Conductivity-depth imaging of helicopter-borne TEM data based on a pseudolayer half-space model

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. F115-F120 ◽  
Author(s):  
Haoping Huang ◽  
Jonathan Rudd
Keyword(s):  
Half Space ◽  
Mineral Exploration ◽  
Synthetic Data ◽  
Depth Imaging ◽  
Space Model ◽  
Depth Images ◽  
Homogeneous Half Space ◽  
Time Domain Electromagnetic ◽  
Speed Up ◽  
Effective Depth

Helicopter-borne time-domain electromagnetic (HTEM) systems with a concentric horizontal coil configuration have been used increasingly in mineral exploration. Conductivity-depth imaging (CDI) is a useful tool for mapping the distribution of geologic conductivity and for identifying conductive targets. A CDI algorithm for HTEM systems with a concentric coil configuration is developed based on the pseudolayer half-space model. Primary advantages of this model are immunity to altimeter errors and better resolution of conductive layers than other half-space models. Effective depth is derived empirically from the diffusion depth and apparent thickness of the pseudolayer. A table lookup procedure is established based on the analytic solution of a half-space model to speed up processing. This efficiency makes generation of real-time conductivity-depth images possible. Tests on synthetic data demonstrate that the pseudolayer conductivity-depth-imaging algorithm maps a wider range of conduc-tivities and does a better job of resolving highly conductive layers, compared with that of the homogeneous half-space model. Effective depths are close to true depths in many circumstances. Field examples show stable and geologically meaningful conductivity-depth images.

Dielectric permittivity and resistivity mapping using high‐frequency, helicopter‐borne EM data

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 727-738 ◽  
Author(s):  
Haoping Huang ◽  
Douglas C. Fraser
Keyword(s):  
Dielectric Permittivity ◽  
Half Space ◽  
High Frequency ◽  
Free Space ◽  
Apparent Resistivity ◽  
Phase Component ◽  
High Frequencies ◽  
Space Model ◽  
Homogeneous Half Space ◽  
Displacement Currents

The interpretation of helicopter‐borne electromagnetic (EM) data is commonly based on the transformation of the data to the apparent resistivity under the assumption that the dielectric permittivity is that of free space and so displacement currents may be ignored. While this is an acceptable approach for many applications, it may not yield a reliable value for the apparent resistivity in resistive areas at the high frequencies now available commercially for some helicopter EM systems. We analyze the feasibility of mapping spatial variations in the dielectric permittivity and resistivity using a high‐frequency helicopter‐borne EM system. The effect of the dielectric permittivity on the EM data is to decrease the in‐phase component and increase the quadrature component. This results in an unwarranted increase in the apparent resistivity (when permittivity is neglected) for the pseudolayer half‐space model, or a decrease in the apparent resistivity for the homogeneous half‐space model. To avoid this problem, we use the in‐phase and quadrature responses at the highest frequency to estimate the apparent dielectric permittivity because this maximizes the response of displacement currents. Having an estimate of the apparent dielectric permittivity then allows the apparent resistivity to be computed for all frequencies. A field example shows that the permittivity can be well resolved in a resistive environment when using high‐frequency helicopter EM data.

On: “A grounded vertical long‐wire source system for plane wave magnetotelluric analog modeling” by R. N. Edwards (GEOPHYSICS, October 1980, p. 1523–1529).

Geophysics ◽  
1981 ◽  
Vol 46 (6) ◽  
pp. 934-935 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Plane Wave ◽  
Half Space ◽  
Radial Distance ◽  
Skin Depth ◽  
Space Model ◽  
Homogeneous Half Space ◽  
The Earth ◽  
Analog Modeling ◽  
Vertical Wire ◽  
Electrical Skin

In an interesting analysis, Edwards shows that a vertical long wire source will produce electromagnetic (EM) fields that satisfy simple impedance relationships for a homogeneous half‐space model of the earth. The important restriction is that the radial distance to the observer be large compared with an electrical skin depth. Certainly the vertical wire structures provide a very convenient modeling scheme for the “average prospector” to interpret magnetotelluric (MT) data collected over confined inhomogeneities within the conductive host region.

Inversion of slingram electromagnetic induction data using a Born approximation

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. E201-E212 ◽  
Author(s):  
Jochen Kamm ◽  
Michael Becken ◽  
Laust B. Pedersen
Keyword(s):  
Half Space ◽  
Born Approximation ◽  
High Efficiency ◽  
Three Dimensions ◽  
Background Model ◽  
Desktop Computer ◽  
Near Surface ◽  
Homogeneous Half Space ◽  
Integral Equation Formulation ◽  
Forward Operator

We present an efficient approximate inversion scheme for near-surface loop-loop EM induction data (slingram) that can be applied to obtain 2D or 3D models on a normal desktop computer. Our approach is derived from a volume integral equation formulation with an arbitrarily conductive homogeneous half-space as a background model. The measurements are not required to fulfill the low induction number condition (low frequency and conductivity). The high efficiency of the method is achieved by invoking the Born approximation around a half-space background. The Born approximation renders the forward operator linear. The choice of a homogeneous half-space yields closed form expressions for the required electromagnetic normal fields. It also yields a translationally invariant forward operator, i.e., a highly redundant Jacobian. In connection with the application of a matrix-free conjugate gradient method, this allows for very low memory requirements during the inversion, even in three dimensions. As a consequence of the Born approximation, strong conductive deviations from the background model are underestimated. Highly resistive anomalies are in principle overestimated, but at the same time difficult to resolve with induction methods. In the case of extreme contrasts, our forward model may fail in simultaneously explaining all the data collected. We applied the method to EM34 data from a profile that has been extensively studied with other electromagnetic methods and compare the results. Then, we invert three conductivity maps from the same area in a 3D inversion.

Quasi-2D inversion of DCR and TDEM data for shallow investigations

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. F239-F250 ◽  
Author(s):  
Fernando A. Monteiro Santos ◽  
Hesham M. El-Kaliouby
Keyword(s):  
Joint Inversion ◽  
Synthetic Data ◽  
Data Sets ◽  
Complex Environments ◽  
Inversion Algorithm ◽  
2D Inversion ◽  
New Approach ◽  
Earth Models ◽  
Time Domain Electromagnetic ◽  
Inversion Techniques

Joint or sequential inversion of direct current resistivity (DCR) and time-domain electromagnetic (TDEM) data commonly are performed for individual soundings assuming layered earth models. DCR and TDEM have different and complementary sensitivity to resistive and conductive structures, making them suitable methods for the application of joint inversion techniques. This potential joint inversion of DCR and TDEM methods has been used by several authors to reduce the ambiguities of the models calculated from each method separately. A new approach for joint inversion of these data sets, based on a laterally constrained algorithm, was found. The method was developed for the interpretation of soundings collected along a line over a 1D or 2D geology. The inversion algorithm was tested on two synthetic data sets, as well as on field data from Saudi Arabia. The results show that the algorithm is efficient and stable in producing quasi-2D models from DCR and TDEM data acquired in relatively complex environments.

Numerical seismograms obtained using ω-κ integrals, for a point P source in a vertically inhomogeneous anelastic model

1996 ◽  
Vol 86 (3) ◽  
pp. 750-760
Author(s):  
F. Abramovici ◽  
L. H. T. Le ◽  
E. R. Kanasewich
Keyword(s):  
Half Space ◽  
Homogeneous Layer ◽  
Variable Step Size ◽  
Step Size ◽  
Adaptive Process ◽  
Cpu Time ◽  
Homogeneous Half Space ◽  
Linear Layer ◽  
Variable Step ◽  
Viscoelastic Layers

Abstract This article presents some numerical experiments in using a computer program for calculating the displacements due to a P source in a vertically inhomogeneous structure, based on the Fourier-Bessel representation. The structure may contain homogeneous, inhomogeneous, elastic, or viscoelastic layers. The source may act in any type of sublayer or in the half-space. Synthetic results for the simple case of a homogeneous layer overlaying a homogeneous half-space compare favorably with computations based on the Cagniard method. Numerical seismograms for an elastic layer having velocities and density varying linearly with depth were computed by integrating numerically the governing differential systems and compared with results based on the Haskell model of splitting the linear layer in homogeneous sublayers. Even an adaptive process with a variable step size based on the Haskell model has a poorer performance on the accuracy-cpu time scale than numerical integration.

Surface-wave dispersion computations

1970 ◽  
Vol 60 (2) ◽  
pp. 321-344 ◽  
Author(s):  
Fred Schwab ◽  
Leon Knopoff
Keyword(s):  
Half Space ◽  
Rayleigh Waves ◽  
Wave Dispersion ◽  
Reduction Technique ◽  
Surface Wave Dispersion ◽  
Single Precision ◽  
Homogeneous Half Space ◽  
Full Control ◽  
Significant Figures ◽  
Rayleigh Wave Dispersion

abstract Fundamental-mode Love- and Rayleigh-wave dispersion computations for multilayered, perfectly-elastic media were studied. The speed of these computations was improved, and the accuracy brought under full control. With sixteen decimal digits employed in these computations, fifteen significant-figure accuracy was found possible with Love waves and twelve to thirteen figure accuracy with Rayleigh waves. In order to ensure that the computed dispersion is correct to a specified accuracy, say σ significant figures, (σ + 1)/4 wavelengths of layered structure must be retained above a homogeneous half-space. To this accuracy, the homogeneous half-space is a sufficient model of the true layering it replaces. Using this result, it was possible to refine the usual layer-reduction technique so as to ensure retention of the specified accuracy while employing reduction. With this reduction technique in effect, and with σ specified below single-precision accuracy, the program can be run entirely in single precision; the specified accuracy is maintained without overflow or loss-of-precision problems being encountered during calculations.

On the Similarity Search With Hamming Space Sketches

2021 ◽  
pp. 97-127
Author(s):  
Vladimir Mic ◽  
Pavel Zezula
Keyword(s):  
Computational Complexity ◽  
Metric Space ◽  
Similarity Search ◽  
Space Model ◽  
Similarity Query ◽  
Speed Up ◽  
Hamming Space ◽  
Definition Of ◽  
Metric Function ◽  
Selection Of

This chapter focuses on data searching, which is nowadays mostly based on similarity. The similarity search is challenging due to its computational complexity, and also the fact that similarity is subjective and context dependent. The authors assume the metric space model of similarity, defined by the domain of objects and the metric function that measures the dissimilarity of object pairs. The volume of contemporary data is large, and the time efficiency of similarity query executions is essential. This chapter investigates transformations of metric space to Hamming space to decrease the memory and computational complexity of the search. Various challenges of the similarity search with sketches in the Hamming space are addressed, including the definition of sketching transformation and efficient search algorithms that exploit sketches to speed-up searching. The indexing of Hamming space and a heuristic to facilitate the selection of a suitable sketching technique for any given application are also considered.

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