Matlab tool REGCONT2: effective source depth estimation by means of Tikhonov’s regularized downwards continuation of potential fields

Abstract

Transformation based on downward continuation of potential fields is an important tool in their interpretation – depths of shallowest important sources can be determined by means of stable downward continuation algorithms. We analyse here selected properties of one from these algorithms (based on Tikhonov’s regularization approach) from the scope of two most important discretization parameters – dimensions of the areal coverage of the interpreted field and the sampling interval size. Estimation of the source depth is based on the analysis of computed LP-norms for various continuation depths. A typical local minimum of these norms disappears at the source depth. We show on several synthetic bodies (sphere, horizontal cylinder, vertical rod) and also real-world data-sets (results from a magnetic survey for unexploded ordnance detection) that there is a need for relatively large surroundings around the interpreted anomalies. Beside of this also the sampling step plays its important role – grids with finer sampling steps give better interpretation results, when using this downward continuation method. From this point of view, this method is more suitable for the interpretation of objects in near surface and mining geophysics (anomalies from cavities, unexploded ordnance objects and ore bodies). Anomalies should be well developed and separable, and densely sampled. When this is not valid, several algorithms of interpolation and extrapolation (grid padding methods) can improve the interpretation properties of studied downward continuation method.

Microgravity method in archaeological prospection: methodical comments on selected case studies from crypt and tomb detection

“…Theoretically these solutions should be focused around the centre of the cavity. Very similar results are produced from the method of stable downward continuation, based on the Tikhonov regularization algorithm (Pašteka, Karcol, Kušnirák, & Mojzeš, 2012; Pašteka, Kušnirák, & Karcol, 2018; Tikhonov, Glasko, Litvinenko, & Melichov, 1968). Using the analysis of special Norm‐functions we can estimate the maximum depth of stable downward continuation, which estimates the source position (Pašteka et al, 2011).…”

“…This method results in a group of depth solutionsa solution cluster. (Pašteka, Karcol, Kušnirák, & Mojzeš, 2012;Pašteka, Kušnirák, & Karcol, 2018;Tikhonov, Glasko, Litvinenko, & Melichov, 1968). Using the analysis of special Norm-functions we can estimate the maximum depth of stable downward continuation, which estimates the source position (Pašteka et al, 2011).…”

Real magnetic stripping method in unexploded ordnance detection and remediation – a case study from Rohožník military training range in SW Slovakia

“…6 but to draw this conclusion could result in the hazardous risk that a dangerous item was overlooked. In an attempt to resolve this ambiguity, we calculated a 0.5 m upward continuation of this data deploying the standard Upward Continuation filter routine in the Fourier spectral domain, using the Matlab script REGCONT2 (Pašteka et al, 2018). In the upward continued field presented in Fig.…”

Depth Estimation of Potential Field Sources by Using Improved Chebyshev‐Padé Downward Continuation in Wave Number Domain

“…We could not obtain any information near the source position. Unlike other methods, the Tikhonov regularization downward continuation method has been proven effective for depth estimation (Pašteka et al, 2018; Wang et al, 2018). To illustrate this, the filtering effect of different downward continuation was compared in the wave number domain.…”