Influence of source region properties on scaling relations forM<0 events

Excavation induced seismic events with moment magnitudesM<0 are examined in an attempt to determine the role geology, excavation geometry, and stress have on scaling relations. Correlations are established based on accurate measurements of excavation geometry and methodology, stress regime, rock mass structure, local tectonics, and seismic locations. Scaling relations incorporated seismic moments and source radii obtained by spectral analysis, accounting for source, propagation, and site effects, and using Madariaga's dynamic circular fault model. Observations suggest that the interaction of stresses with pre-existing fractures, fracture complexity and depth of events are the main factors influencing source characteristics and scaling behaviour. Self-similar relationships were found for events at similar depths or for weakly structured rock masses with reduced clamping stresses, whereas a non-similar behaviour was found for events with increasing depth or for heavily fractured zones under stress confinement. Additionally, the scaling behaviour for combined data sets tended to mask the non-similar trends. Overall, depth and fracture complexity, initially thought as second order effects, appear to significantly influence source characteristics of seismic events withM<0 and consequently favour a non-similar earthquake generation process.     

Is the ocean floor a fractal?

The topographic structure of the ocean bottom is investigated at different scales of resolution to answer the question: Can the seafloor be described as a fractal process? Methods from geostatistics, the theory of regionalized variables, are used to analyze the spatial structure of the ocean floor at different scales of resolution. The key to the analysis is the variogram criterion: Self-similarity of a stochastic process implies self-similarity of its variogram. The criterion is derived and proved here: it also is valid for special cases of self-affinity (in a sense adequate for topography). It has been proposed that seafloor topography can be simulated as a fractal (an object of Hausdorff dimension strictly larger than its topological dimension), having scaling properties (self-similarity or self-affinity). The objective of this study is to compare the implications of these concepts with observations of the seafloor. The analyses are based on SEABEAM bathymetric data from the East Pacific Rise at 13°N/104°W and at 9°N/104°W and use tracks that run both across the ridge crest and along the ridge flank. In the geostatistical evaluation, the data are considered as a stochastic process. The spatial continuity of this process is described by variograms that are calculated for different scales and directions. Applications of the variogram criterion to scale-dependent variogram models yields the following results: Although the seafloor may be a fractal in the sense of the definition involving the Hausdorff dimension, it is not self-similar, nor self-affine (in the given sense). Mathematical models of scale-dependent spatial structures are presented, and their relationship to geologic processes such as ridge evolution, crust formation, and sedimentation is discussed.     

Moment tensors of earthquakes in and near the Tibetan Plateau and their scaling law

Moment tensors of eleven major earthquakes in the Tibetan Plateau and its surrounding region from 1966 to 1980 are estimated by generalized inverse technique. The seismic source time function and focal depth are immediately determined in the inversion. The results show that moment tensors of some events differ significantly from double couple, the deviation increases with decreasing plunge angle of null axis. All these events occurred in the upper crust, much shallower than those reported so far, for example, in NEIS Bulletin. Focal mechanism solution obtained from the moment tensors are consistent with the idea that the Indian plate collides northwards with the Eurasian plate and that an eastward spreading exists in the crust of the Tibetan Plateau. The stress drops for earthquakes of intraplate are systematically higher than those of earthquakes in suture zone. The source process duration becomes longer with seismic moment, but for the same seismic moment, the process duration for earthquakes in suture zone is about 1.4 times of those for intraplate event, these results suggest that the earthquakes near suture zone may be of a special characteristics in source process differently from those in intraplate. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 423 – 434, 1992.     

Research on scale effect of histogram

To describe the spatial relationship among the earth objects compactly, in this paper, we raised the concept of histo-variogram based on the analysis of the characteristics of other spatial analyzing methods such as variogram, information entropy. And we also raised a new spatial analysis method of histogram decomposition based on the definition of standing pixel and contour pixel. At the end of this paper, we demonstrated the characteristics of histo-variogram by two experiments, one for spatial analysis, the other for image fusion.     

Can Damage Mechanics Explain Temporal Scaling Laws in Brittle Fracture and Seismicity?

Time delays associated with processes leading to a failure or stress relaxation in materials and earthquakes are studied in terms of continuum damage mechanics. Damage mechanics is a quasi-empirical approach that describes inelastic irreversible phenomena in the deformation of solids. When a rock sample is loaded, there is generally a time delay before the rock fails. This period is characterized by the occurrence and coalescence of microcracks which radiate acoustic signals of broad amplitudes. These acoustic emission events have been shown to exhibit power-law scaling as they increase in intensity prior to a rupture. In case of seismogenic processes in the Earth's brittle crust, all earthquakes are followed by an aftershock sequence. A universal feature of aftershocks is that their rate decays in time according to the modified Omori's law, a power-law decay. In this paper a model of continuum damage mechanics in which damage (microcracking) starts to develop when the applied stress exceeds a prescribed yield stress (a material parameter) is introduced to explain both laboratory experiments and systematic temporal variations in seismicity.     

Differences Between Mode I and Mode II Crack Propagation

Although mode I and mode II crack propagation show many similarities, in particular when analysed by linear elastic fracture mechanics, they differ significantly in the micro-structural behaviour. These differences, which are clearly noticeable in the fracture surface morphology, lead to fundamental differences in the macroscopic behaviour. Thus, mode II crack expansion under remote loading, appears to obey micro-structural scaling laws, implying that the dimensions of the process region stay essentially constant during crack expansion, rather than increasing with crack length. Therefore, expanding mode II cracks can almost reach the Rayleigh velocity, and actually also intersonic velocities. An expanding mode I crack, on the other hand, seems to obey continuum scaling laws, implying that the dimensions of the process region increase in proportion to crack length, leading to self-similar crack expansion at a velocity significantly below the Rayleigh speed and dependent on the remote load.     

Spectral scaling in Mars topography: effect of craters

Extensive computer simulations aimed at testing a hypothesis that impact craters may explain the scaling behaviour of surface spectra are presented. The simulations show that indeed crater effects alone may explain the spectral scaling of Mars’ topography revealed from MOLA data. The range of the scaling exponents obtained for a wide range of simulation parameters does not exceed the limits observed for Mars. The simulations suggest that the shape of large craters is the key factor leading to the two scaling ranges in the surface spectra. Particular values of the scaling exponents may additionally depend on the depth-diameter relationship and the crater size distribution.     

中国冬季气温的集合典型相关分析和预报

以欧亚大陆地面温度、北半球500 hPa高度、热带印度洋SST(sea surface temperature)以及北太平洋SST为预报因子,通过典型相关分析(canonical correlation analysis,简称CCA)建立预报关系,然后用集合典型相关分析预报(ensemble canonical correlation prediction,简称ECC)方法预报中国冬季气温,并分析预报技巧及进行独立样本检验.结果表明,不同的预报因子对各个地区有不同的预报技巧,以欧亚大陆地面温度为预报因子预报技巧较高,而ECC模式对中国冬季气温有更好的预报能力,预报技巧高于任何一个单因子场的CCA预报;采用回归法的集合平均比简单的等权集合平均预报技巧更稳定.     

多维标度法在矿产预测中的应用

在矿产预测中常涉及一些定性变量,对这些变量的分析和应用,必须将定性描述的地质特征转化为用数值表示的变量,这就需要处理此问题的方法——多维标度法。笔者介绍了计量性的Ｔｏｒｇｅｒｓｏｎ法、准计量性的林知已夫数量化理论和非计量性多维标度法,并列举了其在矿产预测中的应用实例。