MIDEM: an iterative deconvolution of virtual reflections for single channel seismic signals

The present work introduces MIDEM (Minimum-squares Iterative DEconvolution of Multi-reflectors): a simple deconvolution approach, designed for single channel seismic signals and well suited for a straightforward computer coding, with no need of any built-in specialised math function call. The approach is based on the introduction of the concept of virtual reflections and on the a priori estimate of the received signature. MIDEM first reduces the problem statement into a vector transformation, then uses as solutive kernel, a classical self-learning, gradient search approach, finding an optimum estimate of the solution ( deconvolved signal) in a least squares sense. Stability and convergence criteria have been deduced from theory and reduced into bonds well suited for practical use. A further generalisation of the algorithm for the constrained minimisation problem has been presented as well. MIDEM has been tested both on synthetic and real sea trials data, always resulting in sharper scenarios and a resolution enhancement.