TY - JOUR
T1 - Elastodynamic single-sided homogeneous Green’s function representation: Theory and numerical examples
AU - Reinicke Urruticoechea, Christian
AU - Wapenaar, Kees
N1 - Accepted Author Manuscript
PY - 2019
Y1 - 2019
N2 - The homogeneous Green’s function is the difference between an impulse response and its time-reversal. According to existing representation theorems, the homogeneous Green’s function associated with source–receiver pairs inside a medium can be computed from measurements at a boundary enclosing the medium. However, in many applications such as seismic imaging, time-lapse monitoring, medical imaging, non-destructive testing, etc., media are only accessible from one side. A recent development of wave theory has provided a representation of the homogeneous Green’s function in an elastic medium in terms of wavefield recordings at a single (open) boundary. Despite its single-sidedness, the elastodynamic homogeneous Green’s function representation accounts for all orders of scattering inside the medium. We present the theory of the elastodynamic single-sided homogeneous Green’s function representation and illustrate it with numerical examples for 2D laterally-invariant media. For propagating waves, the resulting homogeneous Green’s functions match the exact ones within numerical precision, demonstrating the accuracy of the theory. In addition, we analyse the accuracy of the single-sided representation of the homogeneous Green’s function for evanescent wave tunnelling.
AB - The homogeneous Green’s function is the difference between an impulse response and its time-reversal. According to existing representation theorems, the homogeneous Green’s function associated with source–receiver pairs inside a medium can be computed from measurements at a boundary enclosing the medium. However, in many applications such as seismic imaging, time-lapse monitoring, medical imaging, non-destructive testing, etc., media are only accessible from one side. A recent development of wave theory has provided a representation of the homogeneous Green’s function in an elastic medium in terms of wavefield recordings at a single (open) boundary. Despite its single-sidedness, the elastodynamic homogeneous Green’s function representation accounts for all orders of scattering inside the medium. We present the theory of the elastodynamic single-sided homogeneous Green’s function representation and illustrate it with numerical examples for 2D laterally-invariant media. For propagating waves, the resulting homogeneous Green’s functions match the exact ones within numerical precision, demonstrating the accuracy of the theory. In addition, we analyse the accuracy of the single-sided representation of the homogeneous Green’s function for evanescent wave tunnelling.
KW - Elastic
KW - Interferometry
KW - Internal multiples
KW - Layered
KW - Numerical
UR - http://www.scopus.com/inward/record.url?scp=85064266434&partnerID=8YFLogxK
U2 - 10.1016/j.wavemoti.2019.04.001
DO - 10.1016/j.wavemoti.2019.04.001
M3 - Article
SN - 0165-2125
VL - 89
SP - 245
EP - 264
JO - Wave Motion
JF - Wave Motion
ER -