Publication Details

Category Text Publication
Reference Category Journals
DOI 10.1016/j.jappgeo.2011.08.010
Title (Primary) Bayesian frequency-domain blind deconvolution of ground-penetrating radar data
Author Schmelzbach, C.; Scherbaum, F.; Tronicke, J.; Dietrich, P. ORCID logo
Journal Journal of Applied Geophysics
Year 2011
Department MET
Volume 75
Issue 4
Page From 615
Page To 630
Language englisch
Keywords Deconvolution; inverse filtering; ground penetrating radar; GPR; data processing; vertical resolution

Enhancing the resolution and accuracy 1 of surface ground-penetrating radar (GPR) reflection data by inverse filtering to recover a zero-phased band-limited reflectivity image requires a deconvolution technique that takes the mixed-phase character of the embedded wavelet into account. In contrast, standard stochastic deconvolution techniques assume that the wavelet is minimum phase and, hence, often meet with limited success when applied to GPR data. We present a new general-purpose blind deconvolution algorithm for mixed-phase wavelet estimation and deconvolution that (1) uses the parametrization of a mixed-phase wavelet as the convolution of the wavelet's minimum-phase equivalent with a dispersive all-pass filter, (2) includes prior information about the wavelet to be estimated in a Bayesian framework, and (3) relies on the assumption of a sparse reflectivity. Solving the normal equations using the data autocorrelation function provides an inverse filter that optimally removes the minimum-phase equivalent of the wavelet from the data, which leaves traces with a balanced amplitude spectrum but distorted phase. To compensate for the remaining phase errors, we invert in the frequency domain for an all-pass filter thereby taking advantage of the fact that the action of the all-pass filter is exclusively contained in its phase spectrum. A key element of our algorithm and a novelty in blind deconvolution is the inclusion of prior information that allows resolving ambiguities in polarity and timing that cannot be resolved using the sparseness measure alone. We employ a global inversion approach for non-linear optimization to find the all-pass filter phase values for each signal frequency. We tested the robustness and reliability of our algorithm on synthetic data with different wavelets, 1-D reflectivity models 19 of different complexity, varying levels of added noise, and different types of prior information. When applied to realistic synthetic 2-D data and 2-D field data, we obtain images with increased temporal resolution compared to the results of standard processing.
Persistent UFZ Identifier
Schmelzbach, C., Scherbaum, F., Tronicke, J., Dietrich, P. (2011):
Bayesian frequency-domain blind deconvolution of ground-penetrating radar data
J. Appl. Geophys. 75 (4), 615 - 630