A one-step linear inversion to recover current density pseudo-section from VLF-EM signals

Abstract

Abstract Unquestionably, current density pseudo-section derived from in-phase very low frequency (VLF) data, developed by Karous and Hjelt, has been one of the most popular preliminary schemes for the interpretation of VLF data due to its straightforwardness and applicability. In practice, however, the Karous and Hjelt filtering method does not behave accurately and has some weaknesses: (i) the depth estimation is erratic, even in shallow cases, (ii) to a far lesser extent, the horizontal estimation is inaccurate, in particular when the sources interfere with each other, and (iii) under circumstances where multiple bodies are in close proximity, spurious artifacts appear. These factors could be misleading and result in a wrong interpretation. Changing the Biot–Savart law into a linear equation and employing inverse theory in this paper, the precision of spatial estimations, in the case of superficial objects, becomes far more precise. More importantly, independent of the number of neighboring targets and their closeness, no spurious artifacts are observed. This methodology is tested on synthetic isolated and interfering various models with different sizes, depths, shapes and resistivities. It is also applied to real data over the ‘Ghoori Ghale’ cave in the vicinity of Kermanshah, Iran, and its satisfying and noteworthy solutions are compared with the Karous and Hjelt method.