Corrigendum to:New methods for interpretation of magnetic vector and gradient tensor data I: eigenvector analysis and the normalised source strength

Abstract

Acquisition of magnetic gradient tensor data is likely to become routine in the near future. New methods for inverting gradient tensor surveys to obtain source parameters have been developed for several elementary, but useful, models. These include point dipole (sphere), vertical line of dipoles (narrow vertical pipe), line of dipoles (horizontal cylinder), thin dipping sheet, and contact models. A key simplification is the use of eigenvalues and associated eigenvectors of the tensor. The normalised source strength (NSS), calculated from the eigenvalues, is a particularly useful rotational invariant that peaks directly over 3D compact sources, 2D compact sources, thin sheets and contacts, and is independent of magnetisation direction. In combination the NSS and its vector gradient determine source locations uniquely. NSS analysis can be extended to other useful models, such as vertical pipes, by calculating eigenvalues of the vertical derivative of the gradient tensor. Inversion based on the vector gradient of the NSS over the Tallawang magnetite deposit obtained good agreement between the inferred geometry of the tabular magnetite skarn body and drill hole intersections. Besides the geological applications, the algorithms for the dipole model are readily applicable to the detection, location and characterisation (DLC) of magnetic objects, such as naval mines, unexploded ordnance, shipwrecks, archaeological artefacts, and buried drums.

Closed-Form Formulae for Fractional Gradient Tensor of Magnetic Dipole

“…where n ∈ ℕ, α ∈ ℝ; Γ(•) refers to gamma function. Equation (5) shows that there is a summation remainder after exchanging the fractional-order derivatives and the integer-order derivatives. Due to lim → = 0, the remainder of the third term is equal to 0.…”

“…For the location problem of a magnetic dipole, it is insufficient to obtain its accurate position using the magnetic gradient tensor only [5]. The key reason is that only five of the nine components are independent and six parameters are needed to be solved.…”

“…With the help of the fractional magnetic gradient tensor, we not only can extend the integer tensor measurement area, but also obtain the abundant fractional gradient information. Another example is the localization of a magnetic dipole [5], since only five of the nine components of the magnetic gradient tensor are independent, there are multiple solutions in the inversion problems, which can be solved by the additional information provided by the fractional magnetic gradient tensor.…”

Analysis and Correction of the Magnetometer’s Position Error in a Cross-Shaped Magnetic Tensor Gradiometer

“…The magnetic gradient tensor G is defined as the vector gradient of the magnetic field vector B [3]. It is formally presented in Equation (2).…”

“…Recently, the magnetic gradient tensor system has been extensively applied in geophysical exploration [1], such as underwater target detection and unexploded ordnance [2], due to the advantages of magnetic gradient tensor measurements, the unstoppable development of technology, and the improvement in various platforms [3]. However, the performance of the tensor system is adversely affected by the measurement error caused by specific factors, which are broadly divided into three aspects [4].…”