An adaptive inversion algorithm for one-dimensional magnetotelluric problems

2021 ◽  
Author(s):  
Huang Chen ◽  
Zhengyong Ren ◽  
Jingtian Tang
Keyword(s):  
Model Resolution ◽  
Inversion Algorithm ◽  
Sensitivity Matrix ◽  
One Dimensional ◽  
Error Estimators ◽  
Conductivity Model ◽  
Geometry Model ◽  
Number Of Layers ◽  
A Posterior Error ◽  
Earth Conductivity

<p>      As we know, the traditional one-dimensional (1-D) magnetotelluric (MT) regularization inversion needs the geometry model of the 1-D Earth conductivity model, i.e., the number of layers and the thickness of each layer to be given in advance and cannot be changed during the inversion. In this way, too few layers cannot approximate the 1-D conductivity model accurately, while too many layers will increase the non-uniqueness of the inversion problem and hence may result in unreasonable results. Aiming to solve this issue, an adaptive inversion algorithm has been proposed for 1-D MT problems, where the layer number and the thickness of each layer can be adjusted automatically during the inversion process. To this end, three pseudo a-posterior error estimators has been proposed to guide the adjustment of the 1D geometry model, which are based on the gradient of the data misfit term of the penalty function, the diagonal elements of the model resolution matrix, and the weighted elements of the sensitivity matrix, respectively. The inversion results of the synthetic and field data by using our proposal adaptive inversion algorithm and the traditional regularization inversion not only validate the proposed algorithm, but also show that our proposed algorithm can obtain more accurate and reasonable results than traditional one. Subsequently, the proposed algorithm will be extended for 3-D magnetotelluric inversion problems soon.</p>

Fast 3D magnetic inversion of a surface relief in the space domain

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. J57-J67 ◽  
Author(s):  
Marlon C. Hidalgo-Gato ◽  
Valéria C. F. Barbosa
Keyword(s):  
Hessian Matrix ◽  
Computational Cost ◽  
Magnetization Vector ◽  
Forward Modeling ◽  
Magnetic Data ◽  
Total Field ◽  
Inversion Algorithm ◽  
Sensitivity Matrix ◽  
Magnetic Inversion ◽  
Magnetic Basement

We have developed a fast 3D regularized magnetic inversion algorithm for depth-to-basement estimation based on an efficient way to compute the total-field anomaly produced by an arbitrary interface separating nonmagnetic sediments from a magnetic basement. We approximate the basement layer by a grid of 3D vertical prisms juxtaposed in the horizontal directions, in which the prisms’ tops represent the depths to the magnetic basement. To compute the total-field anomaly produced by the basement relief, the 3D integral of the total-field anomaly of a prism is simplified by a 1D integral along the prism thickness, which in turn is multiplied by the horizontal area of the prism. The 1D integral is calculated numerically using the Gauss-Legendre quadrature produced by dipoles located along the vertical axis passing through the prism center. This new magnetic forward modeling overcomes one of the main drawbacks of the nonlinear inverse problem for estimating the basement depths from magnetic data: the intense computational cost to calculate the total-field anomaly of prisms. The new sensitivity matrix is simpler and computationally faster than the one using classic magnetic forward modeling based on the 3D integrals of a set of prisms that parameterize the earth’s subsurface. To speed up the inversion at each iteration, we used the Gauss-Newton approximation for the Hessian matrix keeping the main diagonal only and adding the first-order Tikhonov regularization function. The large sparseness of the Hessian matrix allows us to construct and solve a linear system iteratively that is faster and demands less memory than the classic nonlinear inversion with prism-based modeling using 3D integrals. We successfully inverted the total-field anomaly of a simulated smoothing basement relief with a constant magnetization vector. Tests on field data from a portion of the Pará-Maranhão Basin, Brazil, retrieved a first depth-to-basement estimate that was geologically plausible.

A One-Dimensional Numerical Model for the Momentum Exchange in Regenerative Pumps

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Francis J. Quail ◽  
Matthew Stickland ◽  
Armin Baumgartner
Keyword(s):  
Experimental Data ◽  
Low Flow ◽  
Correction Factors ◽  
Momentum Exchange ◽  
Pump Design ◽  
Pump Performance ◽  
One Dimensional ◽  
Geometry Model ◽  
Wide Range ◽  
Dimensional Models

The regenerative pump is a rotor-dynamic turbomachine capable of developing high heads at low flow rates and low specific speeds. In spite of their low efficiency, usually less than 50%, they have found a wide range of applications as compact single-stage pumps with other beneficial features. The potential of a modified regenerative pump design is presented for the consideration of the performance improvements. In this paper the fluid dynamic behavior of the novel design was predicted using a one-dimensional model developed by the authors. Unlike most one-dimensional models previously published for regenerative pumps, the momentum exchange is numerically computed. Previous one-dimensional models relied on experimental data and correction factors; the model presented in this paper demonstrates an accurate prediction of the pump performance characteristics without the need for correction with experimental data. The validity of this approach is highlighted by the comparison of computed and measured results for two different regenerative pump standards. The pump performance is numerically assessed without the need of correction factors or other experimental data. This paper presents an approach for regenerative pumps using a physically valid geometry model and by resolving the circulatory velocity in the peripheral direction.

COMPARATIVE STUDY OF ONE-DIMENSIONAL PHOTONIC BANDGAP STRUCTURES USING MULTILAYER NONLINEAR THIN FILMS

1995 ◽  
Vol 04 (01) ◽  
pp. 1-11 ◽  
Author(s):  
Y. ZHAO ◽  
D. HUANG ◽  
C. WU ◽  
R. SHEN
Keyword(s):  
Thin Films ◽  
Comparative Study ◽  
Electromagnetic Radiation ◽  
Photonic Bandgap ◽  
One Dimensional ◽  
Number Of Layers ◽  
Quarter Wavelength ◽  
Visible Wavelength Range ◽  
Nonlinear Devices ◽  
Photonic Bandgap Structures

The transmission of electromagnetic radiation through the nonlinear one-dimensional photonic bandgap structure with different configurations are comparatively studied. It is found that the quarter-wavelength thickness arrangement gives rise to a wide window in the visible wavelength range. The modulated superlattice scheme only produces a number of narrow windows. The scheme using random layer thickness is expected to open a very wide window by making use of film nonlinearity when the number of layers is sufficient large. These nonlinear devices can be fabricated by using available materials.

Selection of Equations-of-State for Blast Attenuation

1971 ◽  
Vol 38 (1) ◽  
pp. 253-261 ◽  
Author(s):  
P. Lieberman
Keyword(s):  
Boundary Condition ◽  
Equations Of State ◽  
Rear Surface ◽  
Applied Pressure ◽  
Rigid Boundary ◽  
One Dimensional ◽  
Number Of Layers ◽  
State Boundary ◽  
Analytical Expressions ◽  
Selection Of

Blast shield materials are described by idealized equations-of-state in both one-dimensional loading and one-dimensional unloading. A square-wave applied pressure history is one boundary condition at the impingement surface of the material and, at the rear surface of the material(s), there is a stationary boundary condition. The objective is to select the equations-of-state that yield the greatest reduction in reflected stress at the rigid-boundary condition, for the smallest overall length, for application to a blast shield. One and two layers of material are considered. Idealizations of the equations-of-state, boundary conditions, length of each layer, and number of layers are arranged to yield simple analytical expressions for the relation of reflected stress to the overall length of the blast shield.

Reflectivity of 1D photonic crystals: A comparison of computational schemes with experimental results

2018 ◽  
Vol 32 (11) ◽  
pp. 1850136 ◽  
Author(s):  
J. S. Pérez-Huerta ◽  
D. Ariza-Flores ◽  
R. Castro-García ◽  
W. L. Mochán ◽  
G. P. Ortiz ◽  
...  
Keyword(s):  
Porous Silicon ◽  
Photonic Crystals ◽  
Spectral Line ◽  
Multilayer Structures ◽  
One Dimensional ◽  
Line Shapes ◽  
Number Of Layers ◽  
Reflectivity Spectra ◽  
Bloch Modes ◽  
Good Agreement

We report the reflectivity of one-dimensional finite and semi-infinite photonic crystals, computed through the coupling to Bloch modes (BM) and through a transfer matrix method (TMM), and their comparison to the experimental spectral line shapes of porous silicon (PS) multilayer structures. Both methods reproduce a forbidden photonic bandgap (PBG), but slowly-converging oscillations are observed in the TMM as the number of layers increases to infinity, while a smooth converged behavior is presented with BM. The experimental reflectivity spectra is in good agreement with the TMM results for multilayer structures with a small number of periods. However, for structures with large amount of periods, the measured spectral line shapes exhibit better agreement with the smooth behavior predicted by BM.

Linear inversion of body‐wave data—Part III: Model parameterization

Geophysics ◽  
1984 ◽  
Vol 49 (12) ◽  
pp. 2088-2093 ◽  
Author(s):  
M. Bée ◽  
R. S. Jacobson
Keyword(s):  
Velocity Gradient ◽  
Model Parameters ◽  
Model Resolution ◽  
Data Set ◽  
Model Parameterization ◽  
Number Of Layers ◽  
Gradient Model ◽  
Data Points ◽  
Constrained Model ◽  
Constrained Models

A velocity gradient model parameterized with the tau‐zeta inversion for seismic refraction data is examined with respect to a synthetic traveltime data set. The velocity‐depth model consists of a stack of laterally homogeneous layers, each with a constant velocity gradient. The free model parameters are the velocities of the layer bounds and the number of layers. The best velocity gradient solutions, i.e., with the least deviation from the true model, were obtained from “constrained” models in which the velocities of the layer bounds are the velocities of the observed refracted waves. An arbitrary selection of layer bound velocities was found to be a suboptimal choice of model parameterization for the tau‐zeta inversion. A trade‐off curve between model resolution and solution variance was constructed with the constrained model parameterization from examination of numerous solutions with a diverse number of layers. A constrained model with as many layers as observed data points represents a satisfactory compromise between model resolution and solution variance. Constrained models with more layers than observed data points, however, can increase the resolution of the velocity gradient model. If model resolution is favored over solution variance, a constrained model with many more layers than observed data points is therefore the best model parameterization with the tau‐zeta inversion technique.

Hindered and compression settling: parameter measurement and modelling

2007 ◽  
Vol 56 (12) ◽  
pp. 101-110 ◽  
Author(s):  
A.-E. Stricker ◽  
I. Takács ◽  
A. Marquot
Keyword(s):  
Dynamic Models ◽  
Settling Velocity ◽  
Data Set ◽  
One Dimensional ◽  
New Methods ◽  
Number Of Layers ◽  
Point Analysis ◽  
Empirical Function ◽  
Settling Performance ◽  
Capacity Rating

The Vesilind settling velocity function forms the basis of flux theory used both in state point analysis (for design and capacity rating) and one-dimensional dynamic models (for dynamic process modelling). This paper proposes new methods to address known shortcomings of these methods, based on an extensive set of batch settling tests conducted at different scales. The experimental method to determine the Vesilind parameters from a series of bench scale settling tests is reviewed. It is confirmed that settling cylinders must be slowly stirred in order to represent settling performance of full scale plants for the whole range of solids concentrations. Two new methods to extract the Vesilind parameters from settling test series are proposed and tested against the traditional manual method. Finally, the same data set is used to propose an extension to one-dimensional (1-D) dynamic settler models to account for compression settling. Using the modified empirical function, the model is able to describe the batch settling interface independently of the number of layers.

Terminal Length Dependent Transmission Spectra for One-Dimensional Photonic Crystals with a Centered Defect

2010 ◽  
Vol 663-665 ◽  
pp. 737-740 ◽  
Author(s):  
Yuan Ming Huang ◽  
Bao Gai Zhai ◽  
Yun Gao Cai ◽  
Qing Lan Ma
Keyword(s):  
Photonic Crystals ◽  
Band Gap ◽  
Stop Band ◽  
Characteristic Matrix ◽  
Frequency Range ◽  
Defect Band ◽  
Transmittance Spectra ◽  
One Dimensional ◽  
Number Of Layers ◽  
The One

The model of the one-dimensional photonic crystals (1-D PCs) with a centered defect with increasing number of layers was considered, and characteristic matrix method was used to calculate the transmittance spectra of the 1-D PCs. From the transmittance spectra, it shown that during the course of the number N of the layers of 1-D PCs’ one side symmetrical increased from 2 to 16, there occurred defect band gap in the stop band gap, when N upped to 16 , the defect band gap disappeared; besides, the defect band gap is at the frequencies around 0.30. In addition, in the progress of N increased from 3 to 16, the defect band gap reduced from the frequency range 0.0570 to 0.00, and the transmittance declined from 73.59% to 13.94% in the defect band gap.

scholarly journals High Sensitivity to Salinity-Temperature Using One-Dimensional Deformed Photonic Crystal

Coatings ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 713
Author(s):  
Naim Ben Ali ◽  
Haitham Alsaif ◽  
Youssef Trabelsi ◽  
Muhammad Tajammal Chughtai ◽  
Vigneswaran Dhasarathan ◽  
...  
Keyword(s):  
Detection Limit ◽  
Temperature Sensor ◽  
High Sensitivity ◽  
Fused Silica ◽  
Q Factor ◽  
Deformation Degree ◽  
One Dimensional ◽  
Number Of Layers ◽  
Structure Thickness ◽  
Quality Factor Q

This paper aims to theoretically study the concept of a photonic salinity and temperature sensor according to a deformed one-dimensional photonic structure. The fundamental capability of the proposed sensor is studied. Simultaneously we search to optimize the thickness of the structure and to get the maximum salinity and temperature sensitivity. The structure is constructed by alternating layers of TiO2 and fused-silica P times. In the middle of the structure, a cavity containing seawater is inserted to measure its salinity and temperature. The transfer matrix method (TMM) is used to simulate the wave-transmittance spectra. It is shown that the quality factor (Q-factor) of the resonance peaks depends on the number (P) of layers. After that, the thickness of the layers is deformed by changing the deformation degree (h). The parameters P and h are optimized to get the maximal Q-factor with the minimal number of layers and structure thickness. The best sensitivity SS of the proposed salinity sensor is 558.82 nm/RFIU with a detection limit of 0.0034 RFIU. In addition, the best sensitivity ST of the designed temperature sensor is 600 nm/RFIU with a detection limit of 0.0005 RFIU.

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