3-D analytic signal in the interpretation of total magnetic field data at low magnetic latitudes
TL;DR: In this article, it was shown that the amplitude of the analytic signal is dependent on magneti-sation strength and the direction of geological strike with respect to the magnetisation vector, this dependency is easier to deal with in the interpretation of analytic signal amplitude than in the original total field data or pole-reduced magnetic field.
Abstract: The interpretation of magnetic field data at low magnetic latitudes is difficult because the vector nature of the magnetic field increases the complexity of anomalies from magnetic rocks. The most obvious approach to this problem is to reduce the data to the magnetic pole (RTP), where the presumably vertical magnetisation vector will simplify observed anomalies. However, RTP requires special treatment of north-south features in data observed in low magnetic latitudes due to high amplitude corrections of such features. Furthermore, RTP requires the assumption of induced magnetisation with the result that anomalies from remanently and anisotropically magnetised bodies can be severely disturbed. The amplitude of the 3-D analytic signal of the total magnetic field produces maxima over magnetic contacts regardless of the direction of magnetisation. The absence of magnetisation direction in the shape of analytic signal anomalies is a particularly attractive characteristic for the interpretation of magnetic field data near the magnetic equator. Although the amplitude of the analytic signal is dependent on magnetisation strength and the direction of geological strike with respect to the magnetisation vector, this dependency is easier to deal with in the interpretation of analytic signal amplitude than in the original total field data or pole-reduced magnetic field. It is also straightforward to determine the depth to sources from the distance between inflection points of analytic signal anomalies.
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TL;DR: A GIS-based application of a radial basis functional link net (RBFLN) to map the potential of SEDEX-type base metal deposits in a study area in the Aravalli metallogenic province (western India) demarcates successfully high favorability zones.
Abstract: This paper describes a GIS-based application of a radial basis functional link net (RBFLN) to map the potential of SEDEX-type base metal deposits in a study area in the Aravalli metallogenic province (western India). Available public domain geodata of the study area were processed to generate evidential maps, which subsequently were encoded and combined to derive a set of input feature vectors. A subset of feature vectors with known targets (i.e., either known mineralized or known barren locations) was extracted and divided into (a) a training data set and (b) a validation data set. A series of RBFLNs were trained to determine the network architecture and estimate parameters that mapped the maximum number of validation vectors correctly to their respective targets. The trained RBFLN that gave the best performance for the validation data set was used for processing all feature vectors. The output for each feature vector is a predictive value between 1 and 0, indicating the extent to which a feature vector belongs to either the mineralized or the barren class. These values were mapped to generate a predictive classification map, which was reclassified into a favorability map showing zones with high, moderate and low favorability for SEDEX-type base metal deposits in the study area. The method demarcates successfully high favorability zones, which occupy 6% of the study area and contain 94% of the known base metal deposits.
219 citations
TL;DR: In this article, a new automatic method of interpretation of magnetic data, called AN-EUL (pronounced "an oil") is presented, which is based on a combination of the analytic signal and the Euler deconvolution methods.
Abstract: We present a new automatic method of interpretation of magnetic data, called AN-EUL (pronounced “an oil”). The derivation is based on a combination of the analytic signal and the Euler deconvolution methods. With AN-EUL, both the location and the approximate geometry of a magnetic source can be deduced. The method is tested using theoretical simulations with different magnetic models placed at different depths with respect to the observation height. In all cases, the method estimated the locations and the approximate geometries of the sources. The method is tested further using ground magnetic data acquired above a shallow geological dike whose source parameters are known from drill logs, and also from airborne magnetic data measured over a known ferrometallic object. In both these cases, the method correctly estimated the locations and the nature of these sources.
168 citations
Book•
01 Apr 2014TL;DR: A state-of-the-art overview of geophysical methods can be found in this paper, where the authors take readers from the basic physical phenomena, through the acquisition and processing of data, to the creation of geological models of the subsurface and data interpretation to find hidden mineral deposits.
Abstract: Providing a balance between principles and practice, this state-of-the-art overview of geophysical methods takes readers from the basic physical phenomena, through the acquisition and processing of data, to the creation of geological models of the subsurface and data interpretation to find hidden mineral deposits. Detailed descriptions of all the commonly used geophysical methods are given, including gravity, magnetic, radiometric, electrical, electromagnetic and seismic methods. Each technique is described in a consistent way and without complex mathematics. Emphasising extraction of maximum geological information from geophysical data, the book also explains petrophysics, data modelling and common interpretation pitfalls. Packed with full-colour figures, also available online, the text is supported by selected examples from around the world, including all the major deposit types. Designed for advanced undergraduate and graduate courses in minerals geoscience, this is also a valuable reference for professionals in the mining industry wishing to make greater use of geophysical methods. In 2015, Dentith and Mudge won the ASEG Lindsay Ingall Memorial Award for their combined effort in promoting geophysics to the wider community with the publication of this title.
160 citations
TL;DR: The concept of the analytic signal goes back at least to Ville (1948) and has been applied to potential field data in two dimensions as mentioned in this paper, where the horizontal and vertical derivatives of a potential field are a Hilbert transform pair.
Abstract: The concept of the analytic signal goes back at least to Ville (1948). The analytic signal a ( x ) of function f ( x ) is a complex quantity defined as where H [ f ( x ) ] represents the Hilbert transform of f ( x ) . Nabighian (1972, 1974) applies the analytic signal concept to potential-field data in two dimensions. For a potential field ϕ ( x ) measured along the x -axis at a constant observation height z and generated by a 2D source aligned parallel to the y -axis, the horizontal derivative ϕ x and the vertical derivative ϕ z are a Hilbert transform pair.
155 citations
Cites background from "3-D analytic signal in the interpre..."
...“It is well known ( MacLeod et al., 1993 ) that the analytic signal [equation 4 in this note] is insensitive to the direction of magnetization....
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...The prospect of an alternative, direct route to edge detection might have been the driving force for different groups that suggested using the ASA of the total magnetic intensity ( MacLeod et al., 1993; Milligan and Gunn, 1997; Rajagopalan, 2003)....
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CGG1
TL;DR: In this paper, an improved version of the Source Parameter ImagingTM (SPITM) method is proposed to estimate the depth to the top of the structure of a magnetic field.
Abstract: Interpretation of an anomalous magnetic response involves determining the parameters that characterize the source of the anomaly. The depth to the top of the structure is a parameter that is commonly sought, and the Source Parameter ImagingTM (SPITM) method is one way of determining this depth estimate. One advantage of the SPI method is that the depths can be displayed on an image. Typically there can be one image for an assumed contact (fault) model and another image for an assumed dipping thin sheet (dike) model. The depth estimate obtained will depend on the model assumed. An improvement to the source parameter imaging method extends the method to horizontal cylinders and at the same time allows the most appropriate model to be determined automatically. This model can be displayed on an image and the correct depth estimate for each anomaly can also be determined. The depth estimates can therefore be summarized on one map independent of an assumed model. The images generated from synthetic and field data show that the improved SPI method makes the task of interpreting magnetic data significantly easier.
149 citations
References
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TL;DR: In this article, a simple transformation in the frequency domain yields an analytic function whose real part is the horizontal derivative of the field profile and whose imaginary part is vertical derivative of field profile.
Abstract: This paper presents a procedure to resoive magnetic anomalies due to two-dimensional structures. The method assumes that all causative bodies have uniform magnetization and a crosssection which can be represented by a polygon of either finite or infinite depth extent. The horizontal derivative of the field profile transforms the magnetization effect of these bodies of polygonal cross-section into the equivalent of thin magnetized sheets situated along the perimeter of the causative bodies A simple transformation in the frequency domain yields an analytic function whose real part is the horizontal derivative of the field profile and whose imaginary part is the vertical derivative of the field profile. The latter can also be recognized as the Hilbert transform of the former. The procedure yields a fast and accurate way of computing the vertical derivative from a given profile. For the case of a single sheet, the amplitude of the analytic function can be represented by a symmetrical function maximizing exactly over the top of the sheet. For the case of bodies with poiygonal cross-section, such symmetrical amplitude functions can be recognized over each corner of each polygon. Reduction to the pole, if desired, can be accomplished by a simple integration of the analytic function, without any cumbersome transformations. Narrow dikes and thin ilat sheets, of thickness less than depth, where the equivalent magnetic sheets are close together, are treated in the same fashion using the field intensity as input data, rather than the horizontal derivative. The method can be adapted straightforwardly for computer treatment. It is also shown that the analytic signal can be interpreted to represent a complex “field intensity,” derivable by differentiation from a complex “potential.” This function has simple poles at each polygon corner. Finally, the Fourier spectrum due to finite or infinite thin sheets and steps is given in the Appendix.
1,144 citations
"3-D analytic signal in the interpre..." refers background in this paper
...D magnetic contact located at (x=0) and at depth h is described by the expression (after Nabighian, 1972): ( ) 2122 1)( xh xA + = α Equation 4 Where: α is the amplitude factor α = −2 1 2 2M d I Asin ( cos ( ) sin ( )) Equation 5 and h is the depth to the top of the contact M is the strength of…...
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...D analytic signal calculated from the total magnetic field (Nabighian, 1972, Roest, 1992, MacLeod, 1993) as a practical alternative to reduction to the pole from low magnetic latitudes....
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...D Analytic Signal Nabighian (1972, 1984) developed the notion of 2-...
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TL;DR: In this article, a new method for magnetic interpretation based on the generalization of the analytic signal concept to three dimensions was developed, where the absolute value of the signal is defined as the square root of the squared sum of the vertical and the two horizontal derivatives of the magnetic field.
Abstract: A new method for magnetic interpretation has been developed based on the generalization of the analytic signal concept to three dimensions. The absolute value of the analytic signal is defined as the square root of the squared sum of the vertical and the two horizontal derivatives of the magnetic field. This signal exhibits maxima over magnetization contrasts, independent of the ambient magnetic field and source magnetization directions. Locations of these maxima thus determine the outlines of magnetic sources. Under the assumption that the anomalies are caused by vertical contacts, the analytic signal is used to estimate depth using a simple amplitude half-width rule. Two examples are shown of the application of the method. In the first example, the analytic signal highlights a circular feature beneath Lake Huron that has been identified as a possible impact crater. The second example illustrates the continuation of terranes across the Cabot Strait between Cape Breton and Newfoundland in eastern Canada.
1,029 citations
"3-D analytic signal in the interpre..." refers methods in this paper
...Atchuta et al (1981) and Roest et al (1992) used the anomaly width at half the amplitude to derive the depths....
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...Automated methods similar to those described by Roest et al (1992) can also be applied to produce depth maps....
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TL;DR: In this paper, the authors describe a method of interpretation based on a transformation of the total magnetic intensity anomalies into simpler anomalies, and the result of this transformation is the elimination of the distortion due to the obliquity of the normal magnetic field, so that the resulting anomalies will be located on the vertical of the disturbing magnetized bodies.
Abstract: The purpose of this paper is to describe a method of interpretation based on a transformation of the total magnetic intensity anomalies into simpler anomalies. The result of this transformation is the elimination of the distortion due to the obliquity of the normal magnetic field, so that the resulting anomalies will be located on the vertical of the disturbing magnetized bodies. The starting point of the theory is the well known relation between magnetic potential V and Newtonian potential U—relation which can be written: I→⋅grad⟶U=fσ⋅V, with: I→ = magnetization, f = 66.7×10−9 u ⋅CGS, σ = assumed density of magnetized bodies. This relation may be considered as a partial differential equation. The boundary condition consists in the measured values of the total field T(P ) known at each point P at the datum plane. As T(P) is the derivative of a harmonic function V, we can determine this function everywhere above the datum plane. Solving then the partial differential equation, we find the Newtonian potentia...
582 citations
"3-D analytic signal in the interpre..." refers methods in this paper
...Baranov (1957) proposed converting 2-D magnetic data to 'pseudo-gravity' using a process that involves reduction to the pole (RTP) and vertical integration....
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...Baranov (1957) proposed converting 2-...
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TL;DR: In this paper, the authors generalized the 2D Cauchy-Riemann relations between a potential function and its Hilbert transform for the 3D case and showed that the vertical and horizontal derivatives are the Hilbert transforms of each other.
Abstract: The paper extends to three dimensions (3-D) the two‐dimensional (2-D) Hilbert transform relations between potential field components. For the 3-D case, it is shown that the Hilbert transform is composed of two parts, with one part acting on the X component and one part on the Y component. As for the previously developed 2-D case, it is shown that in 3-D the vertical and horizontal derivatives are the Hilbert transforms of each other. The 2-D Cauchy‐Riemann relations between a potential function and its Hilbert transform are generalized for the 3-D case. Finally, the previously developed concept of analytic signal in 2-D can be extended to 3-D as a first step toward the development of an automatic interpretation technique for potential field data.
534 citations
Additional excerpts
...D Analytic Signal Nabighian (1972, 1984) developed the notion of 2-...
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TL;DR: In this paper, the horizontal derivative T(x) of the field profile, whether horizontal, vertical, or total field component, is used for the interpretation of potential field data.
Abstract: In a previous paper (Nabighian, 1972), the concept of analytic signal of bodies of polygonal cross‐section was introduced and its applications to the interpretation of potential field data were discussed. The input data for the proposed treatment are the horizontal derivative T(x) of the field profile, whether horizontal, vertical, or total field component. As it is known, this derivative curve can be thought of as being due to thin magnetized sheets surrounding the causative bodies.
422 citations