Multi-Dimensional Deconvolution for Near-Field Thread Seismic Sources in Tunnels

In underground tunnel constructions, belt conveyors or subway trains can be used as passive sources for time-lapse seismic assessments of surrounding formations. The key technology of passive seismic processes is seismic interferometry (SI), which has the ability to extract the Green's function between any two points in a medium of interest. However, since the process results are typically required to meet certain premise assumptions, the current SI methods cannot be directly used for belt conveyors. In the current study, this type of source is referred to as a near-field thread source and the proposed new SI method is adapted to this type of source. There are mainly two types of SI methods: SI by cross-correlation and SI by multi-dimensional deconvolution. The former requires that the passive source be uniformly distributed in the far field, while the latter relaxes the requirements for uniform distribution yet still requires far field sources. When the first assumptions are violated, the correlation function is proportional to a Green's function with a blurred source. The source blurring is then quantified by what is referred to as an interferometric point-spread function, which can be derived from the observed data. Therefore, using SI by MDD can effectively deblur the source of the Green's function by deconvolving the PSF. In this study, one set of geophones is located in one tunnel as the passive source, and another set is in an adjacent tunnel. However, since the setup almost coincided with the distribution of the passive sources, the spatial (wavenumber) spectrum of the PSF is too broad to be inverted. Therefore, a conventional MDD method is not suitable for this study's experiments. This study found that another PSF could be obtained from the data of the adjacent tunnel. Subsequently, a new MDD formula based on the new PSF is derived and compared with the derivation processes of the conventional MDD formula. Then, the feasibility of the proposed method is verified using numerical simulations.