scholarly journals Improved Magnetotelluric Zohdy-Oldenburg Direct Inversion

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Hui Cao ◽  
Yun Liu ◽  
Kun Peng Wang
Keyword(s):  
Jacobian Matrix ◽  
Least Square ◽  
Ratio Method ◽  
Inversion Method ◽  
Model Parameters ◽  
Sparse Linear Systems ◽  
Linear Inversion ◽  
Direct Inversion ◽  
Rugged Topography ◽  
Linear Systems Of Equations

Based on researches of Baiyao (1995) and Zhang and Xu (2001), this paper proposes an improved 2D MT Zohdy-Oldenburg direct inversion method, in the least-square sense, embodying the features of Zohdy’s ratio method and Oldenburg’s difference method, in the condition of rugged topography, with phase information. It bypasses large calculations of the Jacobian matrix and large sparse linear systems of equations and enables direct modifications and comparisons of the model parameters. According to the calculation and analysis of examples, it shows faster convergence and higher precision. In contrast with the conventional linear inversion, the calculation speed of this new method can be increased by more than 10 times.

Non linear inversion of gravity gradients and the GGI gradiometer

2011 ◽  
Vol 3 (4) ◽  
Author(s):  
Manik Talwani
Keyword(s):  
Iterative Procedure ◽  
Least Square ◽  
Inversion Method ◽  
Gravity Gradients ◽  
Linear Inversion ◽  
Non Linear ◽  
Best Fitting ◽  
The Difference ◽  
Differential Curvature ◽  
Fitting Model

AbstractAll gradiometers currently operating for exploration in the field are based on Lockheed Martin’s GGI gradiometer. The working of this gradiometer is described and a method for robust non linear inversion of gravity gradients is presented. The inversion method involves obtaining the gradient response of a trial body consisting of vertical rectangular prisms. The inversion adjusts the depth to the tops or bases of the prisms. In the trial model all the prisms are not required to have the same area of cross section or the same density (which can also be allowed to vary with depth). The depth to the tops and bottoms of each prism can also be different. This response is compared with the observed values of gradient and through an iterative procedure, the difference is minimized in a least square sense to arrive at a best fitting model by varying the position of the tops or bottoms of the prisms. Each gradient can be individually inverted or one or more gradients can be jointly inverted. The method is extended to invert gravity values individually or jointly with gradient values. The use of Differential Curvature, a quantity which is directly obtained by current gradiometers in use and which is an invariant under a rotation in the horizontal plane, is emphasized. Synthetic examples as well as a field example of inversion are given.

scholarly journals A linear inversion method to infer exhumation rates in space and time from thermochronometric data

2014 ◽  
Vol 2 (1) ◽  
pp. 47-65 ◽  
Author(s):  
M. Fox ◽  
F. Herman ◽  
S. D. Willett ◽  
D. A. May
Keyword(s):  
Linear System ◽  
Resolving Power ◽  
Inversion Method ◽  
Model Parameters ◽  
Time Interval ◽  
Time Intervals ◽  
Linear Inversion ◽  
Exhumation Rate ◽  
Space And Time ◽  
Exhumation Rates

Abstract. We present a formal inverse procedure to extract exhumation rates from spatially distributed low temperature thermochronometric data. Our method is based on a Gaussian linear inversion approach in which we define a linear problem relating exhumation rate to thermochronometric age with rates being parameterized as variable in both space and time. The basis of our linear forward model is the fact that the depth to the "closure isotherm" can be described as the integral of exhumation rate, ..., from the cooling age to the present day. For each age, a one-dimensional thermal model is used to calculate a characteristic closure temperature, and is combined with a spectral method to estimate the conductive effects of topography on the underlying isotherms. This approximation to the four-dimensional thermal problem allows us to calculate closure depths for data sets that span large spatial regions. By discretizing the integral expressions into time intervals we express the problem as a single linear system of equations. In addition, we assume that exhumation rates vary smoothly in space, and so can be described through a spatial correlation function. Therefore, exhumation rate history is discretized over a set of time intervals, but is spatially correlated over each time interval. We use an a priori estimate of the model parameters in order to invert this linear system and obtain the maximum likelihood solution for the exhumation rate history. An estimate of the resolving power of the data is also obtained by computing the a posteriori variance of the parameters and by analyzing the resolution matrix. The method is applicable when data from multiple thermochronometers and elevations/depths are available. However, it is not applicable when there has been burial and reheating. We illustrate our inversion procedure using examples from the literature.

scholarly journals Direct inversion of the apparent complex‐resistivity spectrum

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1399-1404 ◽  
Author(s):  
J. Xiang ◽  
N. B. Jones ◽  
D. Cheng ◽  
F. S. Schlindwein
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Optimal Parameter ◽  
Geophysical Methods ◽  
Inversion Method ◽  
Model Parameters ◽  
Complex Resistivity ◽  
Direct Inversion ◽  
Optimal Parameter Estimation ◽  
Cole Model

Cole‐Cole model parameters are widely used to interpret electrical geophysical methods and are obtained by inverting the induced polarization (IP) spectrum. This paper presents a direct inversion method for parameter estimation based on multifold least‐squares estimation. Two algorithms are described that provide optimal parameter estimation in the least‐squares sense. Simulations demonstrate that both algorithms can provide direct apparent spectral parameter inversion for complex resistivity data. Moreover, the second algorithm is robust under reasonably high noise.

scholarly journals A linear inversion method to infer exhumation rates in space and time from thermochronometric data

2013 ◽  
Vol 1 (1) ◽  
pp. 207-259 ◽  
Author(s):  
M. Fox ◽  
F. Herman ◽  
S. D. Willett ◽  
D. A. May
Keyword(s):  
Linear System ◽  
Resolving Power ◽  
Inversion Method ◽  
Model Parameters ◽  
Time Interval ◽  
Time Intervals ◽  
Linear Inversion ◽  
Exhumation Rate ◽  
Space And Time ◽  
Exhumation Rates

Abstract. We present a formal inverse procedure to extract exhumation rates from spatially distributed low temperature thermochronometric data. Our method is based on a Gaussian linear inversion approach in which we define a linear problem relating exhumation rate to thermochronometric age with rates being parameterized as variable in both space and time. The basis of our linear forward model is the fact that the depth to the "closure isotherm" can be described as the integral of exhumation rate, ė, from the cooling age to the present day. For each age, a one-dimensional thermal model is used to calculate a characteristic closure temperature, and is combined with a spectral method to estimate the conductive effects of topography on the underlying isotherms. This approximation to the four-dimensional thermal problem allows us to calculate closure depths for datasets that span large spatial regions. By discretizing the integral expressions into time intervals we express the problem as a single linear system of equations. In addition, we assume that exhumation rates vary smoothly in space, and so can be described through a spatial correlation function. Therefore, exhumation rate history is discretized over a set of time intervals, but is spatially correlated over each time interval. We use an a priori estimate of the model parameters, in order to invert this linear system and obtain the maximum likelihood solution for the exhumation rate history. An estimate of the resolving power of the data is also obtained by computing the a posteriori variance of the parameters, and by analyzing the resolution matrix. Finally, we illustrate our inversion procedure using examples from the literature.

An improved nonlinear innovation-based parameter identification algorithm for ship models

2021 ◽  
pp. 1-9
Author(s):  
Baigang Zhao ◽  
Xianku Zhang
Keyword(s):  
Parameter Identification ◽  
Test Data ◽  
Stochastic Gradient ◽  
Least Square ◽  
Gradient Algorithm ◽  
Model Parameters ◽  
Identification Algorithm ◽  
Process Innovations ◽  
Stochastic Gradient Algorithm ◽  
Tangent Function

Abstract To solve the problem of identifying ship model parameters quickly and accurately with the least test data, this paper proposes a nonlinear innovation parameter identification algorithm for ship models. This is based on a nonlinear arc tangent function that can process innovations on the basis of an original stochastic gradient algorithm. A simulation was carried out on the ship Yu Peng using 26 sets of test data to compare the parameter identification capability of a least square algorithm, the original stochastic gradient algorithm and the improved stochastic gradient algorithm. The results indicate that the improved algorithm enhances the accuracy of the parameter identification by about 12% when compared with the least squares algorithm. The effectiveness of the algorithm was further verified by a simulation of the ship Yu Kun. The results confirm the algorithm's capacity to rapidly produce highly accurate parameter identification on the basis of relatively small datasets. The approach can be extended to other parameter identification systems where only a small amount of test data is available.

APPLICATIONS OF TWO NON-CENTRAL HYPERGEOMETRIC DISTRIBUTIONS OF BIASED SAMPLING STATISTICAL MODELS

2021 ◽  
Vol 4 (4) ◽  
pp. 415-424
Author(s):  
A. A. Issa ◽  
K. O. Adetunji ◽  
T. Alanamu ◽  
E. J. Adefila ◽  
K. A. Muhammed
Keyword(s):  
Statistical Models ◽  
Research Work ◽  
Hypergeometric Distribution ◽  
Biased Sampling ◽  
Inversion Method ◽  
Urn Model ◽  
Fisher Distribution ◽  
Direct Inversion ◽  
Mean And Variance ◽  
Hypergeometric Distributions

Statistical models of biased sampling of two non-central hypergeometric distributions Wallenius' and Fisher's distribution has been extensively used in the literature, however, not many of the logic of hypergeometric distribution have been investigated by different techniques. This research work examined the procedure of the two non-central hypergeometric distributions and investigates the statistical properties which includes the mean and variance that were obtained. The parameters of the distribution were estimated using the direct inversion method of hyper simulation of biased urn model in the environment of R statistical software, with varying odd ratios (w) and group sizes (mi). It was discovered that the two non - central hypergeometric are approximately equal in mean, variance and coefficient of variation and differ as odds ratios (w) becomes higher and differ from the central hypergeometric distribution with ω = 1. Furthermore, in univariate situation we observed that Fisher distribution at (ω = 0.2, 0.5, 0.7, 0.9) is more consistent than Wallenius distribution, although central hypergeometric is more consistent than any of them. Also, in multinomial situation, it was observed that Fisher distribution is more consistent at (ω = 0.2, 0.5), Wallenius distribution at (ω = 0.7, 0.9) and central hypergeometric at (ω = 0.2)    

FULL-WAVEFORM INVERSION WITH SOURCE AND RECEIVER COUPLING EFFECTS CORRECTION

Geophysics ◽  
2021 ◽  
pp. 1-37
Author(s):  
Xinhai Hu ◽  
Wei Guoqi ◽  
Jianyong Song ◽  
Zhifang Yang ◽  
Minghui Lu ◽  
...  
Keyword(s):  
Waveform Inversion ◽  
Nonlinear Least Squares ◽  
Real Data ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Linear Inversion ◽  
Near Surface ◽  
Model Parameter ◽  
Full Waveform ◽  
Coupling Factors

Coupling factors of sources and receivers vary dramatically due to the strong heterogeneity of near surface, which are as important as the model parameters for the inversion success. We propose a full waveform inversion (FWI) scheme that corrects for variable coupling factors while updating the model parameter. A linear inversion is embedded into the scheme to estimate the source and receiver factors and compute the amplitude weights according to the acquisition geometry. After the weights are introduced in the objective function, the inversion falls into the category of separable nonlinear least-squares problems. Hence, we could use the variable projection technique widely used in source estimation problem to invert the model parameter without the knowledge of source and receiver factors. The efficacy of the inversion scheme is demonstrated with two synthetic examples and one real data test.

scholarly journals Determining the AMSR-E SST Footprint from Co-located MODIS SSTs

2018 ◽  
Author(s):  
Brahim Boussidi ◽  
Peter Cornillon ◽  
Gavino Puggioni ◽  
Chelle Gentemann
Keyword(s):  
Aspect Ratio ◽  
Ground Truth ◽  
Major Axis ◽  
Sampling Procedure ◽  
Least Square ◽  
Gaussian Kernel ◽  
Bootstrap Sampling ◽  
Semi Major Axis ◽  
Linear Inversion ◽  
Precise Knowledge

This study was undertaken to derive and analyze the Advanced Microwave Scanning Radiometer - EOS (AMSR-E) sea surface temperature (SST) footprint associated with the Remote Sensing Systems (RSS) Level-2 (L2) product. The footprint, in this case, is characterized by the weight attributed to each 4 4 km square contributing to the SST value of a given AMSR-E pixel. High-resolution L2 SST fields obtained from the MODerate-resolution Imaging Spectroradiometer (MODIS), carried on the same spacecraft as AMSR-E, are used as the sub-resolution “ground truth“ from which the AMSR-E footprint is determined. Mathematically, the approach is equivalent to a linear inversion problem, and its solution is pursued by means of a constrained least square approximation based on the bootstrap sampling procedure. The method yielded an elliptic-like Gaussian kernel with an aspect ratio 1.58, very close to the AMSR-E 6.93GHz channel aspect ratio, 1.7. (The 6.93GHz channel is the primary spectral frequency used to determine SST.) The semi-major axis of the estimated footprint is found to be alignedwith the instantaneous field-of-view of the sensor as expected fromthe geometric characteristics of AMSR-E. Footprintswere also analyzed year-by-year and as a function of latitude and found to be stable – no dependence on latitude or on time. Precise knowledge of the footprint is central for any satellite-derived product characterization and, in particular, for efforts to deconvolve the heavily oversampled AMSR-E SST fields and for studies devoted to product validation and comparison. A preliminarly analysis suggests that use of the derived footprint will reduce the variance between AMSR-E and MODIS fields compared to the results obtained.

scholarly journals New Lindley Half Cauchy Distribution: Theory and Applications

2020 ◽  
Vol 9 (4) ◽  
pp. 1-7
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Cauchy Distribution ◽  
Least Square ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Model Parameters ◽  
Data Set ◽  
Von Mises

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.

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