Multiridge Euler deconvolution
1 Dipartimento di Scienze della Terra, dell’Ambiente e delle Risorse, Università degli Studi di Napoli Federico II, Largo San Marcellino 10, 80138 Napoli, Italy
Geophysical Prospecting, Volume 62, Pagine 333-351, Anno 2014
Potential field interpretation can be carried out using multiscale methods. This class of methods analyses a multiscale data set, which is built by upward continuation of the original data to a number of altitudes conveniently chosen. Euler deconvolution can be cast into this multiscale environment by analysing data along ridges of potential fields, e.g., at those points along lines across scales where the field or its horizontal or vertical derivative respectively is zero. Previous work has shown that Euler equations are notably simplified along any of these ridges. Since a given anomaly may generate one or more ridges we describe in this paper how Euler deconvolution may be used to jointly invert data along all of them, so performing a multiridge Euler deconvolution. The method enjoys the stable and high-resolution properties of multiscale methods, due to the composite upward continuation/vertical differentiation filter used. Such a physically-based field transformation can have a positive effect on reducing both high-wavenumber noise and interference or regional field effects. Multiridge Euler deconvolution can also be applied to the modulus of an analytic signal, gravity/magnetic gradient tensor components or Hilbert transform components. The advantages of using multiridge Euler deconvolution compared to single ridge Euler deconvolution include improved solution clustering, increased number of solutions, improvement of accuracy of the results obtainable from some types of ridges and greater ease in the selection of ridges to invert. The multiscale approach is particularly well suited to deal with non-ideal sources. In these cases, our strategy is to find the optimal combination of upward continuation altitude range and data differentiation order, such that the field could be sensed as approximately homogeneous and then characterized by a structural index close to an integer value. This allows us to estimate depths related to the top or the centre of the structure.
Fig. 1: Multiridge Euler deconvolution for sources characterized by non-integer structural indices: the total field of a vertical fault step (top at z0top = −15 m and thickness of 200 m). The inversion was repeated 14 times by increasing the average altitude of the analytic signal data, from 15 to 650 m; the inversions relative to the lowest altitudes were performed using vertical derivatives of the analytic signal. At high altitudes the source is perceived as a thin sheet (N0 ∼ 1) with a 90 m depth to the centre, while at low altitudes and high-differentiation orders the source is perceived as an infinite contact (N0 ∼ 0) at about −15 m depth to the top.
Key-words: Euler deconvolution, Multiscale methods, Potential fields.