Eigendecomposition of the two-point correlation tensor for optimal characterization of mantle convection

The two-point correlation tensor provides complete information on mantle convection accurate up to second-order statistics. Unfortunately, the two-point spatial correlation tensor is in general a data-intensive quantity. In the case of mantle convection, a simplified representation of the two-point spatial correlation tensor can be obtained by using spherical symmetry. The two-point correlation can be expressed in terms of a planar correlation tensor, which reduces the correlation's dependence to only three independent variables: the radial locations of the two points and their angular separation. The eigendecomposition of the planar correlation tensor provides a rational methodology for further representing the second-order statistics contained within the two-point correlation in a compact manner. As an illustration, results on the planar correlation are presented for the thermal anomaly obtained from the tomographic model of Su, Woodward & Dziewonski (1994 ) and the corresponding velocity field obtained from a simple constant-viscosity convection model Zhang & Christensen 1993 ). The first 10 most energetic eigensolutions of the planar correlation, which constitute an almost three orders of magnitude reduction in the data, capture the two-point correlation to 97 per cent accuracy. Furthermore, the energetic eigenfunctions efficiently characterize the thermal and flow structures of the mantle. The signature of the transition zone is clearly evident in the most energetic temperature eigenfunction, which clearly shows a reversal of thermal fluctuations at a depth of around 830  km. In addition, a local peak in the thermal fluctuations can be observed around a depth of 600  km. In contrast, due to the simplicity of the convection model employed, the velocity eigenfunctions exhibit a simple cellular structure that extends over the entire depth of the mantle and do not exhibit transition-zone signatures.     

Linear programming approach to moment tensor inversion of earthquake sources and some tests on the three-dimensional structure of the upper mantle

Summary. A new method of moment tensor inversion is developed, which combines surface wave data and P -wave first motion data in a linear programming approach. Once surface wave spectra and first motion data are given, the method automatically obtains the solution that satisfies first motion data and minimizes the L1 norm of the surface wave spectra. We show the results of eight events in which the method works and is stable even for shallow events. We also show one event in which surface wave data and P -wave first motion data seem to be incompatible. In such cases, our method does not converge or converges to a solution which has a large minor (second) double couple component. It is an advantage that the method can determine the compatibility of two data sets without trial and error.
Laterally heterogeneous phase velocity corrections are used to obtain spectra at the source. The method is also applied to invert moment tensors of eight events in two recent three-dimensional (3-D) upper mantle structures. In both 3-D models, variances of spectra are smaller than those in a laterally homogeneous model at 256 s. Statistical tests show that those reductions are significant at a high confidence level for five events out of eight examined. For three events, we examined those reductions at shorter periods, 197 and 151 s. The reduction of variances is comparable to the results at 256 s and is again statistically significant at a high confidence level. Orientation of fault planes does not change very much by incorporation of lateral variations of phase velocity or by doing inversions at different periods. This is mainly because of the constraints from P -wave first motion data. Scatter of phase spectra at shorter periods, especially at 151 s, is great and suggests that surface wave ray paths deviate from great circle paths substantially and these effects cannot be ignored.     

北碚与重庆主城核心区的空间联系——基于交通和居民出行调查数据的分析

城镇体系中的空间联系研究可以分为大尺度的网络联系和小尺度的地域联系两种。以国内外研究相对较少的小尺度范围的城市空间联系为研究对象,选择处于快速城镇化进程中的重庆主城核心区与作为其卫星城之一的北碚为案例地,借用数据量需求较大、结论更符合实际的经验主义研究方法,系统分析了北碚区与重庆主城核心区间的空间联系。研究显示:北碚区与重庆主城核心区空间联系发展历程经历了4 个阶段,联系日益紧密;城市功能方面,北碚区已经从独立城市成为重庆主城核心区重要的功能组团,有别于传统的"卧城"概念;空间联系强度方面呈现出明显的距离衰减特征,并与地区的社会因素、经济发展水平等因素有密切关系;通过对二者空间联系解释的框架分析,表明城市政府的政策和规划在两地空间联系发展中起到主导作用。