Reflecting boundary conditions for interferometry by multidimensional deconvolution

Abstract

SUMMARYIn this work we investigate a modification of the formulation of the theory underlying seismic interferometry (SI) by multidimensional deconvolution (MDD). The current formulation, and hence method, relies on separation of waves traveling inward and outward of a volume bounded by receivers. As a consequence, it is predominantly useful when receivers are illuminated from one side only. This puts constraints on the applicability of SI by MDD to omnidirectional wave fields. The proposed modification eliminates the requirement to separate inward-and outward propagating wave field and, consequently, improves the applicability of MDD to omnidirectional wave fields. We therefore envisage the modified MDD formulation to hold significant promise in the application to ambient-noise surface wave data.

Towards monitoring the englacial fracture state using virtual-reflector seismology

“…They are, however, subject to different conditions. In particular, this concerns the illumination pattern and receiver geometry (Wapenaar et al 2011b;Weemstra et al 2017b). SI by CC is most restrictive in terms of medium properties and illumination.…”

“…Taken all together, SI by CC is, strictly speaking, therefore rather restrictive in terms of medium properties and illumination. SI by MDD and VRS circumvent some of the limitations inherent in SI by CC, and, as such, allow the retrieval of more accurate medium responses (Wapenaar et al 2011b;Weemstra et al 2017b). …”

“…Eq. (5) is derived assuming absorbing boundary conditions along S rec in this reference medium (Wapenaar et al 2011b;Weemstra et al 2017b). Anticipating the introduction of VRS in the next section, the absorbing nature of the reference medium is explicitly indicated by means of the superscript (a).…”

“…Recently, Weemstra et al (2017b) introduced an alternative simplification of the acoustic convolution-type Green's function representation by assuming reflecting boundary conditions along S rec in the reference medium. Considering the application to singlemode surface waves, we refer to the technique resulting from this simplification as VRS.…”

“…And because VRS can be derived from a simplification of the same convolution-type Green's function representation, its successful application also does not require the medium to be lossless. However, because S rec , instead of being an absorbing boundary, is subject to reflecting boundary conditions in the reference medium, virtual-source responses retrieved through the application of VRS contain so-called virtual reflections from the receiver contour (Weemstra et al 2017b). In this work, we investigate the suitability of these virtual reflections for the purpose of monitoring a non-scattering medium such as glacier ice.…”