Super-virtual refraction interferometry: Theory

Inverting for the subsurface velocity distribution by refraction traveltime tomography is a well-accepted imaging method by both the exploration and earthquake seismology communities. A significant drawback, however, is that the recorded traces become noisier with increasing offset from the source position, and so prevents accurate picking of traveltimes in far-offset traces. To enhance the signal-to-noise ratio of the far-offset traces, we present the theory of super-virtual refraction interferometry where the signal-to-noise ratio (SNR) of far-offset head-wave arrivals can be theoretically increased by a factor proportional to N; here, N is the number of receiver and source positions associated with the recording and generation of the head-wave arrival. There are two steps to this methodology: correlation and summation of the data to generate traces with virtual head-wave arrivals, followed by the convolution of the data with the virtual traces to create traces with super-virtual head-wave arrivals. This method is valid for any medium that generates head-wave arrivals. There are at least three significant benefits to this methodology: 1). enhanced SNR of far-offset traces so the first-arrival traveltimes of the noisy far-offset traces can be more reliably picked to extend the useful aperture of data, 2). the SNR of head waves in a trace that arrive after the first arrival can be enhanced for accurate traveltime picking and subsequent inversion by traveltime tomography, and 3). common receiver-pair gathers can be analyzed to detect the presence of diving waves in the first arrivals, which can be used to assess the nature of the refracting boundary. © 2011 Society of Exploration Geophysicists.