Refining magnetic amplitude methodology for use in the presence of remanent magnetization

Abstract

The magnetic method is a common geophysical technique used to detect and image magnetically susceptible sources. Interpretation of magnetic data can be difficult in the presence of remanent magnetization. Remanence can alter the total magnetization to an unknown direction and hinder the interpretation of 3D susceptibility models by leading to incorrect shape and size of the sources. The magnetic amplitude method is an effective tool for interpretation of magnetic data in such settings. Amplitude data are the amplitude of the anomalous magnetic field and are weakly dependent on magnetization direction. The data are often used to bypass challenges posed by the presence of remanently magnetized materials as they not rely on known magnetization direction. 3D amplitude inversion plays a particularly important role in quantitative interpretation of magnetic data affected by remanence. Inversion of amplitude data results in an effective susceptibility model capable of delineating geologically interpretable anomalies where susceptibility modeling approaches struggle. Challenges remain, however, with the use of amplitude method. The first challenge is that a methodology for determining the noise statistics relating to amplitude data and associated inversion has not been well developed, hindering the ability to properly estimate the data misfit associated with an inverse model and therefore the model itself. The second challenge is amplitude data, while successful at delineating remanent source bodies, do not contain direction information. This limitation makes it difficult to recover dipping structures affected by remanence. These challenges are the focus of my work. I investigate amplitude error statistics to address the first challenge. I analytically derive the propagation of errors associated with calculating amplitude data and confirm the derivation by implementing parametric bootstrapping. The investigation reveals that the noise in amplitude data is approximately equal to that of the total-field anomaly data. Having characterized the relationship between noise in total-field anomaly and amplitude data, I estimate the noise in total-field anomaly datasets. Using synthetic and field data, I demonstrate that equivalent source technique can recover accurate estimates of noise in magnetic datasets. I use this estimate for inversion of amplitude data to aid in recovering optimal models. I show that noise in magnetic datasets can be estimated by equivalent source technique and that the estimate can be used in inversion resulting in increased confidence in the recovered model. Following this work, I address the second challenge of estimating the magnetization direction. I implement a method to recover the missing direction information using an effective susceptibility model. I segment the amplitude inversion into distinct anomalous bodies and assume a constant magnetization direction for each. Assuming that the effective susceptibility provides a sufficiently accurate representation of the magnitude of the magnetization, I then solve a least-squares problem to recover the magnetization directions of multiple source bodies simultaneously. This approach is able to recover magnetization direction from datasets containing both single and multiple anomalies. The direction estimate can be used in susceptibility inversion to recover accurate dipping structures of anomalies. My work improves amplitude method by increasing confidence in interpretation and by broadening the scope of the method. I demonstrate that a reliable noise estimate can be obtained using equivalent source technique and used to recover an optimal effective susceptibility model. Using the effective susceptibility model, magnetization direction can then be estimated for single and multiple anomaly datasets. Following my research, amplitude data can now be used to fully characterize magnetization in both magnitude and direction.