On: “Magnetic interpretation using the 3-D analytic signal” (Walter R. Roest, Jacob Verhoef, and Mark Pilkington, GEOPHYSICS, 57, 116–125)

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 667-670 ◽  
Author(s):  
Huang Lin‐ping ◽  
Guan Zhi‐ning
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Vertical Gradient ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Magnetic Interpretation ◽  
Vertical Derivative ◽  
Horizontal Gradients ◽  
High Resolution Technique ◽  
Basic Concepts

Over the last decades increasing interest has been expressed for determining boundaries and depths by using the analytic signal. The basic concepts of the analytic signal in 2-D case for magnetic data were extensively discussed by Nabighian (1972, 1974). Roest et al. (1992) discussed a new method for magnetic interpretation based on the generalization of analytic signal concept to 3-D. They considered that the analytic signal exhibits maxima over magnetization contrasts, independent of the ambient magnetic field, and source magnetization directions and locations of these maxima thus determine the outlines of magnetic sources. Afterward, Hsu et al. (1996) adopted a high‐resolution technique (also related to analytic signal) to image geologic boundaries such as contacts and faults. The outlines of the geologic boundaries can be determined by tracing the maximum amplitudes of an enhanced analytic signal composed of the nth‐order vertical derivative values of two horizontal gradients and one vertical gradient.

High‐resolution detection of geologic boundaries from potential‐field anomalies: An enhanced analytic signal technique

Geophysics ◽  
1996 ◽  
Vol 61 (2) ◽  
pp. 373-386 ◽  
Author(s):  
Shu‐Kun Hsu ◽  
Jean‐Claude Sibuet ◽  
Chuen‐Tien Shyu
Keyword(s):  
High Resolution ◽  
Potential Field ◽  
Amplitude Ratio ◽  
Okinawa Trough ◽  
Vertical Gradient ◽  
Analytic Signal ◽  
Magnetic Data ◽  
The Okinawa Trough ◽  
Simple Estimation ◽  
The City

A high‐resolution technique is developed to image geologic boundaries such as contacts and faults. The outlines of the geologic boundaries can be determined by tracing the maximum amplitudes of an enhanced analytic signal composed of the nth‐order vertical derivative values of two horizontal gradients and one vertical gradient. The locations of the maximum amplitudes are independent of the ambient potential field. This technique is particularly suitable when interference effects are considerable and/or when both induced and remanent magnetizations are not negligible. The corresponding depth to each geologic boundary can be estimated from the amplitude ratio of the enhanced and the simple analytic signals, which provides a simple estimation Such a method has been applied to magnetic data acquired in the Ilan Plain of Taiwan located at the southwestern end of the Okinawa Trough. The quantitative analysis shows that the underlying geologic boundaries deepen southward and slightly eastward. The enlargement of the Ilan Plain in the direction of the Okinawa Trough and the existence of north‐northwest and west‐northwest trending faults near the city of Ilan reveal a discontinuity between the Okinawa Trough backarc extension and the compressional process in Taiwan.

Automatic 3-D interpretation of potential field data using analytic signal derivatives

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 87-96 ◽  
Author(s):  
Nicole Debeglia ◽  
Jacques Corpel
Keyword(s):  
Signal Amplitude ◽  
Vertical Gradient ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Practical Implementation ◽  
Potential Field Data ◽  
Gravity And Magnetic ◽  
Second Derivatives ◽  
Gravity And Magnetic Data ◽  
Derivatives Of

A new method has been developed for the automatic and general interpretation of gravity and magnetic data. This technique, based on the analysis of 3-D analytic signal derivatives, involves as few assumptions as possible on the magnetization or density properties and on the geometry of the structures. It is therefore particularly well suited to preliminary interpretation and model initialization. Processing the derivatives of the analytic signal amplitude, instead of the original analytic signal amplitude, gives a more efficient separation of anomalies caused by close structures. Moreover, gravity and magnetic data can be taken into account by the same procedure merely through using the gravity vertical gradient. The main advantage of derivatives, however, is that any source geometry can be considered as the sum of only two types of model: contact and thin‐dike models. In a first step, depths are estimated using a double interpretation of the analytic signal amplitude function for these two basic models. Second, the most suitable solution is defined at each estimation location through analysis of the vertical and horizontal gradients. Practical implementation of the method involves accurate frequency‐domain algorithms for computing derivatives with an automatic control of noise effects by appropriate filtering and upward continuation operations. Tests on theoretical magnetic fields give good depth evaluations for derivative orders ranging from 0 to 3. For actual magnetic data with borehole controls, the first and second derivatives seem to provide the most satisfactory depth estimations.

A comparison of methods for approximating the vertical gradient of one‐dimensional magnetic field data

Geophysics ◽  
1986 ◽  
Vol 51 (9) ◽  
pp. 1725-1735 ◽  
Author(s):  
J. W. Paine
Keyword(s):  
Magnetic Field ◽  
Fourier Transform ◽  
Field Data ◽  
Total Error ◽  
Vertical Gradient ◽  
Magnetic Data ◽  
Total Field ◽  
One Dimensional ◽  
Convolution Filter ◽  
Principal Factors

The vertical gradient of a one‐dimensional magnetic field is known to be a useful aid in interpretation of magnetic data. When the vertical gradient is required but has not been measured, it is necessary to approximate the gradient using the available total‐field data. An approximation is possible because a relationship between the total field and the vertical gradient can be established using Fourier analysis. After reviewing the theoretical basis of this relationship, a number of methods for approximating the vertical gradient are derived. These methods fall into two broad categories: methods based on the discrete Fourier transform, and methods based on discrete convolution filters. There are a number of choices necessary in designing such methods, each of which will affect the accuracy of the computed values in differing, and sometimes conflicting, ways. A comparison of the spatial and spectral accuracy of the methods derived here shows that it is possible to construct a filter which maintains a reasonable balance between the various components of the total error. Further, the structure of this filter is such that it is also computationally more efficient than methods based on fast Fourier transform techniques. The spacing and width of the convolution filter are identified as the principal factors which influence the accuracy and efficiency of the method presented here, and recommendations are made on suitable choices for these parameters.

Ultra-lightweight integrated unmanned aerial systems for a wide range of geophysical magnetic exploration: a single system for high-precision archaeological surveys to rugged topography geological acquisitions

2021 ◽  
Author(s):  
Jeanne Mercier de Lépinay ◽  
Tristan Fréville ◽  
Baptiste Kiemes ◽  
Luis Miguel Sanabria ◽  
Bruno Gavazzi ◽  
...  
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
High Precision ◽  
Adaptive Systems ◽  
Magnetic Measurements ◽  
Magnetic Sensor ◽  
Magnetic Data ◽  
Industrial Sectors ◽  
Wide Range ◽  
The Magnetic Field

<p>Magnetic mapping is commonly used in the academic and industrial sectors for a wide variety of objectives. To comply with a broad range of survey designs, the use of unmanned aerial vehicles (UAVs) has become frequent over the recent years. The majority of existing systems involves a magnetic acquisition equipment and its carrier (an UAV in this context) with no -or very few- connections between the two systems. Terremys is conceiving and optimizing UAVs specifically adapted for geophysical magnetic acquisitions together with the appropriate processing tools, and performs magnetic surveying in challenging environments. Terremys’ “Q6” system weights 2.5 kg in air, including UAV & instrumentation, and allows 30 min swarm or individual flights.</p><p>Rotary-wing UAVs are found to be the most adaptive systems for a wide range of contexts and constraints (extensive range of flights heights even with steep slopes). They offer more flight flexibility than fixed-wing aircrafts. One of the major problems in the use of rotary-wings UAVs for magnetic mapping is the magnetic field generated by the aircraft itself on the measurements. Towing the magnetic sensor 2 to 5 m under the aircraft reduces data positioning accuracy and decreases the performances of the UAV, which can be critical for high-resolution surveys. To overcome these problems, a deployable 1 m long boom is rigidly attached to the UAV. The UAV magnetic signal can be divided between 1-the magnetic field of the whole equipment and 2-a low to high frequency magnetic field mostly originating from the motors. The magnetization of the system is the principal source of magnetic noise. It is modelled and corrected by calibration-compensation processes permitted by the use of three-component fluxgate magnetometers. The time-varying noise depends on the motors rotational speed and is minimized by optimizing the UAV components and characteristics along with the boom’s length.</p><p>The final set-up is able to acquire magnetic data with a precision of 1 to 5 nT at any height from 1 to 150 m above ground level. The high-precision magnetic measurements are coupled with a centimetric RTK navigation system to allow for high-resolution surveying. The quality of the obtained data is similar to that obtained with ground or aerial surveys with conventional carriers and matches industrial standards. Moreover, Terremys’ systems merge in real-time data from all the aircraft instruments in order to integrate magnetic measurements, positioning information and all the UAV’s flight data (full telemetry) into a unique synchronized data file. This opens up many possibilities in terms of QA/QC, data processing and facilitates on-field workflows.</p><p>Case studies with diverse designs, flight altitudes and targets are presented to investigate the acquisition performances for different applications, as distinct as network positioning, archaeological prospecting or geological mapping.</p><p>The full integration of the magnetic sensor to the drone opens the possibility for implementation additional sensors to the system. The adjoining of other magnetic sensors would allow multi-sensors surveying and increases daily productivity. Diverse geophysical sensors can also be added, such as thermal/infrared cameras, spectrometers, radar/SAR.</p>

Next Generation High-Definition Geomagnetic Model for Wellbore Positioning, Incorporating New Crustal Magnetic Data

2021 ◽  
Author(s):  
Manoj Nair ◽  
Arnaud Chulliat ◽  
Adam Woods ◽  
Patrick Alken ◽  
Brian Meyer ◽  
...  
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Error Model ◽  
Magnetic Data ◽  
Magnetic Observatory ◽  
Magnetic Survey ◽  
High Definition ◽  
The Core ◽  
Ground Magnetic ◽  
The Magnetic Field

Abstract Magnetic wellbore positioning depends on an accurate representation of the Earth's magnetic field,where the borehole azimuth is inferred by comparing the magnetic field measured-whiledrilling (MWD) with a geomagnetic reference model. Therefore, model accuracy improvements reduce the position uncertainties. An improved high-resolution model describing the core, crustal and external components of the magnetic field is presented, and it is validated with anindependent set of measurements. Additionally, we benchmark it against other high-resolution geomagnetic models. The crustal part of the improved high-definition model is based on NOAA/NCEI's latest magnetic survey compilation "EMAG2v3" which includes over 50 millionnew observations in several parts of the world, including the Gulf of Mexico and Antarctica, and does not rely on any prior information from sea-floor geology, unlike earlier versions. The core field part of the model covers years 1900 through 2020 andis inferred from polar-orbiting satellite data as well as ground magnetic observatory data. The external field part is modelled to degree and order 1 for years 2000 through 2020. The new model has internal coefficients to spherical harmonic degree and order 790, resolving magnetic anomalies to approximately 51 km wavelength at the equator. In order to quantitatively assess its accuracy, the model was compared with independent shipborne, airborne and ground magnetic measurements. We find that the newmodel has comparable or smaller errors than the other models benchmarkedagainst it over the regions of comparisons. Additionally, we compare theimproved model against magnetic datacollected from MWD; the residual error lies well within the accepted industry error model, which may lead tofuture error model improvements.

Magnetic interpretation using the 3-D analytic signal

Geophysics ◽  
1992 ◽  
Vol 57 (1) ◽  
pp. 116-125 ◽  
Author(s):  
Walter R. Roest ◽  
Jacob Verhoef ◽  
Mark Pilkington
Keyword(s):  
Magnetic Field ◽  
Impact Crater ◽  
Analytic Signal ◽  
Three Dimensions ◽  
Eastern Canada ◽  
Magnetic Interpretation ◽  
Absolute Value ◽  
Cape Breton ◽  
Derivatives Of ◽  
The Magnetic Field

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.

Attributes of the magnetic field, analytic signal, and monogenic signal for gravity and magnetic interpretation

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. J79-J86 ◽  
Author(s):  
Xiong Li ◽  
Mark Pilkington
Keyword(s):  
Magnetic Field ◽  
Magnetic Anomaly ◽  
Field Vector ◽  
Analytic Signal ◽  
Horizontal Gradient ◽  
Monogenic Signal ◽  
Magnetic Interpretation ◽  
Gravity And Magnetic ◽  
Gravity And Magnetic Interpretation ◽  
The Magnetic Field

Many of the transforms and attributes used in gravity and magnetic interpretation can be expressed as a 2D or 3D vector. The horizontal gradient and the 2D analytic signal are 2D vectors. The gravity or magnetic field, the 3D analytic signal, and the monogenic signal are defined by a 3D vector. In practice, we prefer to interpret the amplitude and/or phase of a 2D or 3D vector, but we often forget that a meaningful interpretation requires a magnetic reduction-to-the-pole operation when these techniques are applied to magnetic anomaly data and the source body is 3D. Furthermore, the gravity or magnetic anomaly has an unknown constant level that may affect the amplitude and phase. The horizontal gradient, the analytic signal, and the monogenic signal can be applied to not only the gravity or magnetic anomaly but also any [Formula: see text]th-order derivative or a filtered version of the anomaly. They can be related to each other and to the magnetic field vector. We do not introduce new attributes. Instead, we have explained the relationships among different transforms (or vectors) and addressed precautions and requirements for their practical use.

Using the analytic signal amplitude to determine the location and depth of thin dikes from magnetic data

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. J1-J6 ◽  
Author(s):  
Gordon R. J. Cooper
Keyword(s):  
Magnetic Field ◽  
Magnetic Anomaly ◽  
Magnetization Vector ◽  
Signal Amplitude ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Local Minima ◽  
First Order ◽  
Higher Order Derivative ◽  
The Magnetic Field

A semiautomatic method to determine the location and depth of thin dykes is introduced. The ratio of analytic signal amplitudes of orders 0 and 1 of the magnetic anomaly from a thin dike was used to give the distance [Formula: see text] to the dike. Local minima of [Formula: see text] gave the depth to the dike, and the position of these minima gave its horizontal location. Because in the method we used just the magnetic field and its first-order derivatives, it was less sensitive to noise than were higher order derivative-based methods. Once the position of the dike has been determined, then its dip and susceptibility-thickness product can be calculated from the analytic signal amplitude, providing that the magnetization vector is known.

On: “Magnetic interpretation using the 3-D analytic signal” by W. R. Roest, J. Verhoef, and M. Pilkington (GEOPHYSICS, 1, 116–125, January 1992).

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1214-1214 ◽  
Author(s):  
N. L. Mohan
Keyword(s):  
Magnetic Anomalies ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Magnetic Interpretation ◽  
Vector Addition

It is quite interesting to learn the 3-D analytic signal interpretation of Roest et al. (1992), using the vector addition. However, I am quite skeptical about their objective of determining the depth under the assumption that the magnetic anomalies are caused by vertical contacts from gridded magnetic data which, it appears to me, is nothing but an oversimplification of interpretation.

Imaging of ferroelectric domain walls by electron holography

1992 ◽  
Vol 50 (1) ◽  
pp. 246-247
Author(s):  
Xiao Zhang
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Domain Walls ◽  
Ferroelectric Domain ◽  
Object Wave ◽  
Electron Holography ◽  
High Resolution Imaging ◽  
Quantitative Measurements ◽  
Resolution Imaging ◽  
Electron Microscopes

Electron holography has recently been available to modern electron microscopy labs with the development of field emission electron microscopes. The unique advantage of recording both amplitude and phase of the object wave makes electron holography a effective tool to study electron optical phase objects. The visibility of the phase shifts of the object wave makes it possible to directly image the distributions of an electric or a magnetic field at high resolution. This work presents preliminary results of first high resolution imaging of ferroelectric domain walls by electron holography in BaTiO3 and quantitative measurements of electrostatic field distribution across domain walls.

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