Crosshole radar velocity tomography with finite-frequency Fresnel volume sensitivities

Abstract

S U M M A R YCrosshole-radar velocity tomography is increasingly being used to characterize the electrical and hydrologic properties of the Earth's near-surface. Because radar methods are sensitive to the water content of geologic materials, velocity tomography is a good proxy for imaging soil water retention in the vadose zone and porosity in the saturated zone. In many near-surface environments, radar velocity varies over a few orders of magnitude. Common velocity tomography applies ray theory that assumes infinite frequency propagation. The ray approximation may induce velocity modelling artefacts and loss of localization. We propose an alternative method for computing velocity tomogram sensitivities using Fresnel volumes based on first-order scattering. The Fresnel volume sensitivities account for the finite-frequency of the crosshole radar signal and model the physics of radar propagation more accurately than the ray theory approximation.We demonstrate that applying finite-frequency Fresnel volume sensitivities provides improved radar velocity tomograms in low contrast environments. Analysis of the singular value decomposition of the sensitivity matrix demonstrates how the finite-frequency inversion recovers and localizes velocity heterogeneities better than ray theory. The singular value spectrum obtained from the full waveform sensitivities matches well with the Fresnel volume results. Furthermore, these basis functions are smooth and localized because the kernels capture the first order wave propagation effect compared to ray based sensitivity, which is a high frequency approximation. Through forward modelling experiments, we validate the finite-frequency sensitivity for crosshole radar velocity. In the Fresnel volume approach, the traveltime picking is more efficient because the datum is the peak of the first pulse rather than the first arrival, and therefore, data pre-processing is simpler and may be easily automated. The synthetic Fresnel volume inversion results show improvements in the final model and the data fits are better when compared to the ray theoretical inversions.

Accounting for imperfect forward modeling in geophysical inverse problems — Exemplified for crosshole tomography

“…but to an area around the raypath (see, e.g., Marquering et al, 1999;Dahlen et al, 2000;Jensen et al, 2000;Spetzler and Snieder, 2004;Buursink et al, 2008). For a single-frequency source wavelet, the sensitivity kernel consists of alternating regions of positive and negative sensitivity, known as Fresnel zones (Woodward, 1992).…”

“…Using the Born approximation (considering first-order scattering), an exact analytical expression for the sensitivity kernel for a point source can be derived for seismic (Marquering et al, 1999;Dahlen et al, 2000;Jensen et al, 2000;Spetzler and Snieder, 2004;Liu et al, 2009) and electromagnetic wave propagation (Buursink et al, 2008;Liu et al, 2009). Here, we will make explicit use of the formulation of the sensitivity kernels given by Buursink et al (2008), and we refer to it as the Born forward model g Born .…”

“…Here, we will make explicit use of the formulation of the sensitivity kernels given by Buursink et al (2008), and we refer to it as the Born forward model g Born .…”

“…Note also that sensitivity kernels associated with the Born approximation typically do not reflect the sensitivity of the first-break arrival (as we make use of to determine the traveltime in this paper) but the time delay associated with maximum crosscorrelation between the observed and simulated wavefield. We still consider the sensitivity kernels based on the Born approximation here because they have previously been used to invert traveltime data recorded as first-break arrival (see e.g., Buursink et al, 2008;Liu et al, 2009).…”

Cross-borehole tomography with correlation delay times

“…van Leeuwen and Mulder (2010) propose a weighted crosscorrelation criterion that renders borehole tomography less sensitive to errors in the source time function. Buursink et al (2008) recently extend the finite-frequency tomography to crosshole radar velocity tomography.…”