Estimating the magnetization distribution within rectangular rock samples

Abstract

Over the last decades, scanning magnetic microscopy techniques have been increasingly used in paleomagnetism and rock magnetism. Different from standard paleomagnetic magnetometers, scanning magnetic microscopes produce high‐resolution maps of the vertical component of the magnetic induction field (flux density) on a plane located over the sample. These high‐resolution magnetic maps can be used for estimating the magnetization distribution within a rock sample by inversion. Previous studies have estimated the magnetization distribution within rock samples by inverting the magnetic data measured on a single plane above the sample. Here we present a new spatial domain method for inverting the magnetic induction measured on four planes around the sample in order to retrieve its internal magnetization distribution. We have presumed that the internal magnetization distribution of the sample varies along one of its axes. Our method approximates the sample geometry by an interpretation model composed of a one‐dimensional array of juxtaposed rectangular prisms with uniform magnetization. The Cartesian components of the magnetization vector within each rectangular prism are the parameters to be estimated by solving a linear inverse problem. Our method automatically deals with the averaging of the measured magnetic data due to the finite size of the magnetic sensor, preventing the application of a deconvolution before the inversion. Tests with synthetic data show the performance of our method in retrieving complex magnetization distributions even in the presence of magnetization heterogeneities. Moreover, they show the advantage of inverting the magnetic data on four planes around the sample and how this new acquisition scheme improves the estimated magnetization distribution within the rock sample. We have also applied our method to invert experimentally measured magnetic data produced by a highly magnetized synthetic sample that was manufactured in the laboratory. The results show that even in the presence of apparent position noise, our method was able to retrieve the magnetization distribution consistent with the isothermal remanent magnetization induced in the sample.

Low-latitude reduction-to-the-pole and upward continuation between arbitrary surfaces based on the partial differential equation framework

“…The RTP method has also been applied in numerous large-scale magnetic data-interpretation applications (Pearson & Skinner 1982;Nabighian et al 2005;Fedi et al 2012;Foks & Li 2016;Li & Pilkington 2016). Moreover, it can be utilized as an efficient tool to identify the direction of total magnetization in rocks (Phillips 2005;Dannemiller & Li 2006;Reis et al 2016;Liu et al 2018). Generally, RTP methods can be classified into wavenumber-domain and space-domain methods.…”

Characterizing Complex Mineral Structures in Thin Sections of Geological Samples with a Scanning Hall Effect Microscope

“…It has the potential to elucidate a number of problems in science and engineering that involve magnetization images [1,2,3,4]. The applications involving scanning magnetic microscopy cover many disciplines, ranging from physics and materials science [5,6,7,8] to paleomagnetism, magnetism [9,10] and biophysics [11,12,13]. For example, in paleomagnetism, scanning magnetic microscopy can be used to recover information about past magnetic fields by analyzing the magnetizations of terrestrial or extraterrestrial rocks.…”

Scanning Magnetic Microscope Using a Gradiometric Configuration for Characterization of Rock Samples

“…Besides the cost, another problem related to magnetic microscopy lies in the elimination of some ambiguities inherent in this kind of measurements [7]. For these issues, some solutions have been recently developed, such as nonsuperconducting scanning magnetic microscopes and new methods of micromagnetic processing and modeling [7][8][9][10][11][12]. Based on the issues and solutions presented before, this study presented a development of nonsuperconducting scanning magnetic microscopy, which would be easily reproduced and used in low-cost laboratories, as well as in classrooms to teach physics, engineering, geophysics, and geology.…”