An implementation of the Euler deconvolution to the analysis of vertical profiles of potential fields is presented, with examples illustrating the potentialities of this approach to a detailed study of sources also in presence of noise.
Euler deconvolution has become a standard tool in rapid, semi-automated interpretation of potential fields. Its success derives from its flexibility, providing the source position and a parameter describing the shape of the source (structural index, SI) for all the possible one point sources (point, horizontal or vertical line, dike, contact). The Euler algorithms are particularly prone to regional (even constant) fields and noise (e.g.: FitzGerald et al., 2004). The presence of regional fields was the main reason for the strategy proposed in the first formulation of the method, that considered a moving window approach in which the regional field was approximated as a constant. This constant background (B) and the structural index are coupled in the Euler interpretation formula, and it was noted that the simultaneous estimation of SI, B and z0 was not stable.
For this reason Thompson (1982) suggested to input the value of the structural index to obtain the position (x0, z0) of the point-source and B. Anyway this approach suffers of a certain degree of subjectivity because the choice of SI influences directly the depth estimate. Thus different approaches were devised to deal with the problem of the background fields allowing to obtain the SI as an unknown (e.g.: Stavrev, 1997; Hsu, 2002; Nabighian and Hansen, 2001). Meanwhile, other methods recovering the same parameters (position and SI) were proposed (e.g.: Smith et al., 1998; Salem and Ravat, 2003). Among them, the Continuous Wavelet Transform method (e.g.: Hornby et al., 1999; Sailhac and Gibert, 2003) that uses the information coming from the field upward continued to a set of different altitudes. This method has reduced sensitivity to noise with respect to the Euler deconvolution, because in the upward continued field the high-wave-numbers are naturally attenuated. This method, however, tries to recover the information about the source using simultaneously data at as much altitudes as possible, both with the geometrical method (to recover z0) and the linear regression approach (to recover z0 and SI). In this paper we present a formulation of the Euler deconvolution method that uses a vertical profile of data above an anomaly source. It can be applied to almost all the Euler algorithms to tackle the problem of the regional field and, using upward continued fields, it efficiently deals with the problem of noise.
Our method uses vertical profiles of potential field data. Such profiles are defined with the maxima (or minima) of the field T at all the continuation altitudes, and, analogously to CWT method, we will call them ‘ridges’. For example, a dipolar anomaly will generate two inclined ridges, one relative to the anomaly low and one relative to the anomaly high, that will not be aligned vertically above the low or high at the measurement altitude due to the natural spreading of anomaly with altitude.