Multidimensional wavefront estimation from differential delays

The propagating wavefield measured by complex sources-receivers arrangements can be characterized by a delayed waveform in the n-dimensional (n-D) space of measurements. The authors propose a method for the nonparametric estimation of the time of delay function (also referred to as wavefront) that does not require the knowledge of the waveform. The n-D wavefront is estimated by using a least squares (LS) approach that integrates the local estimates of the differential times of delay of the waveform between neighboring sensors. The method shows a lower sensitivity to errors in local estimates when the overall multidimensionality (and redundancy) of the data is exploited. Examples considered are derived from reflection seismology applications