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A non-iterative waveform sensing approach is proposed toward (i) geometricreconstruction of penetrable fractures, and (ii) quantitative identification oftheir heterogeneous contact condition by seismic i.e. elastic waves. To thisend, the fracture support $\Gamma$ (which may be non-planar and unconnected) isfirst recovered without prior knowledge of the interfacial condition by way ofthe recently established approaches to non-iterative waveform tomography ofheterogeneous fractures, e.g. the methods of generalized linear sampling andtopological sensitivity. Given suitable approximation $\breve\Gamma$ of thefracture geometry, the jump in the displacement field across $\breve\Gamma$i.e. the fracture opening displacement (FOD) profile is computed from remotesensory data via a regularized inversion of the boundary integralrepresentation mapping the FOD to remote observations of the scattered field.Thus obtained FOD is then used as input for solving the traction boundaryintegral equation on $\breve\Gamma$ for the unknown (linearized) contactparameters. In this study, linear and possibly dissipative interactions betweenthe two faces of a fracture are parameterized in terms of a symmetric,complex-valued matrix $\boldsymbol{K}(\boldsymbol{\xi})$ collecting the normal,shear, and mixed-mode coefficients of specific stiffness. To facilitate thehigh-fidelity inversion for $\boldsymbol{K}(\boldsymbol{\xi})$, a 3-stepregularization algorithm is devised to minimize the errors stemming from theinexact geometric reconstruction and FOD recovery. The performance of theinverse solution is illustrated by a set of numerical experiments where acylindrical fracture, endowed with two example patterns of specific stiffnesscoefficients, is illuminated by plane waves and reconstructed in terms of itsgeometry and heterogeneous (dissipative) contact condition.

A synoptic approach to the seismic sensing of heterogeneous fractures: from geometric reconstruction to interfacial characterization