Ridge‐regression algorithm for gravity inversion of fault structures with variable density

Abstract

We derive an analytical expression for gravity anomalies of an inclined fault with density contrast decreasing parabolically with depth. The effect of the regional background, particularly the interference from neighboring sources of a fault structure, is ascribed by a polynomial equation. We have developed an inversion technique employing the ridge‐regression iterative algorithm to infer the shape parameters of the fault structure, in addition to the effect of regional background. We demonstrate the validity of the proposed technique by inverting a gravity anomaly of a theoretical model, both with and without adding a regional background. The technique is insensitive to the effect of regional background. Two density‐depth models of the Godavari subbasin in India are used in our interpretation of the gravity anomalies of the Ahiri‐Cherla master fault. The interpreted results of a parabolic density model are found to be more geologically reasonable in comparison with the constant density model. The variations of the misfit function of the theoretical and observed gravity anomalies, the damping factor, and the shape parameters of the fault against the iteration number indicate the reliability of the interpretation.

Application of particle swarm optimization for gravity inversion of 2.5-D sedimentary basins using variable density contrast

“…We have used 29 vertical prisms, each with equal widths of 2.0 × 10 3 m but with different strike lengths for sedimentary basin modelling. The constants of parabolic density functions used for the Godavari sub-basin are ρ 0 = −0.5×10 3 and α = 0.1518259× 10 3 Kg m −3 per 1000 m (Chakravarthi and Sundararajan, 2004). So with 71 iterations and 45 models, we achieve a good fit between observed and PSO-analysed gravity anomalies.…”

“…Our paper presents the applicability and potentiality of PSO in gravity inverse problems. First, PSO is validated on synthetic gravity anomalies with and without noise, and the developed PSO-based algorithm is finally applied over two kinds of field gravity data taken from different geological terrains: (i) residual gravity anomaly over Gradiz Graben, western Anatolia (Sari and Salk, 2002), and (ii) residual gravity anomaly taken from Godavari sub-basin, India (Chakravarthi and Sundararajan, 2004).…”

Gravity Anomalies of 2.5-D Multiple Prismatic Structures with Variable Density: A Marquardt Inversion

“…where, G is the universal gravitational constant and du dv dw is the volume of an elementary mass, and DqðzÞ is the density contrast represented by the parabolic density function at a given depth, z = w, as described by CHAKRAVARTHI et al (2001) and CHAKRAVARTHI and SUNDARARAJAN (2004),…”

“…The methods enlisted above appear to be efficient only when the observed gravity anomalies are free from regional gravity background. However, in practice the anomaly due to a single geological structure can rarely be isolated perfectly from the interference of neighboring sources (CHAKRAVARTHI and SUNDARARAJAN, 2004) and therefore the interpretation carried out with the aforesaid techniques are often unreliable. Also, it is well known that the density of sedimentary rocks varies with depth (PEIRCE and LIPKOV, 1988;FERGUSON et al, 1988;HINZE, 2003) and hence it is possible to simulate the variation of density by mathematical functions which ensures more reliable results.…”

2D inverse modeling of residual gravity anomalies from Simple geometric shapes using Modular Feed-forward Neural Network

“…In the other words, different geometrical distributions of the subsurface mass can yield the same gravity field at the surface [Skeel 1947]. One way to solve this ambiguity is to assign a suitable geometry to the anomalous mass with a known density followed by inversion of gravity anomalies [Chakravarthi and Sundararajan 2004]. Although simple models may not be geologically realistic, they are usually are sufficient to analyze sources of many isolated anomalies [Abdelrahman and El-Araby 1993].…”