Inversion of inductive electromagnetic data in highly conductive terrains

Geophysics ◽  
2005 ◽  
Vol 70 (1) ◽  
pp. G16-G28 ◽  
Author(s):  
G. Schultz ◽  
C. Ruppel
Keyword(s):  
A Priori ◽  
Two Dimensions ◽  
Forward Model ◽  
Practical Applications ◽  
Shallow Subsurface ◽  
Subsurface Structures ◽  
Conductivity Structure ◽  
Actual Field ◽  
Priori Information ◽  
The Stability

Despite the increasing use of controlled-source frequency-domain EM data to characterize shallow subsurface structures, relatively few inversion algorithms have been widely applied to data from real-world settings, particularly in high-conductivity terrains. In this study, we develop robust and convergent regularized, least-squares inversion algorithms based on both linear and nonlinear formulations of mutual dipole induction for the forward problem. A modified version of the discrepancy principle based on a priori information is implemented to select optimal smoothing parameters that simultaneously guarantee the stability and best-fit criteria. To investigate the problems of resolution and equivalence, we consider typical layered-earth models in one and two dimensions using both synthetic and observed data. Synthetic examples show that inversions based on the nonlinear forward model more accurately resolve subsurface structure, and that inversions based on the linear forward model tend to drastically underpredict high conductivities at depth. Inversions of actual field data from well-characterized sites (e.g., National Geotechnical Experimentation Site; sand-dominated coastal aquifer in the Georgia Bight) are used to test the applicability of the model to terrains with different characteristic conductivity structure. A comparison of our inversion results with existing cone-penetrometer and downhole-conductivity data from these field sites demonstrates the ability of the inversions to constrain conductivity variations in practical applications.

The ILRS Contribution to ITRF2020

2021 ◽  
Author(s):  
Vincenza Luceri ◽  
Erricos C. Pavlis ◽  
Antonio Basoni ◽  
David Sarrocco ◽  
Magdalena Kuzmicz-Cieslak ◽  
...  
Keyword(s):  
Time Series ◽  
Tracking System ◽  
A Priori ◽  
Systematic Errors ◽  
Novel Approach ◽  
Priori Information ◽  
The Stability ◽  
The Individual ◽  
Stability And Consistency

<p>The International Laser Ranging Service (ILRS) contribution to ITRF2020 has been prepared after the re-analysis of the data from 1993 to 2020, based on an improved modeling of the data and a novel approach that ensures the results are free of systematic errors in the underlying data. This reanalysis incorporates an improved “target signature” model (CoM) that allows better separation of true systematic error of each tracking system from the errors in the model describing the target’s signature. The new approach was developed after the completion of ITRF2014, the ILRS Analysis Standing Committee (ASC) devoting almost entirely its efforts on this task. The robust estimation of persistent systematic errors at the millimeter level permitted the adoption of a consistent set of long-term mean corrections for data collected in past years, which are now applied a priori (information provided by the stations from their own engineering investigations are still taken into consideration). The reanalysis used these corrections, leading to improved results for the TRF attributes, reflected in the resulting new time series of the TRF origin and especially in the scale. Seven official ILRS Analysis Centers computed time series of weekly solutions, according to the guidelines defined by the ILRS ASC. These series were combined by the ILRS Combination Center to obtain the official ILRS product contribution to ITRF2020.</p><p>The presentation will provide an overview of the analysis procedures and models, and it will demonstrate the level of improvement with respect to the previous ILRS product series; the stability and consistency of the solution are discussed for the individual AC contributions and the combined SLR time series.</p>

Constraining electric resistivity tomography by direct push electric conductivity logs and vibracores: An exemplary study of the Fiume Morto silted riverbed (Ostia Antica, western Italy)

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. B87-B103 ◽  
Author(s):  
Tina Wunderlich ◽  
Peter Fischer ◽  
Dennis Wilken ◽  
Hanna Hadler ◽  
Ercan Erkul ◽  
...  
Keyword(s):  
A Priori ◽  
Electric Resistivity ◽  
Structural Constraints ◽  
Resistivity Tomography ◽  
Subsurface Structures ◽  
Direct Push ◽  
Ostia Antica ◽  
High Vertical Resolution ◽  
Ground Truthing ◽  
Priori Information

The inversion of geoelectric data is nonunique. Therefore, electric resistivity tomography (ERT) usually results in different subsurface models that fit observed apparent resistivity values equally well. To reduce the uncertainty, constraints on the geometry and resistivity of subsurface structures can be incorporated into the ERT inversion. We test different ways of constraining ERT by applying (1) improved starting models, (2) structural constraints, and (3) structural and resistivity constraints. A priori information is needed for these approaches, which is acquired from direct push electrical conductivity (DP-EC) logs and vibracores in our study. We found that adapting high vertical resolution of DP-EC logs to coarser ERT resolution requires blocking of the logs. These blocked logs can be used for constraining the ERT inversion with resistivity and structural constraints along so-called regions around the log locations, which was found to be the best approach. In this case, ground truthing with additional DP-EC logs that were not used for constraining showed the lowest root-mean-square error between logs and ERT model.

scholarly journals Regularization of the Factorization Method applied to diffuse optical tomography

2021 ◽  
Author(s):  
Isaac Harris
Keyword(s):  
A Priori ◽  
Optical Tomography ◽  
Diffuse Optical Tomography ◽  
Singular Values ◽  
Factorization Method ◽  
Complex Hilbert Space ◽  
Two Dimensions ◽  
Numerical Instabilities ◽  
Priori Information ◽  
Unknown Region

Abstract In this paper, we develop a new regularized version of the Factorization Method for positive operators mapping a complex Hilbert Space into it’s dual space. The Factorization Method uses Picard’s Criteria to define an indicator function to image an unknown region. In most applications the data operator is compact which gives that the singular values can tend to zero rapidly which can cause numerical instabilities. The regularization of the Factorization Method presented here seeks to avoid the numerical instabilities in applying Picard’s Criteria. This method allows one to image the interior structure of an object with little a priori information in a computationally simple and analytically rigorous way. Here we will focus on an application of this method to diffuse optical tomography where will prove that this method can be used to recover an unknown subregion from the Dirichlet-to-Neumann mapping. Numerical examples will be presented in two dimensions.

Practical applications of uniqueness theorems in gravimetry: Part II—Pragmatic incorporation of concrete geologic information

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 795-800 ◽  
Author(s):  
Valéria C. F. Barbosa ◽  
João B. C. Silva ◽  
Walter E. Medeiros
Keyword(s):  
Gravity Data ◽  
A Priori ◽  
Gravity Inversion ◽  
Solution Stability ◽  
Practical Applications ◽  
Density Distributions ◽  
Alternative Method ◽  
True Source ◽  
Priori Information ◽  
Simply Connected

We illustrate the importance of establishing solution uniqueness through mathematical restrictions reflecting a source attribute. We also illustrate the validity and utility of a guideline derived in an accompanying paper for constructing sound gravity inversion methods for the class of sources presenting either homogeneous or depth‐independent density distributions. The two‐part guideline is (1) to introduce a priori information favoring uniqueness, either by assuming that a nonnull density distribution depending only on x and y is confined to the interior of a horizontal slab with known position or by limiting the class of possible solutions to homogeneous, simply connected polygons (or polyhedra) with known density, displaying no fancy shapes and no curling apophyses at their borders, and (2) to introduce information favoring solution stability by estimating only the features of the source which may be resolved by the data. Following the guideline, we apply different methods to gravity data using interpretation models consisting of a grid of cells on the x‐y and x‐z planes. In both cases the estimates are very close to the true synthetic source. The data produced by the distribution varying with x and z are also inverted using the method, which minimizes the norm of the first‐order derivative of the density. This constraint does not reflect a true source attribute but is strong enough to stabilize the solution and to guarantee its uniqueness. Because of the strong bias imposed to the solution, the estimated distribution, although unique and stable, is far from the true source, concentrating most of the anomalous mass at the surface. Finally, we present an alternative method which redistributes the estimated anomalous mass downward. To be effective, this technique requires prior knowledge about the source depth to the top. In addition, the source should not be too small and deep. Although being able to produce good results, this alternative method requires a great dose of the interpreter's art.

User-Adaptable Comfort Control for HVAC Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 474-486 ◽  
Author(s):  
Clifford C. Federspiel ◽  
Haruhiko Asada
Keyword(s):  
Thermal Sensation ◽  
Human Subjects ◽  
A Priori ◽  
Hvac Systems ◽  
Lumped Parameter Model ◽  
New Approach ◽  
Tuning Parameters ◽  
Lumped Parameter ◽  
Priori Information ◽  
The Stability

This paper describes a new approach to the control of heating, ventilating, and air-conditioning (HVAC) systems. The fundamental concept of the new approach is that the controller learns to predict the actual thermal sensation of the specific occupant by tuning parameters of a model of the occupant’s thermal sensation. The parameters are adjusted with respect to thermal sensation ratings acquired from the specific occupant and measurements of physical variables that affect thermal sensation so that with time the model accurately reflects the thermal sensation of the specific occupant. From a lumped-parameter model of a singleroom enclosure, it is shown that the stability of the nominal system can be maintained by utilizing a priori information about the parameters of the thermal sensation model. The method is implemented on a ductless, split-system heat pump. Experiments using human subjects verify the feasibility of the method.

Practical applications of uniqueness theorems in gravimetry: Part I—Constructing sound interpretation methods

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 788-794 ◽  
Author(s):  
João B. C. Silva ◽  
Walter E. Medeiros ◽  
Valéria C. F. Barbosa
Keyword(s):  
Inverse Problem ◽  
A Priori ◽  
Stable Solution ◽  
Gravity Inversion ◽  
Uniqueness Theorems ◽  
A Priori Information ◽  
Practical Applications ◽  
Inversion Methods ◽  
Geological Information ◽  
Priori Information

To obtain a unique and stable solution to the gravity inverse problem, a priori information reflecting geological attributes of the gravity source must be used. Mathematical conditions to obtain stable solutions are established in Tikhonov's regularization method, where the a priori information is introduced via a stabilizing functional, which may be suitably designed to incorporate some relevant geological information. However, there is no unifying approach establishing general uniqueness conditions for a gravity inverse problem. Rather, there are many theorems, usually establishing just abstract mathematical conditions and making it difficult to devise the type of geological information needed to guarantee a unique solution. In Part I of these companion papers, we show that translating the mathematical uniqueness conditions into geological constraints is an important step not only in establishing the type of geological setting where a particular method may be applied but also in designing new gravity inversion methods. As an example, we analyze three uniqueness theorems in gravimetry restricted to the class of homogeneous bodies with known density and show that the uniqueness conditions established by them are more probably met if the solution is constrained to be a compact body without curled protrusions at their borders. These conditions, together with stabilizing conditions (assuming a simple shape for the source), form a guideline to construct sound gravity inversion methods. A historical review of the gravity interpretation methods shows that several methods implicitly follow this guideline. In Part II we use synthetic examples to illustrate the theoretical results derived in Part I. We also illustrate that the presented guideline is not the only way to design sound inversion methods for the class of homogeneous bodies. We present an alternative approach which produces good results but whose design requires a good dose of the interpreter's art.

Effects of Mandrel, Borehole, and Invasion for Tilt-Coil Antennas

2005 ◽  
Vol 8 (03) ◽  
pp. 255-263 ◽  
Author(s):  
Teruhiko Hagiwara ◽  
Erik J. Banning ◽  
Richard M. Ostermeier ◽  
Mark S. Haugland
Keyword(s):  
A Priori ◽  
Finite Size ◽  
Depositional Environments ◽  
Forward Model ◽  
Point Dipole ◽  
A Priori Information ◽  
Cylindrical Structure ◽  
Resistivity Measurements ◽  
Priori Information ◽  
Drill Collar

Summary Several recently published studies discuss the concept of inductive resistivity-logging devices with oblique transmitting and/or receiving coils. Both wireline induction and logging-while-drilling (LWD) propagation resistivity-tool concepts have been considered. Directional resistivity measurements and improved anisotropy measurements are among the benefits promised by this type of device. Analyses based on point-magnetic dipole antennas were used to illustrate these potential benefits. The effects of a metallic mandrel, borehole, and invasion were not considered because of the absence of a suitable forward model. This paper characterizes mandrel, borehole, and invasion effects for a variety of candidate tilt-coil devices with antenna array parameters similar to those of the previous studies. The characterization is based on calculations from a new forward model that includes tilted transmitting and receiving coils of finite diameter embedded in a concentric cylindrical structure. Important details of the forward model used in the calculations are also provided. Introduction Conventional propagation resistivity devices are routinely used for geosteering applications. Because data from these devices have essentially no azimuthal sensitivity, the LWD engineer is greatly aided by a priori information regarding the proximity of the target bed relative to other geologic features such as shales and water-bearing zones. Suitable a priori information is often available from offset logs. In cases in which offset logs are not fully useful because of changing depositional environments or different tectonic settings, azimuthally sensitive resistivity data would improve the quality of the geosteering effort. One way to achieve azimuthal sensitivity to benefit geo-steering (and to use it for imaging) is to construct a tool similar to a conventional propagation resistivity device, but with the transmitters and/or receivers tilted with respect to the axis of the drill collar. In fact, directional resistivity tools(DRTs) have been proposed in the literature for this pur-pose.1–3 To the knowledge of the authors, DRTs have only been analyzed with point-dipolemodels, which ignore both the drill collar and the finite size of the antennas. For apparent lack of a suitable forward model, mandrel, borehole, and invasion effects have not been considered in the literature. A model has been developed that accounts for tilted transmitters and receivers embedded in arbitrary layers of a concentric cylindrical structure. Many important details of this model are discussed in Appendix A. The term mandrel effect is used here to denote the difference between values calculated with a point-dipole model and the model that accounts for the mandrel encompassed by the antennas. Mandrel effects on DRT measurements will be grouped into three categories:Absolute effects where the mandrel primarily attenuates the signals because of a reduction in the magnetic moment of the antennas.Residual effects that remain after an air-hang calibration is applied to the data.Perturbations to the azimuthal sensitivity of the measurement caused by the finite size of the antennas and the drill collar. Algorithms that transform raw tool measurements to resistivity values can be based on computationally simple point-dipole solutions without significantly degrading the accuracy of the results if mandrel effects associated with categories 1 and 2 can be suppressed. For conventional LWD propagation resistivity measurements, mandrel effects of type 1 are addressed by air-hang calibration. Algorithms that suppress type 2 mandrel effects are discussed in the literature.4 Type 3 mandrel effects are not discussed here.

Innovative Approach to Information Search by Example of a Patent Analysis of an Important Substitution Plan

2020 ◽  
pp. 143-157
Author(s):  
Maria A. Milkova
Keyword(s):  
Information Search ◽  
Topic Modeling ◽  
Cognitive Biases ◽  
A Priori ◽  
Import Substitution ◽  
Innovative Approach ◽  
Iterative Search ◽  
Comprehensive Picture ◽  
Priori Information ◽  
Selection Of

Nowadays the process of information accumulation is so rapid that the concept of the usual iterative search requires revision. Being in the world of oversaturated information in order to comprehensively cover and analyze the problem under study, it is necessary to make high demands on the search methods. An innovative approach to search should flexibly take into account the large amount of already accumulated knowledge and a priori requirements for results. The results, in turn, should immediately provide a roadmap of the direction being studied with the possibility of as much detail as possible. The approach to search based on topic modeling, the so-called topic search, allows you to take into account all these requirements and thereby streamline the nature of working with information, increase the efficiency of knowledge production, avoid cognitive biases in the perception of information, which is important both on micro and macro level. In order to demonstrate an example of applying topic search, the article considers the task of analyzing an import substitution program based on patent data. The program includes plans for 22 industries and contains more than 1,500 products and technologies for the proposed import substitution. The use of patent search based on topic modeling allows to search immediately by the blocks of a priori information – terms of industrial plans for import substitution and at the output get a selection of relevant documents for each of the industries. This approach allows not only to provide a comprehensive picture of the effectiveness of the program as a whole, but also to visually obtain more detailed information about which groups of products and technologies have been patented.

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