3D forward modeling and response characteristics of low-resistivity overburden of the CFS-PML absorbing boundary for ground-well transient electromagnetic method

This study used the stable and convergent Dufort-Frankel method to differentially discretize the diffusion equation of the ground-well transient electromagnetic secondary field.The absorption boundary condition of complex frequency-shifted perfectly matched layer(CFS-PML)was used for truncation so that the low-frequency electromagnetic wave can be better absorbed at the model boundary.A typical three-dimensional(3D)homogeneous half-space model was established and a low-resistivity cube model was analyzed under the half-space condition.The response patterns and drivers of the low-resistivity cube model were discussed under the influence of a low-resistivity overburden.The absorption boundary conditions of CFS-PML significantly affected the low-frequency electromagnetic waves.For a low-resistivity cube around the borehole,its response curve exhibited a single-peak,and the extreme point of the curve corresponded to the center of the low-resistivity body.When the low-resistivity cube was directly below the borehole,the response curve showed three extreme values(two high and one low),with the low corresponding to the center of the low-resistivity body.The total field response of the low-resistivity overburden was stronger than that of the uniform half-space model due to the low-resistivity shielding effect of electromagnetic waves.When the receiving-transmitting distance gradually increased,the effect of the low-resistivity overburden was gradually weakened,and the response of the low-resistivity cube was strengthened.It was affected by the ratio of the overburden resistivity to the resistivity of the low-resistivity body.

A Fixed-Point Fast Sweeping WENO Method with Inverse Lax-Wendroff Boundary Treatment for Steady State of Hyperbolic Conservation Laws

Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical methods to solve steady-state solutions of hyperbolic partial differential equations(PDEs).The Gauss-Seidel iterations and alternating sweeping strategy are used to cover characteristics of hyperbolic PDEs in each sweeping order to achieve fast convergence rate to steady-state solutions.A nice property of fixed-point fast sweeping WENO methods which distinguishes them from other fast sweeping methods is that they are explicit and do not require inverse operation of nonlinear local systems.Hence,they are easy to be applied to a general hyperbolic system.To deal with the difficulties associated with numerical boundary treatment when high-order finite difference methods on a Cartesian mesh are used to solve hyperbolic PDEs on complex domains,inverse Lax-Wendroff(ILW)procedures were developed as a very effective approach in the literature.In this paper,we combine a fifthorder fixed-point fast sweeping WENO method with an ILW procedure to solve steadystate solution of hyperbolic conservation laws on complex computing regions.Numerical experiments are performed to test the method in solving various problems including the cases with the physical boundary not aligned with the grids.Numerical results show highorder accuracy and good performance of the method.Furthermore,the method is compared with the popular third-order total variation diminishing Runge-Kutta(TVD-RK3)time-marching method for steady-state computations.Numerical examples show that for most of examples,the fixed-point fast sweeping method saves more than half CPU time costs than TVD-RK3 to converge to steady-state solutions.

A Modified Back/Forward Sweep Method Based on the Electricity Consumption Data

With the development of distribution automation system, the centralized meter reading system has been adopted more and more extensively, which provides real-time electricity consumption data of end-users, and consequently lays foundation for operating condition on-line analysis of distribution network. In this paper, a modified back/forward sweep method, which directly uses real-time electricity consumption data acquired from the centralized meter reading system, is proposedto realize voltage analysis based on 24-hour electricity consumption data of a typical transformer district. Furthermore, the calculated line losses are verified through data collected from the energy metering of the distribution transformer, illustrating that the proposed method can be applied in analyzing voltage level and discovering unknown energy losses, which will lay foundation for on-line analysis, calculation and monitoring of power distribution network.

An adaptive finite-difference method for seismic traveltime modeling based on 3D eikonal equation

3D eikonal equation is a partial differential equation for the calculation of first-arrival traveltimes and has been widely applied in many scopes such as ray tracing,source localization,reflection migration,seismic monitoring and tomographic imaging.In recent years,many advanced methods have been developed to solve the 3D eikonal equation in heterogeneous media.However,there are still challenges for the stable and accurate calculation of first-arrival traveltimes in 3D strongly inhomogeneous media.In this paper,we propose an adaptive finite-difference(AFD)method to numerically solve the 3D eikonal equation.The novel method makes full use of the advantages of different local operators characterizing different seismic wave types to calculate factors and traveltimes,and then the most accurate factor and traveltime are adaptively selected for the convergent updating based on the Fermat principle.Combined with global fast sweeping describing seismic waves propagating along eight directions in 3D media,our novel method can achieve the robust calculation of first-arrival traveltimes with high precision at grid points either near source point or far away from source point even in a velocity model with large and sharp contrasts.Several numerical examples show the good performance of the AFD method,which will be beneficial to many scientific applications.

Sparse-Grid Implementation of Fixed-Point Fast Sweeping WENO Schemes for Eikonal Equations

Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping order.The resulting iterative schemes have a fast convergence rate to steady-state solutions.Moreover,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local system.Hence,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the literature.For multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational costs.In this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational costs.Here,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)equations.Numerical experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.

Forward modeling of marine DC resistivity method for a layered anisotropic earth

Since the ocean bottom is a sedimentary environment wherein stratification is well developed, the use of an anisotropic model is best for studying its geology. Beginning with Maxwell＇s equations for an anisotropic model, we introduce scalar potentials based on the divergence-free characteristic of the electric and magnetic （EM） fields. We then continue the EM fields down into the deep earth and upward into the seawater and couple them at the ocean bottom to the transmitting source. By studying both the DC apparent resistivity curves and their polar plots, we can resolve the anisotropy of the ocean bottom. Forward modeling of a high-resistivity thin layer in an anisotropic half-space demonstrates that the marine DC resistivity method in shallow water is very sensitive to the resistive reservoir but is not influenced by airwaves. As such, it is very suitable for oil and gas exploration in shallowwater areas but, to date, most modeling algorithms for studying marine DC resistivity are based on isotropic models. In this paper, we investigate one-dimensional anisotropic forward modeling for marine DC resistivity method, prove the algorithm to have high accuracy, and thus provide a theoretical basis for 2D and 3D forward modeling.

Fatigue crack growth rate test using a frequency sweep method

Fatigue crack propagation characteristics of a diesel engine crankshaft are studied by measuring the fatigue crack growth rate using a frequency sweep method on a resonant fatigue test rig. Based on the phenomenon that the system frequency will change when the crack becomes large, this method can be directly applied to a complex component or structure. Finite element analyses （FEAs） are performed to calibrate the relation between the frequency change and the crack size, and to obtain the natural frequency of the test rig and the stress intensity factor （SIF） of growing cracks. The crack growth rate i.e. da/dN-AK of each crack size is obtained by combining the testing-time monitored data and FEA results. The results show that the crack growth rate of engine crankshaft, which is a component with complex geometry and special surface treatment, is quite different from that of a pure material. There is an apparent turning point in the Paris＇s crack partition. The cause of the fatigue crack growth is also discussed.

Three-dimensional forward modeling for magnetotelluric sounding by finite element method

A finite element algorithm combined with divergence condition was presented for computing three-dimensional(3D) magnetotelluric forward modeling. The finite element equation of three-dimensional magnetotelluric forward modeling was derived from Maxwell's equations using general variation principle. The divergence condition was added forcedly to the electric field boundary value problem, which made the solution correct. The system of equation of the finite element algorithm was a large sparse, banded, symmetric, ill-conditioned, non-Hermitian complex matrix equation, which can be solved using the Bi-CGSTAB method. In order to prove correctness of the three-dimensional magnetotelluric forward algorithm, the computed results and analytic results of one-dimensional geo-electrical model were compared. In addition, the three-dimensional magnetotelluric forward algorithm is given a further evaluation by computing COMMEMI model. The forward modeling results show that the algorithm is very efficient, and it has a lot of advantages, such as the high precision, the canonical process of solving problem, meeting the internal boundary condition automatically and adapting to all kinds of distribution of multi-substances.

Three-dimensional land FD-CSEM forward modeling using edge finite-element method

A modeling tool for simulating three-dimensional land frequency-domain controlled-source electromagnetic surveys,based on a finite-element discretization of the Helmholtz equation for the electric fields,has been developed.The main difference between our modeling method and those previous works is edge finite-element approach applied to solving the three-dimensional land frequency-domain electromagnetic responses generated by horizontal electric dipole source.Firstly,the edge finite-element equation is formulated through the Galerkin method based on Helmholtz equation of the electric fields.Secondly,in order to check the validity of the modeling code,the numerical results are compared with the analytical solutions for a homogeneous half-space model.Finally,other three models are simulated with three-dimensional electromagnetic responses.The results indicate that the method can be applied for solving three-dimensional electromagnetic responses.The algorithm has been demonstrated,which can be effective to modeling the complex geo-electrical structures.This efficient algorithm will help to study the distribution laws of3-D land frequency-domain controlled-source electromagnetic responses and to setup basis for research of three-dimensional inversion.

Finite difference time domain method forward simulation of complex geoelectricity ground penetrating radar model

The ground penetrating radar(GPR) forward simulation all aims at the singular and regular models, such as sandwich model, round cavity, square cavity, and so on, which are comparably simple. But as to the forward of curl interface underground or “v” figure complex model, it is difficult to realize. So it is important to forward the complex geoelectricity model. This paper takes two Maxwell’s vorticity equations as departure point, makes use of the principles of Yee’s space grid model theory and the basic principle finite difference time domain method, and deduces a GPR forward system of equation of two dimensional spaces. The Mur super absorbed boundary condition is adopted to solve the super strong reflection on the interceptive boundary when there is the forward simulation. And a self-made program is used to process forward simulation to two typical geoelectricity model.

A Gravity Forward Modeling Method based on Multiquadric Radial Basis Function

It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method widely used.Due to self-adaptability lack of division meshes and the difficulty of high-dimensional calculation.

Three-dimensional forward modeling for the SBTEM method using an unstructured fi nite-element method

In this study,we propose a three-dimensional(3D)forward modeling algorithm of surface-to-borehole transient electromagnetic(SBTEM)fields based on an unstructured vector fi nite-element method to analyze the characteristics of SBTEM responses for complex geoelectrical models.To solve the double-curl diff usion equation for the electric fi eld,we use an unstructured tetrahedral mesh to discretize the model domain and select the unconditionally stable backward Euler scheme to discretize the time derivative.In our numerical experiments,we use a grounded wire as a transmitting source.After validating the algorithm’s eff ectiveness,we first analyze the diffusion characteristics and detectability of the electromagnetic field.After that,we focus our attention on the distribution and the cause of zero bands for Ex and dBy/dt components with the hope of guiding future field surveys.Finally,by simulating diff erent models,we analyze the capability of the SBTEM method in detecting typical mineral veins so that we can provide a reference for mineral resource exploration in the deep earth.

Experimental Investigation of a Fixed-geometry Two-dimensional Mixed-compression Supersonic Inlet with Sweep-forward High- light and Bleed Slot in an Inverted ＂X＂-type Layout

A fixed-geometry two-dimensional mixed-compression supersonic inlet with sweep-forward high-light and bleed slot in an inverted ＂X＂-form layout was tested in a wind tunnel. Results indicate： （1） with increases of the free stream Mach number, the total pressure recovery decreases, while the mass flow ratio increases to the maximum at the design point and then decreases; （2） when the angle of attack, a, is less than 6°, the total pressure recovery of both side inlets tends to decrease, but, on the lee side inlet, its values are higher than those on the windward side inlet, and the mass flow ratio on lee side inlet increases first and then falls, while on the windward side it keeps declining slowly with the sum of mass flow on both sides remaining almost constant; （3） with the attack angle, a, rising from 6° to 9°, both total pressure recovery and mass flow ratio on the lee side inlet fall quickly, but on the windward side inlet can be observed decreases in the total pressure recovery and increases in the mass flow ratio; （4） by comparing the velocity and back pressure characterristics of the inlet with a bleed slot to those of the inlet without, it stands to reason that the existence of a bleed slot has not only widened the steady working range of inlet, but also made an enormous improvement in its performance at high Mach numbers. Besides, this paper also presents an example to show how this type of inlet is designed.

Solution of scattering from rough surface with a 2D target above it by a hybrid method based on the reciprocity theorem and the forward-backward method

This paper proposes a hybrid method based on the forward-backward method （FBM） and the reciprocity theorem （RT） for evaluating the scattering field from dielectric rough surface with a 2D target above it. Here, the equivalent electric/magnetic current densities on the rough surface as well as the scattering field from it are numerically calculated by FBM, and the scattered field from the isolated target is obtained utilizing the method of moments （MOM）. Meanwhile, the rescattered coupling interactions between the target and the surface are evaluated employing the combination of FBM and RT. Our hybrid method is first validated by available MOM results. Then, the functional dependences of bistatic and monostatic scattering from the target above rough surface upon the target altitude, incident and scattering angles are numerically simulated and discussed. This study presents a numerical description for the scattering mechanism associated with rescattered coupling interactions between a target and an underlying randomly rough surface.

Iterative methods for a forward-backward heat equation in two-dimension

A finite difference method is introduced to solve the forward-backward heat equation in two space dimensions. In this procedure, the backward and forward difference scheme in two subdomains and a coarse-mesh second-order central difference scheme at the middle interface are used. Maximum norm error estimate for the procedure is derived. Then an iterative method based on domain decomposition is presented for the numerical scheme and the convergence of the given method is established. Then numerical experiments are presented to support the theoretical analysis.

Employing the ForWaRD Method to Improve Resolution of Conventional OTDR for Application in SHM

As a fiber sensor, optical time domain L reflectometer becomes more and more popular to measure parameters, such as strain and temperature in structural health monitoring （SHM） simultaneously. Since the accuracy of range resolution in optical time domain reflectometer （OTDR） is determined by the pulse width of laser, the range resolution in order of centimeter is achieved by employing of picoseconds lasers which are not commercial. In this paper, to achieve this accuracy with conventional OTDR, Fourier wavelet regularized deconvolution （ForWaRD） method is employed to deconvolve and denoise the detected signal simultaneously. Simulations show that this method improves resolution of conventional OTDR system to the order of several centimeters.

THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE

This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.

求解二阶锥绝对值方程组的惯性two-sweep迭代法

提出一种求解二阶锥绝对值方程组(SOCAVE)的惯性two-sweep迭代法。通过引入一个惯性项和一个恒等式,在系统矩阵和迭代矩阵满足一定条件的情况下,分析该算法的收敛性,数值结果表明所提出的方法是可行且有效的。

基于2.5D有限元的高密度电法不同装置勘探效果研究

高密度电法是一种适用性广泛的电阻率勘探方法,拥有多种电极排列装置选择。不同装置由于电极分布方式的差异,在针对不同地质目标和测区环境时往往表现出明显不同的探测能力。为探究各排列装置的特点及其适用情况,推导了2.5D电位的变分问题,采用Delaunay三角化算法实现了非结构化网格剖分,进而实现了有限元正演模拟。结合实践,对常见地质情况进行建模,分别使用温纳α、温纳β、施伦贝谢尔、偶极-偶极4种装置开展正反演对比研究。研究发现:(1)在探测未知区域单个异常体时,温纳β、施伦贝谢尔2种排列的效果更好;(2)在探测相邻较近的多个异常体时,应优先采用具有更高水平分辨率的施伦贝谢尔和偶极-偶极排列;(3)对于低阻破碎带的勘探,温纳β和偶极-偶极排列更为适用;(4)当地层具有较好分层界限时,4种排列均可体现良好的分层效果。因此,高密度电法勘探实践中应综合考虑不同排列装置的特点,根据具体情况选用合适的多种排列方式进行测量,并对采集数据进行综合对比分析,以获得更为准确的解释结果。

基于有限差分低秩分解策略的黏声各向异性纯qP波正演模拟方法

地下介质的黏弹性和各向异性特征会导致地震波出现相位频散和振幅衰减,如果在地震数据处理中忽略这些影响,那么成像结果会出现同相轴畸变和偏移假象。常规黏声TTI介质拟声波方程可用于模拟地震波在黏声各向异性介质中的传播特征,但存在伪横波干扰和受模型参数限制(各向异性参数ε必须大于δ)等问题。为了解决上述问题,将基于声学近似的纯qP波频散关系与常Q衰减模型相结合,推导了一种黏声TTI介质纯qP波方程。该方程包含解耦的相位频散和振幅衰减项,便于实现衰减补偿逆时偏移。基于新推导的方程,发展了有限差分低秩分解求解策略,实现了黏声TTI介质纯qP波正演模拟。数值模拟结果表明,该方程克服了黏声TTI介质拟声波方程的局限,可较为准确且稳定地模拟地震波在黏声各向异性介质中的传播过程。同时,该有限差分低秩分解求解策略继承了有限差分求解方法高效的优势,相比于传统低秩分解法具有更高的计算效率。