Inversion of borehole normal resistivity logs

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1541-1548 ◽  
Author(s):  
Fang‐Wei Yang ◽  
Stanley H. Ward
Keyword(s):  
Theoretical Model ◽  
Ridge Regression ◽  
Arbitrary Number ◽  
Inverse Method ◽  
Apparent Resistivity ◽  
Random Noise ◽  
High Resistivity ◽  
Number Of Layers ◽  
Boundary Position ◽  
Resistivity Logs

This paper reports on an investigation of the inversion of borehole normal resistivity data via ridge regression. Interpretation is afforded of individual thin beds and of complicated layered structures. A theoretical solution is given for a layered model containing an arbitrary number of layers in the forward problem. Two forward model results for resistive and conductive thin beds indicate that for high‐resistivity contrasts, the departure between true and apparent resistivity may be more important than the effects caused by the variations in borehole diameter and mud resistivity. Four normal resistivity logs were chosen to test the inversion scheme. Two of the logs were theoretical logs with and without random noise added, and the remaining two were field examples. Theoretical model results and field examples indicate that the inverse method can be used to obtain the resistivity for each layer when the boundary position is known, but it also can be used to obtain the thickness and resistivity for each layer simultaneously.

INTERPRETATION OF MAGNETOTELLURIC RESISTIVITY AND PHASE SOUNDINGS OVER HORIZONTAL LAYERS

Geophysics ◽  
1976 ◽  
Vol 41 (1) ◽  
pp. 96-105 ◽  
Author(s):  
D. Patella
Keyword(s):  
Inverse Method ◽  
Apparent Resistivity ◽  
Layered Medium ◽  
Lower Boundary ◽  
Wave Impedance ◽  
Phase Lag ◽  
Master Curves ◽  
Number Of Layers ◽  
Electronic Calculator ◽  
Horizontal Layers

The present paper deals with a new inverse method for quantitatively interpreting magnetotelluric apparent resistivity and phase‐lag sounding curves over horizontally stratified earth sections. The recurrent character of the general formula relating the wave impedance of an (n−1)‐layered medium to that of an n‐layered medium suggests the use of the method of reduction to a lower boundary plane, as originally termed by Koefoed in the case of dc resistivity soundings. The layering parameters are so directly derived by a simple iterative procedure. The method is applicable for any number of layers but only when both apparent resistivity and phase‐lag sounding curves are jointly available. Moreover no sophisticated algorithm is required: a simple desk electronic calculator together with a sheet of two‐layer apparent resistivity and phase‐lag master curves are sufficient to reproduce earth sections which, in the range of equivalence, are all consistent with field data.

scholarly journals Inverse problem for tripotential measures in the study of buried cavities

1996 ◽  
Vol 39 (1) ◽  
Author(s):  
P. Cosentino ◽  
D. Luzio ◽  
R. Martorana
Keyword(s):  
Apparent Resistivity ◽  
Random Noise ◽  
Source Parameters ◽  
Spherical Shape ◽  
Average Diameter ◽  
Unknown Parameters ◽  
Fundamental Parameters ◽  
Spherical Models ◽  
Source Models ◽  
Biased Estimates

This paper presents a solution to the inverse electrical problem for the interpretation of apparent resistivity anomalies due to empty buried cavities of quasi-spherical shape when tripotential measures are carried out. The anomalies of the apparent resistivities ra,rb andrg,and the composed resistivitiesrmand rt were previously calculated for a sufficient class of spherical models of resistivity anomalies. Then, for the whole class of models, some functionals of spatial distribution of the apparent and composed resistivity were identified and analyzed. They represent the average characteristics of the anomalies and, depending in a simple way on the fundamental parameters of the sources of the anomalies (average diameter and depth), they allow reliable estimates to be determined. Among the studied functionals, those allowing the most stable and less biased estimates of the anomaly source parameters are identified by numerical simulations with random noise perturbed data. Finally the trend of standard deviation and bias of the estimates of the unknown parameters were analyzed by varying the source models and the set of functionals used for the inversion.

Exploration of permafrost with audiomagnetotelluric data for gas hydrates in the Juhugeng Mine of the Qilian Mountains, China

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. B247-B258 ◽  
Author(s):  
Bo Yang ◽  
Xiangyun Hu ◽  
Wule Lin ◽  
Shuang Liu ◽  
Hui Fang
Keyword(s):  
Gas Hydrates ◽  
Gas Hydrate ◽  
Qilian Mountains ◽  
High Resistivity ◽  
Electromagnetic Methods ◽  
Survey Technique ◽  
Resistivity Logs ◽  
Gas Hydrate Deposits ◽  
The Qilian Mountains ◽  
The Impact

In China, gas hydrates in onshore permafrost areas have so far only been found in the Juhugeng Mine of the Qilian Mountains. However, their subsurface distribution remains unclear. Electrical resistivity logs have revealed that zones containing gas hydrates have higher resistivity than surrounding zones, which makes electromagnetic methods viable for detecting gas-hydrate deposits. We have deployed a natural-source audio-magnetotelluric (AMT) survey at the Juhugeng Mine. AMT data were collected at 176 sites along five profiles, and resistivity models were derived from 2D inversions after detailed data analysis. After the available geologic and geophysical observations were combined, the inversion results from profile 1 suggested that permafrost near the surface with high resistivity and thickness is essential for underlying gas hydrates to be present. The decrease in resistivity and/or thickness of permafrost due to climate change may lead to gas-hydrate dissociation. The other four AMT transects suggested three prospective gas-hydrate sites. Our results indicate that the AMT survey technique is suitable for exploring gas hydrates in permafrost areas and analyzing the impact of permafrost characteristics on gas-hydrate occurrence.

scholarly journals Cloaking Using the Anisotropic Multilayer Sphere

Photonics ◽  
2020 ◽  
Vol 7 (3) ◽  
pp. 52 ◽  
Author(s):  
Sidra Batool ◽  
Mehwish Nisar ◽  
Fabrizio Frezza ◽  
Fabio Mangini
Keyword(s):  
Mathematical Model ◽  
Arbitrary Number ◽  
Static Approximation ◽  
Quasi Static Approximation ◽  
Number Of Layers ◽  
Multilayer Sphere ◽  
Tangential Directions

We studied a Spherically Radially Anisotropic (SRA) multilayer sphere with an arbitrary number of layers. Within each layer permittivity components are different from each other in radial and tangential directions. Under the quasi-static approximation, we developed a more generalized mathematical model that can be used to calculate polarizability of the SRA multilayer sphere with any arbitrary number of layers. Moreover, the functionality of the SRA multilayer sphere as a cloak has been investigated. It has been shown that by choosing a suitable contrast between components of the permittivity, the SRA multilayer sphere can achieve threshold required for invisibility cloaking.

SALT BED IDENTIFICATION FROM UNFOCUSED RESISTIVITY LOGS

Geophysics ◽  
1961 ◽  
Vol 26 (3) ◽  
pp. 320-341
Author(s):  
J. R. Lishman
Keyword(s):  
Electrical Resistivity ◽  
Apparent Resistivity ◽  
Borehole Diameter ◽  
Drilling Fluids ◽  
Characteristic Shape ◽  
Resistivity Logs

Salt beds have almost infinite electrical resistivity. They differ from other infinitely resistive beds in that they are usually soluble in drilling fluids, and give rise to enlarged boreholes. An infinitely resistive bed lying between shales may be recognized from the characteristic shape of the electric log resistivity curves, and the ratios of their readings. Any one of the curves may then be used to compute the borehole diameter, and hence decide whether the bed is salt. Where a washed out salt bed is adjacent to another infinitely resistive bed in which the borehole is to gauge, the configuration of the curves is very characteristic. Apparent resistivity ratios again help to identify the salt.

Magnetotelluric response on vertically inhomogeneous earth having conductivity varying exponentially with depth

Geophysics ◽  
1982 ◽  
Vol 47 (1) ◽  
pp. 89-99 ◽  
Author(s):  
D. Kao
Keyword(s):  
Half Space ◽  
Apparent Resistivity ◽  
Bessel Functions ◽  
Homogeneous Layer ◽  
Modified Bessel Functions ◽  
Layer Model ◽  
Transitional Layer ◽  
Number Of Layers ◽  
Inhomogeneous Models ◽  
Electric And Magnetic Fields

Magnetotelluric (MT) response is studied for a vertically inhomogeneous earth, where conductivity (or resistivity) varies exponentially with depth as [Formula: see text]. Horizontal electric and magnetic fields in such an inhomogeneous medium are given in terms of modified Bessel functions. Impedance and apparent resistivity are calculated for (1) an inhomogeneous half‐space having conductivity varying exponentially with depth, (2) an inhomogeneous half‐space overlain by a homogeneous layer, and (3) a three‐layer model with the second layer as an inhomogeneous or transitional layer. Results are presented graphically and are compared with those of homogeneous multilayer models. In the case of resistivity increasing exponentially with depth, the results of the above inhomogeneous models are equivalent to those of Cagniard two‐layer models, with [Formula: see text]. In the case of resistivity decreasing exponentially with depth, the homogeneous multilayer approximation depends upon the number of layers and the layer parameters chosen; |Z/ωμ| as a function of frequency is more useful than the apparent resistivity in determining the values of p and [Formula: see text].

scholarly journals Elément de poutre multicouche avec glissement d’interface

2007 ◽  
pp. 559-581
Author(s):  
Blaise Rebora ◽  
François Frey
Keyword(s):  
Arbitrary Number ◽  
Beam Element ◽  
Large Displacements ◽  
Corotational Formulation ◽  
Geometric Nonlinearities ◽  
Small Strains ◽  
Number Of Layers ◽  
Von Karman ◽  
Interlayer Slip ◽  
Von Kármán

This paper presents a multilayered two node planar beam element, straight or shallow, of Bernoulli type, with an arbitrary number of layers with interlayer slip. Material and geometric nonlinearities are included. Small strains and slips are assumed. Large displacements are dealt with von Karman strain coupled with corotational formulation. No locking appears. Various tests show the capabilities of this element.

scholarly journals Exploring the regolith with electrical resistivity tomography in largescale surveys: electrode spacing related issues and possibility

2020 ◽  
Author(s):  
Laurent Gourdol ◽  
Rémi Clément ◽  
Jérôme Juilleret ◽  
Laurent Pfister ◽  
Christophe Hissler
Keyword(s):  
Electrical Resistivity ◽  
Apparent Resistivity ◽  
Large Scale ◽  
Electrical Resistivity Tomography ◽  
Subsurface Layer ◽  
Electrode Spacing ◽  
High Resistivity ◽  
Constant Thickness ◽  
Resistivity Tomography

Abstract. Within the Critical Zone, regolith plays a key role in the fundamental hydrological functions of water collection, storage, mixing and release. Electrical Resistivity Tomography (ERT) is recognized as a remarkable tool for characterizing the geometry and properties of the regolith, overcoming limitations inherent to conventional borehole-based investigations. For exploring shallow layers, a small electrode spacing (ES) will provide a denser set of apparent resistivity measurements of the subsurface. As this option is cumbersome and time-consuming, smaller ES – albeit offering poorer shallow apparent resistivity data – are often preferred for large horizontal ERT surveys. To investigate the negative trade-off between larger ES and reduced accuracy of the inverted ERT images for shallow layers, we use a set of synthetic conductive/resistive/conductive three-layered soil–saprock/saprolite–bedrock models in combination with a reference field dataset. Our results suggest that an increase in ES causes a deterioration of the accuracy of the inverted ERT images in terms of both resistivity distribution and interface delineation and, most importantly, that this degradation increases sharply when the ES exceeds the thickness of the top subsurface layer. This finding, which is obvious for the characterization of shallow layers, is also relevant even when solely aiming for the characterization of deeper layers. We show that an oversized ES leads to overestimations of depth to bedrock and that this overestimation is even more important for subsurface structures with high resistivity contrast. To overcome this limitation, we propose adding interpolated levels of surficial apparent resistivity relying on a limited number of ERT profiles with a smaller ES. We demonstrate that our protocol significantly improves the accuracy of ERT profiles when using large ES, provided that the top layer has a rather constant thickness and resistivity. For the specific case of large-scale ERT surveys the proposed upgrading procedure is cost-effective in comparison to protocols based on small ES.

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