Improving stochastic reconstructions by weighting correlation functions in an objective function

¹ CSIRO Land and Water - Glen Osmond, PB2, SA 5064, Australia
² The University of Melbourne, Department of Infrastructure Engineering - Parkville, VIC, 3010, Australia
³ Institute of Geosphere Dynamics of the Russian Academy of Sciences - Leninsky prosp. 38/1, Moscow, 119334, Russia
⁴ Institute of Physics of the Earth of Russian Academy of Sciences - Bolshaya Gruzinskaya 10, Moscow, 107031, Russia

Received: 7 August 2015
Accepted: 24 August 2015

Abstract

Spatial correlation functions (CFs) are prominent descriptors of any structure. In this letter, we show for the first time how proper weighting of CFs in an objective function can lead to significant improvements in reconstruction accuracy and in the likelihood of convergence. We develop a simple weighting scheme and display its effectiveness on two- and three-dimensional structures utilizing up to 27 CFs in one set. Proper weighting of the objective functions led to completely accurate reconstructions not achievable by conventional unweighted approaches. The proposed approach combining numerous CFs can potentially characterize and reconstruct structures of any complexity.