Advances in three‐dimensional magnetotelluric modeling using integral equations

Geophysics ◽  
1991 ◽  
Vol 56 (11) ◽  
pp. 1716-1728 ◽  
Author(s):  
Philip E. Wannamaker
Keyword(s):  
Transverse Electric ◽  
Normal Component ◽  
Three Dimensional ◽  
Transverse Magnetic ◽  
Basis Functions ◽  
The Body ◽  
Equation Modeling ◽  
Short Version ◽  
D Model ◽  
Good Agreement

Recent progress in integral equation modeling of three‐dimensional magnetotelluric responses includes the ability to simulate 3-D structures which outcrop (excluding topography), which transect layer interfaces, and which extend indefinitely in one or more directions. The most important factor in achieving this capability is an accurate treatment of the electric surface charge. In particular, a previous integro‐difference formulation for evaluating charges has been abandoned in favor of true surface integrations over the source cells with potential differencing across the field cells in the 3-D body. The new procedure constitutes a good approximation to Galerkin’s method while preserving internal consistency in terms of pulse basis functions. To verify outcropping structures, juxtaposed conductive and resistive prisms at the surface are simulated and compared to 2-D results. An elongate version of the 3-D model shows good agreement with both transverse electric and transverse magnetic modes of the 2-D response at both high and low frequencies. Apparent finite strike length effects for a short version of the 3-D body are physically reasonable. To verify structures cut by layer interfaces, an elongate tabular conductor at the base of a resistive overburden layer, which is in immediate contact with a tabular resistor at the top of a conductive basal half‐space is considered. All 3-D field components are in good agreement with 2-D transverse electric and transverse magnetic calculations from the surface down through or beside the body into the conductive basement below. The proper discontinuity of the normal component of the electric field across inhomogeneity boundaries is simulated well by the algorithm, but not exactly because of the pulse nature of the basis functions. Finally, outcropping and infinitely extended structures are checked by comparison of an offset basin model with very low frequency, thin‐layer calculation. In general, best results are obtained at cell body centers or face centers, but are not reliable over cell corners. From the offset basin study, we show also that 2-D transverse magnetic mode modeling of corresponding 3-D responses cannot be carried out indiscriminately over arbitrary structures without propagating errors to substantial depths in the 2-D model cross‐section.

The asymptotic response of three‐dimensional basin offsets to magnetotelluric fields at long periods: The effects of current channeling

Geophysics ◽  
1982 ◽  
Vol 47 (11) ◽  
pp. 1562-1573 ◽  
Author(s):  
John F. Hermance
Keyword(s):  
Thin Sheet ◽  
Three Dimensional ◽  
Sedimentary Basins ◽  
Transverse Magnetic ◽  
Clear Correlation ◽  
One Dimensional ◽  
Skewness Coefficient ◽  
Order Of Magnitude ◽  
D Model ◽  
Telluric Currents

A simple, inexpensive numerical algorithm is used to analyze the asymptotic long‐period behavior of magnetotelluric (MT) fields in the vicinity of lateral offsets in sedimentary basins. The model is based on the distortion or channeling of telluric currents in a horizontal thin sheet. Although a gross oversimplification of nature, the model represents a class of structures which, because of excessive computer costs, have been relatively unstudied previously. Within, and closely adjacent to, the region of the three‐dimensional (3-D) offset, significant distortion of the MT parameters occurs. Skewness coefficients vary from negligible values to over 0.7. Principal resistivities vary by an order of magnitude. On the other hand, there is not a clear correlation between the degree of distortion of the parameters usually evaluated during MT surveys and the magnitude of conventional 3-D indicators (e.g., the skewness coefficient). Calculations have simulated the technique of averaging resistivity parameters from a large number of field sites in order to arrive at a regionally representative one‐dimensional (1-D) model. The results indicate that unless care is taken in adapting the nature of the averaging algorithm to the class of distortions encountered, significant bias of the averaged parameters may result. Our results also suggest that for this class of structures grave problems may be associated with using the principal resistivity perpendicular to geologic strike, the so‐called transverse magnetic (TM) mode, to infer an equivalent two‐dimensional (2-D) model for the region. A 2-D model would likely show significant modulations in the physical character of the basement which are, in fact, an artifact of telluric distortion caused by current channeling in the surficial heterogeneity.

Calculation of Nonlifting Potential Flow About Arbitrary Three-Dimensional Bodies

1964 ◽  
Vol 8 (04) ◽  
pp. 22-44 ◽  
Author(s):  
John L. Hess ◽  
A. M. O. Smith
Keyword(s):  
Body Surface ◽  
Potential Flow ◽  
Fluid Velocity ◽  
Normal Component ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
The Body ◽  
Algebraic Equations ◽  
Source Density ◽  
Linear Algebraic Equations

A general method is described for calculating, with the aid of an electronic computer, the incompressible potential flow about arbitrary, nonlifting, three-dimensional bodies. The method utilizes a source density distribution on the surface of the body and solves for the distribution necessary to make the normal component of fluid velocity zero on the boundary. Plane quadrilateral surface elements are used to approximate the body surface, and the integral equation for the source density is replaced by a set of linear algebraic equations for the values of the source density on the quadrilateral elements. When this set of equations has been solved, the flow velocity both on and off the body surface is calculated. After the basic ideas and equations have been derived end discussed, the accuracy of the method is exhibited by means of comparisons with analytic solutions, and its usefulness is shown by comparing calculated pressure distributions with experimental data. Some of the design problems to which the method has been applied are also presented, to indicate the variety of flow situations that can be calculated by this approach.

Design of graded honeycomb radar absorbing structure with wide-band and wide-angle properties

2018 ◽  
Vol 11 (2) ◽  
pp. 143-150 ◽  
Author(s):  
Yuchen Zhao ◽  
Fang Ren ◽  
Li He ◽  
Jinsheng Zhang ◽  
Yanning Yuan ◽  
...  
Keyword(s):  
Transverse Electric ◽  
Incident Angle ◽  
Wide Band ◽  
Transverse Magnetic ◽  
Magnetic Polarization ◽  
Wide Range ◽  
Transverse Magnetic Polarization ◽  
Radar Absorbing Structure ◽  
Theoretical Limitation ◽  
Good Agreement

AbstractIn this paper, the design of a graded honeycomb radar absorbing structure (RAS) is presented to realize both a wide bandwidth and absorption over a wide range of angles. For both transverse-electric and transverse-magnetic polarization, a fractional bandwidth of more than 118.6% is achieved for at least a 10 dB reflectivity reduction when the incident angle is <45°, an 8 dB reduction when the incident angle is <55° and a 5 dB reduction when the incident angle is <70°. Meanwhile the 10 dB reduction upper angle limit is approximately 30° for the uniform coating honeycomb RAS in the literature, which loses its absorbing ability when the incident angle is larger than 55°. Furthermore, the total thickness of our design is 10.7 mm, which is only approximately 1.29 times that of the theoretical limitation. The good agreement between the calculated, simulated, and measured results demonstrates the validity of this optimization.

Integral equation solution for the transient electromagnetic response of a three‐dimensional body in a conductive half‐space

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 798-809 ◽  
Author(s):  
William A. SanFilipo ◽  
Gerald W. Hohmann
Keyword(s):  
Integral Equation ◽  
Frequency Domain ◽  
Half Space ◽  
Time Constant ◽  
Free Space ◽  
Numerical Scheme ◽  
Three Dimensional ◽  
Basis Functions ◽  
The Body ◽  
Spatial Discretization

The time‐domain integral equation for the three‐dimensional vector electric field is formulated as a convolution of the scattering current with the tensor Green’s function. The convolution integral is divided into a sum of integrals over successive time steps, so that a numerical scheme can be formulated with a time stepping approximation of the convolution of past values of the solution with the system impulse response. This, together with spatial discretization, leads to a matrix equation in which previous solution vectors are multiplied by a series of matrices and fed back into the system by adding to the primary field source vector. The spatial discretization, based on a modification of the usual pulse basis formulation in the frequency domain, includes an additional subset of divergence‐free basis functions generated by integrating the Green’s function around concentric closed rectangular paths. The inductive response of the body is more accurately modeled with these additional basis functions, and a meaningful solution can be obtained for a body in free space. The resulting algorithm produces good results even for large conductivity contrasts. Internal checks, including convergence with respect to spatial and temporal discretization, and reciprocity, demonstrate self‐consistency of the numerical scheme. Independent checks include (a) comparison with results computed for a prism in free space, (b) comparison with results computed for a thin plate, (c) comparison of our conductive half‐space algorithm with an asymptotic solution for a sphere, and (d) comparison with results from inverse Fourier transformation of values computed using a frequency‐domain integral equation algorithm. Qualitative features of the results show that the relative importance of current channeling and confined eddy currents induced in the body depends upon both conductivity contrast and geometry. If the free‐space time constant is less than the time window during which currents in the host have not yet propagated well beyond the body, current channeling dominates the response. In such cases, simple superposition of free‐space results and the background is a poor approximation. In cases where the host currents diffuse beyond the body in a time less than the free‐space time constant of the body, the total response is approximately the sum of the free‐space and background (half‐space) responses.

The Simulation of Ship Motions Using a B-Spline–Based Panel Method in Time Domain

2007 ◽  
Vol 51 (03) ◽  
pp. 267-284
Author(s):  
Ranadev Datta ◽  
Debabrata Sen
Keyword(s):  
Time Domain ◽  
Three Dimensional ◽  
Basis Functions ◽  
The Body ◽  
Irregular Waves ◽  
Ship Motions ◽  
B Spline ◽  
Head Waves ◽  
Wigley Hull ◽  
Spline Basis

In this paper, a B-spline-based higher-order method is developed for simulating three-dimensional ship motions with forward speed. The problem is formulated in time domain using a transient free surface Green function. The body geometry is defined by open uniform or nonuniform B-spline basis functions depending on the hull type, whereas the unknown field variables are described by open uniform B-spline basis functions. The collocation method is applied to discretize the integral equation and then solved for the unknown potentials and source strengths. Motion computations in head waves are carried out for three types of ship hulls: a mathematically defined Wigley hull, a typical containership (S175 hull), and a Series 60 hull. Results are obtained for regular and irregular waves and compared with available experimental and computational results. It is found that the results from the present method are in very good agreement with the published results, and in particular with experimental data. Long-duration simulations have also been carried out with an ordinary desktop PC (PIV with 512 MB RAM) to demonstrate the ability of the method to simulate motions over long periods without any visible deterioration using only modest computational resources.

Higher Order Boundary Element Method Applied to the Hydrofoil Beneath the Free Surface

2009 ◽  
Author(s):  
Hassan Ghassemi ◽  
Ahmad Reza Kohansal ◽  
Abdollah Ardeshir
Keyword(s):  
Free Surface ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Wave Pattern ◽  
Higher Order ◽  
The Body ◽  
Hydrodynamic Characteristics ◽  
Good Agreement ◽  
Element Method

In this paper a three-dimensional numerical model using the higher order boundary element method (HOBEM) is developed to analyze hydrodynamic characteristics of hydrofoils beneath the free surface. The method uses combinations of the source and doublet by linear disctribution on each element of the body and free surface. The geometry of the element is represented by quadratic bilinear elements. The method is applied to three-dimensional hydrofoils of the symmetric Joukowski and NACA4412 profiles moving beneath the free surface in constant speed. Some results (pressure distribution, lift, wave-making drag and wave elevation and wave pattern) are presented. It is shown that this approach is accurate, efficient and the results are in good agreement with the experimental measurements and other calculated results.

Isogeometric Analysis Prediction of Stress Concentration Factor of Trivariate NURBS-Based Rectangular Plate with Central Elliptical Hole

2014 ◽  
Vol 556-562 ◽  
pp. 742-746
Author(s):  
Yusuf Olatunbosun Tafa ◽  
Gang Zhao ◽  
Wei Wang
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Isogeometric Analysis ◽  
Concentration Factor ◽  
Three Dimensional ◽  
Elliptical Hole ◽  
The Body ◽  
Geometric Discontinuities ◽  
Trivariate Nurbs ◽  
Good Agreement

Experimental, analytical and finite element techniques are commonly known methods used in determining highly localized stress occurring in the body under loading as a result of geometric discontinuities. In this study, we use NURBS-based isogeometric analysis (IGA) to investigate the stress concentration factor (SCF) on three-dimensional geometry with discontinuity feature. The results show that IGA technique is in good agreement with analytical values, thus providing a more effective realistic way of determining SCF.

Scanning electron microscopy of freeze-fractured prescapular lymph node of caprine

1984 ◽  
Vol 42 ◽  
pp. 244-245
Author(s):  
O. Faroon ◽  
F. Al-Bagdadi ◽  
T. G. Snider ◽  
C. Titkemeyer
Keyword(s):  
Lymph Node ◽  
Lymph Nodes ◽  
Lymphatic System ◽  
Three Dimensional ◽  
Meat Products ◽  
The Body ◽  
Morphological Data ◽  
The World ◽  
Cellular Constituent ◽  
Scanning Electron

The lymphatic system is very important in the immunological activities of the body. Clinicians confirm the diagnosis of infectious diseases by palpating the involved cutaneous lymph node for changes in size, heat, and consistency. Clinical pathologists diagnose systemic diseases through biopsies of superficial lymph nodes. In many parts of the world the goat is considered as an important source of milk and meat products.The lymphatic system has been studied extensively. These studies lack precise information on the natural morphology of the lymph nodes and their vascular and cellular constituent. This is due to using improper technique for such studies. A few studies used the SEM, conducted by cutting the lymph node with a blade. The morphological data collected by this method are artificial and do not reflect the normal three dimensional surface of the examined area of the lymph node. SEM has been used to study the lymph vessels and lymph nodes of different animals. No information on the cutaneous lymph nodes of the goat has ever been collected using the scanning electron microscope.

Single-peak-regulation and wide-angle dual-band metamaterial absorber based on hollow-cross and solid-cross resonators

2020 ◽  
Vol 91 (3) ◽  
pp. 30901
Author(s):  
Yibo Tang ◽  
Longhui He ◽  
Jianming Xu ◽  
Hailang He ◽  
Yuhan Li ◽  
...  
Keyword(s):  
Transverse Electric ◽  
Surface Current ◽  
Dielectric Substrate ◽  
Transverse Magnetic ◽  
Metamaterial Absorber ◽  
Absorption Peak ◽  
Dual Band ◽  
Single Peak ◽  
Wide Angle ◽  
Surface Current Density

A dual-band microwave metamaterial absorber with single-peak regulation and wide-angle absorption has been proposed and illustrated. The designed metamaterial absorber is consisted of hollow-cross resonators, solid-cross resonators, dielectric substrate and metallic background plane. Strong absorption peak coefficients of 99.92% and 99.55% are achieved at 8.42 and 11.31 GHz, respectively, which is basically consistent with the experimental results. Surface current density and changing material properties are employed to illustrate the absorptive mechanism. More importantly, the proposed dual-band metamaterial absorber has the adjustable property of single absorption peak and could operate well at wide incidence angles for both transverse electric (TE) and transverse magnetic (TM) waves. Research results could provide and enrich instructive guidances for realizing a single-peak-regulation and wide-angle dual-band metamaterial absorber.

A Free Energy Perturbation Approach to Estimate the Intrinsic Solubilities of Drug-like Small Molecules

2019 ◽  
Author(s):  
Sayan Mondal ◽  
Gary Tresadern ◽  
Jeremy Greenwood ◽  
Byungchan Kim ◽  
Joe Kaus ◽  
...  
Keyword(s):  
Solid State ◽  
Small Molecules ◽  
Three Dimensional ◽  
Aqueous Solubility ◽  
Computational Approach ◽  
Free Energy Perturbation ◽  
Perturbation Approach ◽  
Energy Perturbation ◽  
State Form ◽  
Good Agreement

<p>Optimizing the solubility of small molecules is important in a wide variety of contexts, including in drug discovery where the optimization of aqueous solubility is often crucial to achieve oral bioavailability. In such a context, solubility optimization cannot be successfully pursued by indiscriminate increases in polarity, which would likely reduce permeability and potency. Moreover, increasing polarity may not even improve solubility itself in many cases, if it stabilizes the solid-state form. Here we present a novel physics-based approach to predict the solubility of small molecules, that takes into account three-dimensional solid-state characteristics in addition to polarity. The calculated solubilities are in good agreement with experimental solubilities taken both from the literature as well as from several active pharmaceutical discovery projects. This computational approach enables strategies to optimize solubility by disrupting the three-dimensional solid-state packing of novel chemical matter, illustrated here for an active medicinal chemistry campaign.</p>

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