基于数学建模的潜在地震破裂面源检测方法研究

大多数地震破裂面源检测方法都是通过简化地震震源,将地震震源表示成线源或者点源,无法有效描述地震带地震破裂面源产状和大小,不适用地震震级较大的情况下地震危险性检测。因此提出基于数学建模的潜在地震破裂面源检测方法,在地震震级较大时仍能检测出地震危险性概率。选取适宜的地震基岩水平峰值加速度衰减关系,分析地震震级、破裂长度、破裂宽度相互关系,确定地震引起的潜在地震破裂面源大小,计算给定地震动小于在场点处产生地震动的概率,将该概率同地震动加速度衰减关系结合,得到地震动年超越概率,分析地震危险性。经过实验检测发现,所提方法检测出的年超越概率与峰值加速度、最大震级有关,该概率能精准表示地震带地震破裂面源产状和大小,说明该方法检测地震危险性是合理的。     

The Gravity Module Assembly used in airborne full tensor gradiometry surveys

In airborne gravity gradiometry, the Gravity Module Assembly is an optional gravimeter unit that is mounted on the same stabilized platform as the Full Tensor Gradiometer. Direct measurements of the gravity field are needed from this device to constrain the long wavelengths when gradient data are integrated mathematically to form high-resolution gravity fields. The Gravity Module Assembly is, however, capable of providing independent gravity data with a specification approaching that expected from a dedicated airborne gravity system. Presented here is an error analysis of data from this instrument collected alongside the Full Tensor Gradiometer during an airborne survey. By having both gradiometry and gravity datasets, comparisons of the information content in these two types of measurement are made.     

二维位场在有源空间的解析延拓

位场的向下延拓对重、磁等位场资料的处理与解释具有重要意义,但现有的延拓方法在位场向下接近场源时会产生剧烈震荡,计算过程很不稳定,而且理论上都不能越过场源.本文在复数域里定义了一个具有位场和几何双重特性的新函数PFGR,提出了一套新的延拓方法,在理论上实现了位场在包含场源的下半空间里的解析延拓,经过模型试算验证,表明该方法可以延拓越过场源,准确确定场源奇点,计算过程稳定,对测量中的随机噪声也具有较好的抗干扰能力.     

Review paper: Exploration geophysics for intrusion‐hosted rare metals

Igneous intrusions, notably carbonatitic–alkalic intrusions, peralkaline intrusions, and pegmatites, represent significant sources of rare‐earth metals. Geophysical exploration for and of such intrusions has met with considerable success. Examples of the application of the gravity, magnetic, and radiometric methods in the search for rare metals are presented and described. Ground gravity surveys defining small positive gravity anomalies helped outline the shape and depth of the Nechalacho (formerly Lake) deposit within the Blatchford Lake alkaline complex, Northwest Territories, and of spodumene‐rich mineralization associated with the Tanco deposit, Manitoba, within the hosting Tanco pegmatite. Based on density considerations, the bastnaesite‐bearing main ore body within the Mountain Pass carbonatite, California, should produce a gravity high similar in amplitude to those associated with the Nechalacho and Tanco deposits. Gravity also has utility in modelling hosting carbonatite intrusions, such as the Mount Weld intrusion, Western Australia, and Elk Creek intrusion, Nebraska. The magnetic method is probably the most successful geophysical technique for locating carbonatitic–alkalic host intrusions, which are typically characterized by intense positive, circular to sub‐circular, crescentic, or annular anomalies. Intrusions found by this technique include the Mount Weld carbonatite and the Misery Lake alkali complex, Quebec. Two potential carbonatitic–alkalic intrusions are proposed in the Grenville Province of Eastern Quebec, where application of an automatic technique to locate circular magnetic anomalies identified several examples. Two in particular displayed strong similarities in magnetic pattern to anomalies accompanying known carbonatitic or alkalic intrusions hosting rare‐metal mineralization and are proposed to have a similar origin. Discovery of carbonatitic–alkalic hosts of rare metals has also been achieved by the radiometric method. The Thor Lake group of rare‐earth metal deposits, which includes the Nechalacho deposit, were found by follow‐up investigations of strong equivalent thorium and uranium peaks defined by an airborne survey. Prominent linear radiometric anomalies associated with glacial till in the Canadian Shield have provided vectors based on ice flow directions to source intrusions. The Allan Lake carbonatite in the Grenville Province of Ontario is one such intrusion found by this method. Although not discovered by its radiometric characteristics, the Strange Lake alkali intrusion on the Quebec–Labrador border is associated with prominent linear thorium and uranium anomalies extending at least 50 km down ice from the intrusion. Radiometric exploration of rare metals hosted by pegmatites is evaluated through examination of radiometric signatures of peraluminous pegmatitic granites in the area of the Tanco pegmatite.     

2.5D direct‐current resistivity forward modelling and inversion by finite‐element–infinite‐element coupled method

To reduce the numerical errors arising from the improper enforcement of the artificial boundary conditions on the distant surface that encloses the underground part of the subsurface, we present a finite‐element–infinite‐element coupled method to significantly reduce the computation time and memory cost in the 2.5D direct‐current resistivity inversion. We first present the boundary value problem of the secondary potential. Then, a new type of infinite element is analysed and applied to replace the conventionally used mixed boundary condition on the distant boundary. In the internal domain, a standard finite‐element method is used to derive the final system of linear equations. With a novel shape function for infinite elements at the subsurface boundary, the final system matrix is sparse, symmetric, and independent of source electrodes. Through lower upper decomposition, the multi‐pole potentials can be swiftly obtained by simple back‐substitutions. We embed the newly developed forward solution to the inversion procedure. To compute the sensitivity matrix, we adopt the efficient adjoint equation approach to further reduce the computation cost. Finally, several synthetic examples are tested to show the efficiency of inversion.     

位场各阶垂向导数换算的新正则化方法

位场垂向导数大量应用于位场数据处理与解释中.当前广泛采用的位场各阶垂向导数换算方法为基于Laplace方程并结合波数域和空间域方法的具有递推特性的ISVD(integrated second vertical derivative)算法.本文在位场垂向导数换算的正则化方法和径向平均功率谱的基础上,提出一种位场各阶垂向导数换算的新正则化方法.新正则化方法仅需通过分析位场径向平均功率谱来确定一个截止波数,即可稳定换算位场各阶垂向导数.理论模型和实测数据实验结果表明:(1)新正则化方法物理意义明确、计算简单,且各阶垂向导数换算的稳定性和精度明显优于ISVD算法;(2)在用新正则化方法求得各阶垂向导数的基础上,利用泰勒级数法可以获得大深度、高精度的位场向下延拓结果.     

地球形成和演化过程中的分异能计算方法研究

地球形成初期,构成地球的物质在组成上是大致均一的.目前地球的地核-地幔-地壳圈层结构,是由分异作用形成的.分异过程释放的能量称为分异能.Sorokhtin和Chilingarian等人从行星吸积的定义出发,导出了基于地球内部密度分布的势能计算公式,计算出的分异能大小为1.698×1031J.本文采用计算球体势能的思路,导出分异能计算的解析公式和数值计算公式,通过求取原始地球模型与均匀分层模型、PREM模型的势能差计算分异能.两种方法的计算结果分别为1.535×1031J和1.698×1031J.前者与Sorokhtin等的结果相近,后者与之相同.本文初步分析了方法间的异同以及造成结果偏差的主要原因.     

利用加强水平方向总水平导数对位场全张量数据进行边界识别

位场全张量梯度数据以其信息量大、含有更高频的信号成分,能更好地描述小的异常特征等优点在地球物理领域中得到广泛应用.边界检测是位场解释中不可缺少的任务,需要新的边界探测器来处理位场梯度张量数据.为了充分利用位场梯度张量数据的多信息成分,本文定义了方向总水平导数和加强方向总水平导数,并利用其定义新的边界检测器.为了能同时显示不同振幅大小异常的边界,本文对其进行了归一化处理.通过模型试验,证明了归一化方法能更加清晰准确地显示浅部和深部的地质体边界信息.最后将该边界检测方法用于加拿大圣乔治湾实际测得全张量重力梯度数据和中国朱日和地区的磁异常数据中,并得到了较好的边界检测结果.     

东亚夏季风降雨的可预报性研究

本文根据CMAP(The Climate Prediction Center Merged Analysis of Precipitation)观测资料,使用相关系数和均方根误差,对CHFP2(Coupled Historical Forecast Project, phase 2 )的2个模式对东亚夏季降雨的季节预报技巧作出评价。在完美模式的理论框架下,分别使用基于信噪比的潜在相关系数和基于信息熵的潜在可预报性指标,对该区域主要针对夏季降雨的可预报性作出评价。通过最可预报分量分析(PrCA),得到季节降雨的最可预报型。将最可预报型投影到海温场,得到了降水最可预报型对应的海温分布。研究发现:相关系数所反映的预报和观测的线性相关程度总体上是低纬度海洋区域比高纬度陆地区域高,而均方根误差反映的则是在海洋区域降雨预报偏离实际值的程度较陆地区域大,预报水平与目前降雨的季节预报水平相符。潜在可预报性估计表明,潜在可预报率存在空间上的变化,从低纬度向高纬度、从海洋到内陆,呈衰减趋势。同时,信号和噪音的分析表明,信号成分占主导作用,形成了潜在可预报率的空间分布格局,暗示了海洋外强迫的重要作用;中国大陆缺少像海洋区域那样明显的外强迫,因此降水季节预报技巧相比热带海洋区域非常有限。海温投影的分析表明海洋的外强迫是东亚降雨季节预报的重要来源。尽管厄尔尼诺本身的复杂性,它对东亚夏季风的重要影响及其与东亚降雨预报之间的遥相关揭示了它们内在的联系。     

Multiridge Euler deconvolution

Potential field interpretation can be carried out using multiscale methods. This class of methods analyses a multiscale data set, which is built by upward continuation of the original data to a number of altitudes conveniently chosen. Euler deconvolution can be cast into this multiscale environment by analysing data along ridges of potential fields, e.g., at those points along lines across scales where the field or its horizontal or vertical derivative respectively is zero. Previous work has shown that Euler equations are notably simplified along any of these ridges. Since a given anomaly may generate one or more ridges we describe in this paper how Euler deconvolution may be used to jointly invert data along all of them, so performing a multiridge Euler deconvolution. The method enjoys the stable and high‐resolution properties of multiscale methods, due to the composite upward continuation/vertical differentiation filter used. Such a physically‐based field transformation can have a positive effect on reducing both high‐wavenumber noise and interference or regional field effects. Multiridge Euler deconvolution can also be applied to the modulus of an analytic signal, gravity/magnetic gradient tensor components or Hilbert transform components. The advantages of using multiridge Euler deconvolution compared to single ridge Euler deconvolution include improved solution clustering, increased number of solutions, improvement of accuracy of the results obtainable from some types of ridges and greater ease in the selection of ridges to invert. The multiscale approach is particularly well suited to deal with non‐ideal sources. In these cases, our strategy is to find the optimal combination of upward continuation altitude range and data differentiation order, such that the field could be sensed as approximately homogeneous and then characterized by a structural index close to an integer value. This allows us to estimate depths related to the top or the centre of the structure.