平面Radon变换的反演公式

本文借助球面平均法和Ｈｉｌｂｅｒｔ空间算子理论,给出了平面上Ｒａｄｏｎ变换的反演公式,此公式是具体的、构造性的,便于数值计算,或者进一步探讨重建图象的性质。     

半湿润流域水文模型比较与集合预报

选择7种水文模型分别在中国北部3个半湿润流域做模拟对比,分析不同水文模型在各流域的适用性,并使用贝叶斯模型平均法对不同模型集合,比较各种集合方法的优势,研究贝叶斯模型平均法的应用效果.研究结果表明,以蓄满产流模式为主的模型在半湿润流域应用效果较好,针对不同流域特点对传统模型进行改进可以提高模拟精度.贝叶斯模型平均法能提供较好的确定性预报结果和概率预报结果,仅对少数模拟效果好的模型进行集合,并不能有效提高预报精度,适当增加参与集合的模型数量能使贝叶斯模型平均法更好地综合各模型优势,提高预报结果的精度.     

利用熵平均法对地面γ能谱数据局部干扰消除的应用研究

阐述了熵平均法对地面γ能谱测量局部干扰的消除的基本原理和方法,应用此方法对浅覆盖区地质填图的γ能谱测量剖面数据及应用γ能谱测量确定古城墙位置的平面测量数据进行了处理,处理结果表明该方法对于消除地表植被及局部土壤元素富集随机干扰、突出弱异常具有明显的效果,使地质填图中进行岩性划分界线明显,考古中古城墙表现的弱异常突出,边界清晰.通过对熵平均法应用的讨论,可以看到5点熵平均对于局部干扰压制较多而对异常削弱较少的特点;与多点平滑相比,熵平均对于突跳点具有更好的压制作用.熵平均法对于地面γ能谱测量随机影响的消除起到了较好的效果,使地面γ能谱测量得到了较好的应用.     

一种求解黏弹塑性介质流动的全隐格式算法

在岩石圈动力学数值模拟中,现有的黏弹塑性数值模型通常在每个时间步先使用迎风间断Galerkin方法对偏应力张量进行旋转,然后使用Particle-In-Cell (PIC)方法或场方法求解对流方程,所构成的时间离散格式为显格式或半隐格式.我们将黏弹塑性介质的经典数值模型和非牛顿流体力学领域的黏弹性流体问题计算方法相结合,提出了一种基于有限单元法的求解黏弹塑性介质流动的全隐格式算法.本文通过数值实验将这种全隐格式算法与PIC方法和半隐格式算法进行了详细的对比,实验结果表明全隐格式算法的数值稳定性优于PIC方法,而当Deborah数较高时精度优于半隐格式算法.同时,我们在应力场引入三阶WENO (Weighted Essentially Non-Oscillatory)限制器,可以在保留数值解精度的同时有效消除应力集中引起的数值振荡.     

三维层状孔隙介质中弹性波的一种积分表达式I：理论

孔隙介质弹性波传播理论在地球物理勘探、地震工程和岩土动力学等领域有着广泛的应用.而孔隙介质中的弹性波受孔隙度、渗透率、流体黏滞系数等参数的影响,因此研究波场的传播特征将有助于分析和提取这些信息.本文在Biot理论的基础上,针对三维层状孔隙介质模型,利用在合成理论地震图的研究中已经被证实具有稳定、高效且适用范围较广的Luco-Apsel-Chen（LAC）广义反透射方法,给出了弹性波场的一种积分形式的半解析解,可通过数值方法高效、准确地计算层状孔隙介质中的理论波场,所以该积分形式的半解析解可为三维层状孔隙介质波场传播特征的理论数值模拟研究提供一种新的途径和手段.     

浅析长波辐射数值处理方法在判断震前异常中的应用

对4种常用的OLR数值处理方法如距平处理、涡度处理、5日滑动平均值法、小波包分解法与距平涡度综合处理进行对比研究,分析各种方法适用范围和优缺点.结果表明:距平法和涡度法能够反映区域内的总体状况,属于宏观层面;滑动平均法和小波包分解重构法都是针对某一震例,应用范围较小.单一数值处理方法在存在固有缺陷,在试用中应结合区域实际情况,结合各种方法的特性,充分挖掘数据的使用效率.     

基于神经网络的视电阻率快速算法

本文从瞬变电磁均匀半空间二次磁场响应公式出发,提出了一种基于神经网络的视电阻率快速计算方法.以中心回线为例,根据瞬变响应公式的特点,简化网络结构,选用三层BP神经网络和误差训练算法,用均匀半空间样本数据进行训练,确定了收敛快、误差小的一步正割法和隐含单元数,得到基于不同采样时窗的一组网络参数.用本文方法与二分法、牛顿迭代法做模型计算比较,及最后的实验计算,说明算法的快速,准确.本文方法不依赖初始模型,避开了复杂的电磁场数值计算,实现了视电阻率的快速计算,对瞬变电磁法资料的快速解释有一定的参考价值.     

复杂介质有限元法2.5维可控源音频大地电磁法数值模拟

利用有限元2.5维可控源音频大地电磁法（简称CSAMT）数值模拟方法,对100Ωm均匀半空间介质中有限长度的电偶极源产生的电场、磁场及视电阻率、相位特征进行了数值模拟,研究了场的空间变化规律. 在一个象限中,场的特征存在双叶现象,当收发距大于4个趋肤深度时,电阻率较接近介质真实的电阻率,这些结果为观测系统和收发距的选择提供了依据. 波数域场的特征表明,低波数对源的贡献占较大的比例. 有限元法2.5维CSAMT数值模拟的优势在于能较准确地获得复杂介质结构的波场特征. 本文结合直立异常体、倾斜异常体及断陷模型对CSAMT电阻率、相位剖面特征及频率曲线特征的可靠性进行了研究. 数值模拟结果直观地给出了异常体的剖面异常形态. 通过对比研究异常体的剖面异常形态和半空间场的特征进一步说明本文方法和软件在模拟复杂介质结构场特征时是可靠的. 这为认识观测数据,指导反演解释提供了较好的依据.     

Hamilton体系及弹性波在层状介质中的传播问题

利用结构力学与最优控制的模拟理论,研究弹性波在层状介质中传播的数值计算方法. 将弹性波传播问题导向哈密顿(Hamilton)体系,在哈密顿体系中,推导出一种新的半解析单元,称之为动力-部分杂交元,由此导出一套哈密顿体系下的半解析数值计算方法. 本文给出了该方法在层状正交各向异性材料介质的弹性波传播问题的数值算例,分析了一定频率的弹性波在层状介质中传播时的位移、应力的模式. 计算结果展现了Hamilton体系和辛几何在弹性波传播问题研究的应用前景.     

利用谱元法计算SNREI地球的表面负荷变形

谱元法作为一种基于变分原理的数值方法,已经成为地球动力学数值模拟的重要手段.本文旨在对Martinec(2000)正演模拟表面负荷问题的谱-有限元方法进行改进.简单地介绍了谱元法计算负荷边值问题的相关理论,并推导了中性分层液体中的平衡方程以及其对应的弱形式解.在地球半径方向上,采取高阶样条函数作为负荷解的基函数,并利用高斯-勒让德方法进行数值积分.均质地球模型数值试验表明,相较于Martinec的方法,本文方法可以有效地加快数值解的收敛速度.最后,利用PREM模型计算了SNREI地球的负荷勒夫数.数值计算结果表明本文方法的收敛性和稳定性都非常好.本文方法获得的负荷勒夫数与采用传统龙格-库塔积分方法获得的结果相对误差在0.01%的量级.     

An Efficient Numerical Method for Computing Synthetic Seismograms for a Layered Half-space with Sources and Receivers at Close or Same Depths

— It is difficult to compute synthetic seismograms for a layered half-space with sources and receivers at close to or the same depths using the generalized R/T coefficient method (Kennett, 1983; Luco and Apsel, 1983; Yao and Harkrider, 1983; Chen, 1993), because the wavenumber integration converges very slowly. A semi-analytic method for accelerating the convergence, in which part of the integration is implemented analytically, was adopted by some authors (Apsel and Luco, 1983; Hisada, 1994, 1995). In this study, based on the principle of the Repeated Averaging Method (Dahlquist and Björck, 1974; Chang, 1988), we propose an alternative, efficient, numerical method, the peak-trough averaging method (PTAM), to overcome the difficulty mentioned above. Compared with the semi-analytic method, PTAM is not only much simpler mathematically and easier to implement in practice, but also more efficient. Using numerical examples, we illustrate the validity, accuracy and efficiency of the new method.     

利用反透射系数确定理论地震图计算过程中的积分限阈值

本文尝试基于理论分析来求解积分限阈值k_c,即通过反透射系数来确定k_c。根据计算理论地震图的广义反透射系数法,在反透射系数中进行求逆运算的矩阵行列式的零点将会使得被积函数产生较大的变化,通过具体实例显示出自由界面处的反射系数中含有的零点可以作为合适的k_c。多种情况的实例显示,通过反射系数来确定k_c具有较好的普适性。通过与经验公式的计算结果进行比对,表明根据本文方案所确定的k_c在保证准确性的同时可以有效地提高计算效率。      

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 3. Single-fluid-phase flow

This work is the third in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach to modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works in this series, we demonstrate the TCAT approach for the case of single-fluid-phase flow. The formulated model is based upon conservation equations for mass, momentum, and energy and a general entropy inequality constraint, which is developed to guide model closure. A specific example of a closed model is derived under limiting assumptions using a linearization approach and these results are compared and contrasted with the traditional single-phase-flow model. Potential extensions to this work are discussed. Specific advancements in this work beyond previous averaging theory approaches to single-phase flow include use of macroscale thermodynamics that is averaged from the microscale, the use of derived equilibrium conditions to guide a flux–force pair approach to simplification, use of a general Lagrange multiplier approach to connect conservation equation constraints to the entropy inequality, and a focus on producing complete, closed models that are solvable.     

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 7. Single-phase megascale flow models

This work is the seventh in a series that introduces and employs the thermodynamically constrained averaging theory (TCAT) for modeling flow and transport in multiscale porous medium systems. This paper expands the previous analyses in the series by developing models at a scale where spatial variations within the system are not considered. Thus the time variation of variables averaged over the entire system is modeled in relation to fluxes at the boundary of the system. This implementation of TCAT makes use of conservation equations for mass, momentum, and energy as well as an entropy balance. Additionally, classical irreversible thermodynamics is assumed to hold at the microscale and is averaged to the megascale, or system scale. The fact that the local equilibrium assumption does not apply at the megascale points to the importance of obtaining closure relations that account for the large-scale manifestation of small-scale variations. Example applications built on this foundation are suggested to stimulate future work.     

Addressing snow model uncertainty for hydrologic prediction

Streamflow forecasting methods are moving towards probabilistic approaches that quantify the uncertainty associated with the various sources of error in the forecasting process. Multi-model averaging methods which try to address modeling deficiencies by considering multiple models are gaining much popularity. We have applied the Bayesian Model Averaging method to an ensemble of twelve snow models that vary in their heat and melt algorithms, parameterization, and/or albedo estimation method. Three of the models use the temperature-based heat and melt routines of the SNOW17 snow accumulation and ablation model. Nine models use heat and melt routines that are based on a simplified energy balance approach, and are varied by using three different albedo estimation schemes. Finally, different parameter sets were identified through automatic calibration with three objective functions. All models use the snow accumulation, liquid water transport, and ground surface heat exchange processes of the SNOW17. The resulting twelve snow models were combined using Bayesian Model Averaging (BMA). The individual models, BMA predictive mean, and BMA predictive variance were evaluated for six SNOTEL sites in the western U.S. The models performed best and the BMA variance was lowest at the colder sites with high winter precipitation and little mid-winter melting. An individual snow model would often outperform the BMA predictive mean. However, observed snow water equivalent (SWE) was captured within the 95% confidence intervals of the BMA variance on average 80% of the time at all sites. Results are promising that consideration of multiple snow structures would provide useful uncertainty information for probabilistic hydrologic prediction.     

宁夏中部小震震源机制解研究

本文利用宁夏区域台网共27个台的宽频带数字地震记录,采用CAP方法和Snoke方法反演了宁夏中部19次ML3.0以上地震震源机制解。结果显示:东侧牛首山-罗山-固原断裂带和中部的烟洞山断裂带主要以右旋走滑为主,带少量逆冲分量,与实际主控断层的情况一致;西侧的中卫-同心断裂带以左旋走滑为主;19次地震的CAP法计算结果中的16次地震机制解走向在105~189o之间,另有2次为350o和353o,和断层走向基本一致。综合应力场研究结果表明该区域地震产生的震源区构造变形是近北东向发生压缩,近北西向发生相对扩张。对比2种方法计算结果发现,Snoke方法计算结果不理想。分析认为,一方面,宁夏台网台站间距较大,分布不理想;另一方面,识别小地震的初动及振幅比时存在误差。因此,对于西部台站稀疏地区CAP方法计算小震震源机制结果更为可靠。     

ADVANCED METHOD FOR SELF-ADAPTIVE ESTIMATION OF RESIDUAL STATIC CORRECTIONS*

The estimation of residual static corrections is investigated as a linear system. For 1200% coverage shot one way offset weighting functions—or in other words, estimation error operators—are computed. Assuming zero time shift determination errors and zero RNMO it is seen that large residual corrections will distort the effectivity of the estimation. With an iterative procedure which includes the repeated averaging according to depth point, shot point, and geophone point the effectivity of the method becomes more favourable. This can be learnt from the evaluation of estimation error operators computed by recursive formulae. In practice, due to the time shift determination errors, the routine does not give improved results in the desired level. Errors can be reduced with a more reliable time shift determination routine. For detecting and suppressing the unfavourable effect of time shift errors still remaining in the data a self-adaptive method was developed. In this non linear routine the data are evaluated at all three averaging processes according to limit values and weighting factors computed from the data itself. Field examples processed in different ways are presented.     

Thermodynamically Constrained Averaging Theory Approach for Modeling Flow and Transport Phenomena in Porous Medium Systems: 5. Single-Fluid-Phase Transport

This work is the fifth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are used to develop models that describe species transport and single-fluid-phase flow through a porous medium system in varying physical regimes. Classical irreversible thermodynamics formulations for species in fluids, solids, and interfaces are developed. Two different approaches are presented, one that makes use of a momentum equation for each entity along with constitutive relations for species diffusion and dispersion, and a second approach that makes use of a momentum equation for each species in an entity. The alternative models are developed by relying upon different approaches to constrain an entropy inequality using mass, momentum, and energy conservation equations. The resultant constrained entropy inequality is simplified and used to guide the development of closed models. Specific instances of dilute and non-dilute systems are examined and compared to alternative formulation approaches.