Reply to Comment on ‘‘Depth Estimation of Simple Causative Sources from Gravity Gradient Tensor Invariants and Vertical Component’’ by Beiki and Pedersen

Abstract

First, I thank BEIKI and PEDERSEN (2010) for their comments and interest in my paper. I welcome further investigation of the issues raised in my published paper ‘‘Depth estimation of simple causative sources from gravity gradient tensor invariants and vertical component’’ (ORUC, 2010). In this reply I wish to clarify the problems in my paper. 1. As is well known, the complex geological structures can be approximated by simple bodies. For example: salt domes can be approximated by spheres; anticlines can be approximated by a long horizontal cylinder. These bodies are important features and form the reservoir for a number of oilfields. 2. PEDERSEN and RASMUSSEN (1990) have developed an effective method based on the dimensionality map from the ratio of scalar invariants. There is no other method to estimate the depth to the anomalous sources based on the ratio between scalar invariants (I1 and I2) in geophysical literature, as far as I am aware. 3. BEIKI and PEDERSEN (2010) stated that the Eq. (10) in my paper is not valid since an infinite horizontal cylinder is in 2D. From theoretical point of view, I agree that the gradients of the gravity field along the y direction and subsequently the invariant, I2 are equal to zero. As shown in Fig. 2b in my paper, an observation point may be defined in terms of x and y and the horizontal location of this source is given as x0 and y0. The gravity anomaly map, illustrated in Fig. 4 in my paper is computed at an interval of 0.01 km on a grid of 1 9 1 km using the following (Eq. B1 in my paper): Gz 1⁄4 2cM z0 r2 : ð1Þ