400 Discussion/Errata.qxd

We have read with great interest the paper entitled " 3D inversion of gravity and magnetic data with depth resolution " by Fedi and Rapolla. We realize that many discussions we had with one of the authors had not resolved our differences and, therefore, we are writing this comment to document out concerns regarding the authors' conclusion that the upward-continued gravity or magnetic data contain extra information and provide depth resolution. As is well known in potential-field theory, the fields produced by the subsurface source at any two nonintersecting observational surfaces are linearly related to each other and one contains no more information than does the other. Furthermore, the field on the observational surface above the source can be reproduced by an infinite number of equivalent sources below that surface. As a consequence, gravity or magnetic data do not provide any information about the subsurface structure unless the source is assumed to have certain restrictive properties. No amount of upward continuation will create any new information and, consequently, the addition of upward-continued data will not resolve the depth distribution of the source. In practical applications, when the data are available in a small area and/or when the data are coursely sampled, then exact numerical continuation is not possible to perform. In such circumstances, independently-measured data at a different level will provide extra information that is not contained in the data at the original level. The maximum amount of additional information that any upper-level data can supply is that which is contained in the missing portion of the data map at the lower level. Fedi and Rapolla provide two examples which they claim support their hypothesis that data along the vertical direction are needed to obtain depth resolution and, furthermore, that upward-continued data serve this purpose. As is shown below, both results arise because of a priori restrictions upon the model space used to carry out the inversion. The first example (Figures 3 and 4 of their paper) compares the recovery of a buried susceptible block when only surface data are used, and when data at 10 different heights are used. When the surface data are inverted, the susceptibility maximum is at the surface, whereas when data at all 10 levels are inverted, the recovered susceptibility compares well with the true values. In both inversions the earth was modeled with a 7 × 7 × 7 set of prismatic cells. Each …