Window constrained inversion of gravity gradient tensor data using dike and contact models

Abstract

We have developed a constrained inversion technique for interpretation of gravity gradient tensor data. For dike and contact models striking in the y-direction, the measured g xz and g zz components can be jointly inverted for estimating the model parameters horizontal position, depth to the top, thickness, dip angle, and density contrast. For a given measurement point, the strike direction of the gravity gradient tensor caused by a quasi 2D structure can be estimated from the eigenvector corresponding to the smallest eigenvalue. Then, the measured components can be transformed into the strike coordinate system. It is assumed that the maximum of g zz is approximately located above the causative body. In the case of gridded data, all measurement points enclosed by a square window centered at the maximum of g zz are used to estimate the source parameters. The number of data points used for estimating source parameters is increased by increasing the size of the window. Solutions with the smallest data-fit error were selected as the most reliable solutions from any set of solutions. The gravity gradient tensor data are deconvolved using both dike and contact models within a set of square windows. Then, the model with the smallest data-fit error is chosen as the best model. We studied the effect of random noise and interfering sources using synthetic examples. The method is applied to a gravity gradient tensor data set from the Vredefort impact structure in South Africa. In this particular case, the dike model provides solutions with smaller data-fit errors than the contact model. This supports the idea that in the central dome area there is a predominance of vertical structures related to the formation of the transient crater and subsequent central uplift of the lower and middle crustal material.

2.5D regularized inversion for the interpretation of residual gravity data by a dipping thin sheet: numerical examples and case studies with an insight on sensitivity and non-uniqueness

“…Gravity and magnetic methods have many successful applications in mineral prospecting, environmental applications, and crustal imaging (e.g., Abdelrahman et al 1989;Ateya and Takemoto 2002;Batista-Rodríguez et al 2013;Beiki and Pedersen 2011;Fedi 2007;Hinze 1990;Hinze et al 2013;LaFehr and Nabighian 2012;Long and Kaufmann 2013;Mehanee 2014a;Nettleton 1976;Okubo et al 2013;Paoletti et al 2013;Pei et al 2014).…”

“…One can refer to Holstein and Ketteridge (1996) and Holstein et al (2014), and the references therein, for a more detailed and comprehensive information on this particular thin-polygonal sheet subject. Beiki and Pedersen (2011) developed a data window constrained two-dimensional (2D) inversion technique for the interpretation of gravity gradient tensor data using dike/sheet and contact models. By definition, a data window contains a number of particular data points out of the entire measured gravity profile (Beiki and Pedersen 2011).…”

“…Beiki and Pedersen (2011) developed a data window constrained two-dimensional (2D) inversion technique for the interpretation of gravity gradient tensor data using dike/sheet and contact models. By definition, a data window contains a number of particular data points out of the entire measured gravity profile (Beiki and Pedersen 2011). These particular data points are measured with respect to the center (that is located at the maximum response of the profile) of this window.…”

“…In other words, the full measured gravity signature (that is, primarily influenced by the buried anomalous structure) was not considered in the interpretation. A series of successive data windows is constructed by increasing the number of data points used (out of the whole gravity profile) for estimating the target parameters (Beiki and Pedersen 2011). Beiki and Pedersen (2011) used the MATLAB nonlinear least squares optimization tool "lsqnonlin" to solve the minimization problem of their scheme.…”

“…A series of successive data windows is constructed by increasing the number of data points used (out of the whole gravity profile) for estimating the target parameters (Beiki and Pedersen 2011). Beiki and Pedersen (2011) used the MATLAB nonlinear least squares optimization tool "lsqnonlin" to solve the minimization problem of their scheme. This minimization tool is based on the Levenberg-Marquardt method (Levenberg 1944;Marquardt 1963).…”