Structural data constraints for implicit modeling of folds

Abstract

International audienceA recent method for modeling folds uses a fold frame with coordinates based on the structural geology of folds: fold axis direction, fold axial surface and extension direction. The fold geometry can be characterised by rotating the fold frame by the pitch of the fold axis in the axial surface and the angle between the folded foliation and the axial surface. These rotation angles can be expressed as 1D functions of the fold frame coordinates. In this contribution we present methods for extracting and automatically modeling the fold geometries from structural data. The fold rotation angles used for characterising the fold geometry can be calculated locally from structural observations. The fold rotation angles incorporate the structural geology of the fold and allow for individual structural measurements to be viewed in the context of the folded structure. To filter out the effects of later folding the fold rotation angles are plotted against the coordinates of the fold frame. Using these plots the geometry of the folds can be interpolated directly from structural data where we use a combination of radial basis function and harmonic analysis to interpolate and extrapolate the fold geometry. This contribution addresses a major limitation in existing methods where the fold geometry was not constrained from structural data. We present two case studies: a proof of concept synthetic model of a non-cylindrical fold and an outcrop of an asymmetrical fold within the Lachlan Fold belt at Cape Conran, Victoria, Australia

Inversion of Structural Geology Data for Fold Geometry

“…Grose et al () use the wavelength parameter estimated from the S‐Variogram as a fixed constraint for the fold wavelength and solve the Fourier coefficients using least squares regression. The quality of the resulting fold profiles is dependent on the wavelength estimated from the S‐Variogram.…”

“…(d) Cross plot showing the change in fold limb rotation angle α L plotted against changes in the fold axis rotation angle α P . Adapted from Grose et al ().…”

“…The fold rotation angles ( α P , L ) are first transformed to gradients ranging from , using the transformation, (Grose et al, ). The transformed fold rotation angles (fold gradients) can then be represented using a Fourier series, that is, a linear combination of trigonometric basis functions.…”

“…This technique has been applied extensively in the geophysical literature (e.g., Bodin, Sambridge, Rawlinson, & Arroucau, ; Bodin, Sambridge, Tkalcic, et al, ; Kolb & Lekić, ; Muir & Tkalčić, ). This is an improvement on Grose et al () where the data are smoothed using a radial basis interpolation scheme and no specific assumptions are made about the noise in the data.…”

“…The geological map (Figure ) is inverted to find the joint posterior distribution for the fold geometry. Each sample of the posterior distribution defines interpolation constraints for the implicit folding algorithm (Grose et al, ; Laurent et al, ). Two hundred model realizations (Figures e and f) are generated by sampling parameter values from the joint posterior distribution to inform the fold interpolation constraints.…”