion. Moving into the area of near-field and strong ground motion (v_m>30 cm/s), the site response becomes progressively more affected by the nonlinear soil response. Based on the published results, it is concluded that site amplification factors determined from small amplitude waves (aftershocks, small earthquakes, coda waves) and their transfer-function representation may be useful for small and distant earthquake motions, where soils and structures respond to earthquake waves in a linear manner. However in San Fernando Valley, during the Northridge earthquake, the observed distribution of damage did not correlate with site amplification determined from spectra of recorded weak motions. Mapping geographical distribution of site amplification using other than very strong motion data, therefore appears to be of little use for seismic hazard analyses.     

高阶非线性海浪波面斜率的联合概率统计分布

基于非线笥随机海洋模型,对各向异性波面斜率统计分布进行了理论研究,结果表明,在高阶近似下,波面斜率统计分布为截断的Ｇｒａｍ－Ｃｈａｒｌｉｅｒ级数。如果忽略波－波相互作用的非线性影响,则Ｃｒａｍ－Ｃｈａｒｌｉｅｒ级数分布蜕化为正态分布。