Improved temporal and spatial focusing using deconvolution: theoretical, numerical and experimental studies

Abstract

Time Reversal can be used to time reverse and propagate the measured scattered waveforms to a point in both time and space, ideally to a delta function [delta(r with an arrow over it)delta(t)]. This is commonly referred to as time reversal focusing and has led to time reversal being applied in a wide variety of fields such as medicine, communications, nondestructive evaluation (NDE), and seismology. In practice, time reversal is not optimal for generating a delta function focus if certain conditions are not upheld. For time reversal to work perfectly, the following four conditions must be present: (1) one must record for an infinitely long period of time; (2) Green's functions must be assumed to contain infinite bandwidth; (3) attenuation must be absent within the medium; and (4) one must have full coverage of the wavefield. Due to the need for these conditions, much research is being carried out in order to enhance the time reversal process in practice. We introduce deconvolution, a simple and robust approach, in order to calculate an optimal signal for back propagation designed to give an improved focus. We demonstrate experimentally that deconvolution is able to dramatically improve the temporal focus compared to time reversal. Through a joint project with Los Alamos National Laboratory, we compared time reversal to deconvolution. The results showed that deconvolution was able to dramatically improve the temporal focus for a source and a receiver which were both located on the surface of our object. We then continued our experimental studies of deconvolution by doing a joint project with researcher Dr. Ernst Niederleithinger from the Federal Institute for Materials Research and Testing (BAM). For this experiment, we placed multiple sources within a concrete block and recorded the source wavefields on the surface with a single receiver. This experiment was designed to further test the robust nature of deconvolution and compare its temporal focusing capability to that of time reversal. All of these experimental studies show that deconvolution was able to improve the temporal focus compared to time reversal. We continued our comparison study between time reversal and deconvolution and demonstrated theoretically, experimentally, and numerically that deconvolution also improves spatial focusing. We give a proof explaining why one would expect improved spatial focusing when there is improved temporal focusing for both a acoustic and elastic media. We then demonstrate in our experiments the improved spatial focus achieved using deconvolution by scanning around the source location with a laser vibrometer at the time of focus for an acoustic case. Finally, we use deconvolution to locate synthetic microseismic events to prove numerically that improved temporal focusing leads to improved spatial focusing for both acoustic and elastic media.