Interferometry by Deconvolution of Multicomponent Multioffset GPR Data

Abstract

Evert Slob received the M.Sc. degree in mining and petroleum engineering and the Ph.D. degree (cum laude) in applied sciences from Delft University of

A lossless earth Green's function representation between any two subsurface points from surface reflection GPR data

“…The horizontal components of the electric and magnetic field vectors can be written in terms of the up-and downgoing magnetic and electric fields as [11] …”

“…There are 2 n−1 events in f 1 and 2 n in f 2 for n reflectors above the focus depth. Then we compute the magnetic field Green's functions for an electric dipole source at the surface in the frequency domain using equations (11) and (12) for virtual receiver positions from the surface to 0.25 m below the bottom reflector. The result is shown in the time domain for virtual receivers at all depth levels in the top plot of Figure 4.…”

Data-driven inversion of GPR surface reflection data for lossless layered media

“…Quantities in the horizontal Fourier transformed-frequency domain are denoted with a diacritical tilde, e.g., the electric field vector is denotedẼ. Here we use the procedure of [5] and store the measured horizontal components of the electric,Ẽ, and the magnetic, H, field vectors in the field vectorF asF = (F 1 ,F 2 ), withF 1 = (Ẽ x ,Ẽ y ) andF 2 = (−H y ,H x ). The decomposed TM-mode and TE-mode wavefields are connected to the measurements through composition matricesL 1,2 .…”

“…The decomposed TM-mode and TE-mode wavefields are connected to the measurements through composition matricesL 1,2 . The decomposed down-and upgoing TM-and TE-modes are stored in the vectorP = (p [5]. This choice ofL 1,2 is known as flux-normalization and has the advantage that upgoing and downgoing transmission responses are equal [9].…”

“…If these are in the subsurface the reflection response of the medium below the receiver (or source) level can be obtained through multidimensional deconvolution of the upgoing wavefield by the downgoing wavefield at this level [4], [5]. To obtain information below this level, model driven methods are being used to first create reflection images and then medium parameters are estimated from the reflection coefficients.…”