Detection of potential fields source boundaries by enhanced horizontal derivative method

A high-resolution method to image the horizontal boundaries of gravity and magnetic sources is presented (the enhanced horizontal derivative (EHD) method). The EHD is formed by taking the horizontal derivative of a sum of vertical derivatives of increasing order. The location of EHD maxima is used to outline the source boundaries. While for gravity anomalies the method can be applied immediately, magnetic anomalies should be previously reduced to the pole. We found that working on reduced-to-the-pole magnetic anomalies leads to better results than those obtainable by working on magnetic anomalies in dipolar form, even when the magnetization direction parameters are not well estimated. This is confirmed also for other popular methods used to estimate the horizontal location of potential fields source boundaries. The EHD method is highly flexible, and different conditions of signal-to-noise ratios and depths-to-source can be treated by an appropriate selection of the terms of the summation. A strategy to perform high-order vertical derivatives is also suggested. This involves both frequencyand space-domain transformations and gives more stable results than the usual Fourier method. The high resolution of the EHD method is demonstrated on a number of synthetic gravity and magnetic fields due to isolated as well as to interfering deep-seated prismatic sources. The resolving power of this method was tested also by comparing the results with those obtained by another high-resolution method based on the analytic signal. The success of the EHD method in the definition of the source boundary is due to the fact that it conveys efficiently all the different boundary information contained in any single term of the sum. Application to a magnetic data set of a volcanic area in southern Italy helped to define the probable boundaries of a calderic collapse, marked by a number of magmatic intrusions. Previous interpretations of gravity and magnetic fields suggested a subcircular shape for this caldera, the boundaries of which are imaged with better detail using the EHD method. I N T R O D U C T I O N The horizontal location of the boundaries of gravity and magnetic anomaly sources is a commonly requested task in potential field interpretation. However, the location of the horizontal boundaries of potential field sources is not straightforward, because of the intrinsic loss of resolution of the anomaly shape with respect to the shape of their sources. Knowledge of the locations of the horizontal boundaries of gravity and magnetic sources can be important when investigating the structural setting of a region as well as 40 q 2001 European Association of Geoscientists & Engineers Paper presented at the 61st EAGE Conference ± Geophysical Division, Helsinki, Finland, June 1998. for environmental and engineering applications and this information could be included as a constraint in 2D and 3D modelling. Boundary analysis of gridded gravity or magnetic anomalies is at present accomplished using a number of methods involving directional derivatives of different orders. Vertical derivatives have been used for many years to enhance the measured gravity field (Evjen 1936). A well-known method of locating source boundaries is to consider the zero contour of the second vertical derivative of gravity or reduced-to-the-pole magnetic fields. However, as is well known (e.g. Thurston and Smith 1997), the boundaries estimated by this technique are systematically shifted from the true position even for vertical-sided sources, and application of this method produces fairly complicated results in multisource cases. For these reasons, in recent years this method has lost popularity in favour of methods enabling the generation of maps displaying boundaries more clearly and precisely. Cordell and Grauch (1985) showed that the maxima of the horizontal derivative of gravity or pseudogravity anomalies are located above abrupt changes of density or magnetization. This technique, coupled with an automated method to locate maxima (Blakely and Simpson 1986), proved to be an effective tool for the boundary analysis. Some authors (Nabighian 1984; Roest, Verhoef and Pilkington 1992) showed that the amplitude of the analytic signal has useful properties, presenting its maxima directly over vertical and abrupt magnetization contrasts. Its most interesting characteristic is the relative insensitivity to the magnetization direction. Another method, based on Euler's equation (Thompson 1982; Reid et al. 1990), is often used to determine both boundaries and depths-to-source of magnetic or gravity anomalies. Results of this method are dependent to a limited extent on the magnetization direction, but it is necessary to input a parameter, the so-called `structural index', depending on the unknown geometrical characteristics of the source and of its depth. More recently, the analytic-signal method was generalized to higher-order derivatives to increase the resolving power of this technique (Hsu, Sibuet and Shyu 1996; Hsu, Coppens and Shyu 1998). These authors suggested the computation of the `enhanced' analytic signal starting from the second vertical derivative of the first derivatives along the x-, yand z-directions of the magnetic field, and showed also some formulae to compute the depth-to-source by means of amplitude ratios between analytic signals of different orders. The most appealing characteristic of all these methods is that it is possible to obtain quantitative results on gridded data in a semi-automatic way and with only a few assumptions. One of the main limitations to making a good estimate of the position of a boundary of a source are interference effects caused by nearby sources, especially when they are deep-seated. The enhanced horizontal derivative (EHD) method is presented here as a high-resolution boundary-analysis technique. T H E E H D M E T H O D