应用计算机“推导”位场圆滑滤波及二次导数公式的方法

根据台劳级数展开式,将窗口内网格结点位场数据在计算点展开,且对应点两两相加,由最小二乘法求得窗口内网格结点的圆滑滤波算子和二次导数算子,将此算子与观测的位场数据褶积,就可得到位场圆滑后的数据及水平、垂直二次导数。     

用欧拉方程估算埋深和形状因数

本文论述了用欧拉方程估算埋深和形状因数的方法原理,并用模型计算加以验证,最后用湖南某地含原生金刚石的钾镁煌斑岩筒上的ΔＴ异常证实这种估算方法是值得推广的。     

重力场向下延拓Milne法

重力场向下延拓能够突出局部和浅部的异常信息,分离叠加的异常特征.但是向下延拓通常具有过程不稳定、下延深度小、结果不准确等问题.针对向下延拓所存在的不足,本文利用重力场及其垂向一阶导数,基于辛普森(Simpson)求积公式,推导出重力场向下延拓米尔尼(Milne)公式.将本文向下延拓方法应用于模型数据,向下延拓模型结果及误差曲线表明,相对于向下延拓快速傅里叶变换(FFT)法和积分迭代法,向下延拓Milne法的深度更大,相对误差更小;相对模型值,向下延拓Milne法能够获得稳定且准确的结果.对加拿大乃查科(Nechako)盆地地区实测航空重力数据进行本文方法向下延拓验证,处理结果表明,相对于实测异常,本文方法向下延拓结果能够很好还原实测数据,并且在进一步向下延拓中反映原始异常的趋势,增强局部和细小异常信息.     

地层格架正则化约束下的二维立体层析反演

通过把地层格架信息作用于立体层析Fréchet导数矩阵,使得更新后的速度模型呈现出符合地质规律的块状特征.地层格架信息基于立体层析反演中得到的反射点位置进行非规则B样条插值拟合得到,因此在反演中它将会随着反射点位置的更新自然得到更新.与前人提出的保边缘层析算法或多层立体层析算法相比,本文提出的地层格架正则化无需引入混合正则化项或定义某种复杂的混合速度格式,更为直接也更容易实现.理论和实际数据算例证实了该正则化技巧的稳健性和可靠性,能够得到与实际地质构造特征更为一致的地质一致性反演结果.     

Prediction of one-dimensional compression behavior of Nansha clay using fractional derivatives

Nansha clay is an interactive marine and terrestrial deposited soft clay that is widely spread in Guangzhou, Pearl River Delta, China. To avoid excessive settlement after construction, there is a need for better quantifying the time-dependent deformation of the soft clay. This paper presents a preliminary study to predict the one-dimensional compression of Nansha clay using fractional derivatives. A fractional Merchant model was introduced to describe the time-dependent settlement, and analytical solutions were obtained in terms of the Mittag-Leffler function. The oedometer test results were presented to validate this model. Compared with classical rheological models, the fractional derivative-based model enabled close estimation of the one-dimensional compression with fewer parameters. The meaning of the order of fractional derivative and its relationship with the clay physical properties were explored. It shows that a smaller value of this order corresponded to a higher coefficient of consolidation and a lower coefficient of secondary consolidation. The amplitude of both the primary and secondary consolidation of clay may be estimated quantitatively by the order of fractional derivative. Taken together, these results may open up new avenues for theoretical and empirical modeling of rheological phenomena in clay using fractional derivatives.     

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.     

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.     

归一化总水平导数法在位场数据解释中的应用

本文提出归一化总水平导数法,通过对总水平导数进行空间归一化计算实现了异常体水平位置和深度的估计,此外还推导出基于归一化总水平导数的欧拉反褶积法来估算地下地质体的空间位置,两种方法反演结果的相互验证可有效地提高反演结果的可信度.理论模型试验证明空间归一化总水平导数法和归一化总水平导数欧拉反褶积法均能有效地完成异常体的水平位置和深度的估计,所获得的位置参数与理论值相一致.在利用归一化总水平导数法进行磁异常解释时,对数据进行化磁极计算可得到更加准确的结果.将其应用于实际航磁数据的解释,获得了岩脉的大致分布特征.     

Spectral Reflectance Analysis of the Caribbean Sea

Reflectance spectral curves were analysed by a derivative method. Derivative reflectance spectra revealed concealed peaks of both reflectance and absorption curves of Caribbean seawater and elements contained within it. Reflectance curves showed a predominant blue colour (400–500 nm) characteristic of Caribbean oligotrophic waters, conspicuous peaks result from the optical properties of chlorophyll a and seawater. Reflectance curves had a similar spectral response. This paper analyses reflectance spectra of surface seawater at 31 stations in the Caribbean Sea during the summer of 2001.     

Unified fractional differential approach for transient interporosity flow in naturally fractured media

A unified approach to modeling flows of slightly compressible fluids through naturally fractured media is presented. The unified fractional differential model is derived by combining the flow at micro scale for matrix blocks and macro scale for fractures, using the transient interporosity flow behavior at the interface between matrix blocks and fractures. The derived model is able to unify existing transient interporosity flow models formulated for different shapes of matrix blocks in any medium dimensions. The model is formulated in the form of a fractional order partial differential equation that involves Caputo derivative of order 1/2 with respect to time. Explicit solutions for the unified model are derived for different axisymmetrical spatial domains using Hankel or Hankel–Weber finite or infinite transforms. Comparisons between the predictions of the unified model and those obtained from existing transient interporosity flow models for matrix blocks in the form of slabs, spheres and cylinders are presented. It is shown that the unified fractional derivative model leads to solutions that are very close to those of transient interporosity flow models for fracture-dominant and transitional fracture-to-matrix dominant flow regimes. An analysis of the results of the unified model reveals that the pressure varies linearly with the logarithm of time for different flow regimes, with half slope for the transitional fracture-to-matrix dominant flow regime vs. the fracture and matrix dominant flow regimes. In addition, a new re-scaling that involves the characteristic length in the form of matrix block volume to surface area ratio is derived for the transient interporosity flow models for matrix blocks of different shapes. It is shown that the re-scaled transient interporosity flow models are governed by two dimensionless parameters Θ and Λ compared to only one dimensionless parameter Θ for the unified model. It is shown that the solutions of the transient interporosity flow models for different shapes of matrix blocks are almost identical for the re-scaled variables. Furthermore, the driving parameters for solution behavior are identified based on asymptotic approximations for different flow regimes. It is found that the matrix diffusion and the matrix area-to-volume ratio affect the solution behavior only for the transitional fracture-to-matrix dominant flow regime, that the capacitance ratio affects the solution behavior only for transitional and matrix dominant flow regimes and that the fracture diffusion is involved in all three flow regimes. Similar identification of the driving parameters is also presented in the re-scaled case.