Giovanni Angelo Meles

A New Vector Waveform Inversion Algorithm for Simultaneous Updating of Conductivity and Permittivity Parameters From Combination Crosshole/Borehole-to-Surface GPR Data

We have developed a new full-waveform groundpenetrating radar (GPR) multicomponent inversion scheme for imaging the shallow subsurface using arbitrary recording configurations. It yields significantly higher resolution images than conventional tomographic techniques based on first-arrival times and pulse amplitudes. The inversion is formulated as a nonlinear least squares problem in which the misfit between observed and modeled data is minimized. The full-waveform modeling is implemented by means of a finite-difference time-domain solution of Maxwells equations. We derive here an iterative gradient method in which the steepest descent direction, used to update iteratively the permittivity and conductivity distributions in an optimal way, is found by cross-correlating the forward vector wavefield and the backward-propagated vectorial residual wavefield. The formulation of the solution is given in a very general, albeit compact and elegant, fashion. Each iteration step of our inversion scheme requires several calculations of propagating wavefields. Novel features of the scheme compared to previous full-waveform GPR inversions are as follows: 1) The permittivity and conductivity distributions are updated simultaneously (rather than consecutively) at each iterative step using improved gradient and step length formulations; 2) the scheme is able to exploit the full vector wavefield; and 3) various data sets/survey types (e.g., crosshole and borehole-to-surface) can be individually or jointly inverted. Several synthetic examples involving both homogeneous and layered stochastic background models with embedded anomalous inclusions demonstrate the superiority of the new scheme over previous approaches.

Full-waveform inversion of cross-hole ground-penetrating radar data to characterize a gravel aquifer close to the Thur River, Switzerland

Cross-hole radar tomography is a useful tool for mapping shallow subsurface electrical properties viz. dielectric permittivity and electrical conductivity. Common practice is to invert cross-hole radar data with ray-based tomographic algorithms using first arrival traveltimes and first cycle amplitudes. However, the resolution of conventional standard ray-based inversion schemes for cross-hole ground-penetrating radar (GPR) is limited because only a fraction of the information contained in the radar data is used. The resolution can be improved significantly by using a full-waveform inversion that considers the entire waveform, or significant parts thereof. A recently developed 2D time-domain vectorial full-waveform cross-hole radar inversion code has been modified in the present study by allowing optimized acquisition setups that reduce the acquisition time and computational costs significantly. This is achieved by minimizing the number of transmitter points and maximizing the number of receiver positions. The improved algorithm was employed to invert cross-hole GPR data acquired within a gravel aquifer (4–10 m depth) in the Thur valley, Switzerland. The simulated traces of the final model obtained by the full-waveform inversion fit the observed traces very well in the lower part of the section and reasonably well in the upper part of the section. Compared to the ray-based inversion, the results from the full-waveform inversion show significantly higher resolution images. At either side, 2.5 m distance away from the cross-hole plane, borehole logs were acquired. There is a good correspondence between the conductivity tomograms and the natural gamma logs at the boundary of the gravel layer and the underlying lacustrine clay deposits. Using existing petrophysical models, the inversion results and neutron-neutron logs are converted to porosity. Without any additional calibration, the values obtained for the converted neutron-neutron logs and permittivity results are very close and similar vertical variations can be observed. The full-waveform inversion provides in both cases additional information about the subsurface. Due to the presence of the water table and associated refracted/reflected waves, the upper traces are not well fitted and the upper 2 m in the permittivity and conductivity tomograms are not reliably reconstructed because the unsaturated zone is not incorporated into the inversion domain.

Physical and non-physical energy in scattered wave source-receiver interferometry

Source-receiver interferometry allows Greens functions between sources and receivers to be estimated by means of convolution and cross-correlation of other wavefields. Source-receiver interferometry has been observed to work surprisingly well in practical applications when theoretical requirements (e.g., complete enclosing boundaries of other sources and receivers) are contravened: this paper contributes to explain why this may be true. Commonly used inter-receiver interferometry requires wavefields to be generated around specific stationary points in space which are controlled purely by medium heterogeneity and receiver locations. By contrast, application of source-receiver interferometry constructs at least kinematic information about physically scattered waves between a source and a receiver by cross-convolution of scattered waves propagating from and to any points on the boundary. This reduces the ambiguity in interpreting wavefields generated using source-receiver interferometry with only partial boundaries (as is standard in practical applications), as it allows spurious or non-physical energy in the constructed Greens function to be identified and ignored. Further, source-receiver interferometry (which includes a step of inter-receiver interferometry) turns all types of non-physical or spurious energy deriving from inter-receiver interferometry into what appears to be physical energy. This explains in part why source-receiver interferometry may perform relatively well compared to inter-receiver interferometry when constructing scattered wavefields.

GPR Full-Waveform Sensitivity and Resolution Analysis Using an FDTD Adjoint Method

GPR tomography is a useful tool for mapping the conductivity and permittivity distributions in the shallow subsurface. By exploiting the full GPR waveforms it is possible to image sub-wavelength features and improve resolution relative to what is possible using ray-based approaches. Usually, mere convergence in the data space is the only criterion used to appraise the goodness of the final result, therefore limiting the reliability of the inversion. A better indication of the correctness of an inverted model and its various parts could be obtained by means of a formal resolution and information content analysis. We present here a novel method for computing the sensitivity kernels (Jacobian matrix) based on an FDTD adjoint method. We show that the column sum of absolute values of the Jacobian, often used as a proxy for model resolution, is inadequate, such that a formal resolution analysis should be performed. The eigenvalue spectrum of the pseudo-Hessian matrix provides a measure of the information content of the experiment and shows the extent of the unresolved model space.

Full-waveform inversion of crosshole ground penetrating radar data to characterize a gravel aquifer close to the Thur River, Switzerland

Imaging results of crosshole GPR can be significantly improved by using full-waveform inversion compared to conventional ray-based inversion schemes. A recently developed 2D finite difference time domain (FDTD) vectorial full-waveform crosshole radar inversion method was made more flexible to allow using an optimized acquisition setup that reduces the measurement speed and the computational cost. This improved algorithm was used to invert crosshole GPR data acquired within a gravel aquifer in northern Switzerland. Compared to the ray-based inversion, the results from the full-waveform inversion show significantly higher resolution images in the depth range of 6m - 10m. Comparison of the inversion results with borehole logs shows that porosity estimates obtained from Neutron-Neutron data correspond well with the GPR porosities derived from the permittivity distribution in the depth range 6 m - 10 m and that the trends are in good qualitative agreement. Furthermore, there is a good correspondence between the conductivity tomograms and natural Gamma logs at the boundary between the gravel layer and the underlying lacustrine clay sediments.

Automatic identification of multiply diffracted waves and their ordered scattering paths

An automated algorithm uses recordings of acoustic energy across a spatially-distributed array to derive information about multiply scattered acoustic waves in heterogeneous media. The arrival time and scattering-order of each recorded diffracted acoustic wave, and the exact sequence of diffractors encountered by that wave, are estimated without requiring an explicit model of the medium through which the wave propagated. Individual diffractors are identified on the basis of their unique single-scattering relative travel-time curves (move-outs) across the array, and secondary (twice-scattered) waves are detected using semblance analysis along temporally offset primary move-outs. This information is sufficient to estimate travel times and scattering paths of all multiply diffracted waves of any order, and for these events to be identified in recorded data. The algorithm is applied to synthetic acoustic data sets from a variety of media, including different numbers of point-diffractors and a medium with strong heterogeneity and non-hyperbolic move-outs.

Marchenko Imaging of Volve Field, North Sea

Marchenko redatuming estimates the full response (including internal multiples) from a virtual source inside of an medium, using only reflection measurements at the Earth’s surface and a smooth estimate of the velocity model. As such, it forms a new way to obtain full field propagators to form images of target zones in the subsurface by means of Marchenko imaging, without necessarily have to create detailed models of overburden structure. One of the main obstacles to the application of such novel techniques to field datasets is the set of requirements of the reflection response: it should be wideband, acquired with wide aperture, densely sampled arrays of co-located sources and receivers, and should have undergone removal of direct waves, source and receiver ghosts and free-surface multiples. We use a wave-equation approach to jointly redatum, demultiple, and source designature to transform data recorded using ocean-bottom acquisition systems into a suitable proxy of the reflection response required by the Marchenko scheme. We briefly review the Marchenko redatuming scheme, and present the first encouraging field results of 2D target-oriented imaging of an ocean-bottom cable dataset, acquired over the Volve field. We further discuss the ‘challenge of convergence’ of the Marchenko redatuming scheme for real data.

Constructing new seismograms from old earthquakes: Retrospective seismology at multiple length scales

If energy emitted by a seismic source such as an earthquake is recorded on a suitable backbone array of seismometers, source-receiver interferometry (SRI) is a method that allows those recordings to be projected to the location of another target seismometer, providing an estimate of the seismogram that would have been recorded at that location. Since the other seismometer may not have been deployed at the time at which the source occurred, this renders possible the concept of “retrospective seismology” whereby the installation of a sensor at one period of time allows the construction of virtual seismograms as though that sensor had been active before or after its period of installation. Here we construct such virtual seismograms on target sensors in both industrial seismic and earthquake seismology settings, using both active seismic sources and ambient seismic noise to construct SRI propagators, and on length scales ranging over 5 orders of magnitude from ∼40 m to ∼2500 km. In each case we compare seismograms constructed at target sensors by SRI to those actually recorded on the same sensors. We show that spatial integrations required by interferometric theory can be calculated over irregular receiver arrays by embedding these arrays within 2-D spatial Voronoi cells, thus improving spatial interpolation and interferometric results. The results of SRI are significantly improved by restricting the backbone receiver array to include approximately those receivers that provide a stationary-phase contribution to the interferometric integrals. Finally, we apply both correlation-correlation and correlation-convolution SRI and show that the latter constructs fewer nonphysical arrivals.

Characterizing a low-velocity waveguide using crosshole GPR full-waveform inversion

For accurate prediction of flow and contaminant transport a detailed quantification of the local spatial hydraulic conductivity is necessary. In particular, decimeter-scale high contrast layers caused by increased porosity or clay content are important because they can have a dominant effect on solute transport. Such embedded layers when characterized by high dielectric permittivity can act as low-velocity electromagnetic waveguides and be readily identified and characterized using high-frequency crosshole GPR. We show by means of a GPR field example from a hydrological test site in Switzerland that the full-waveform inversion, which exploits the full information content of the data, is able to image a sub-wavelength thickness dipping low-velocity wave-guiding layer. Further, we show an approach to identify low-velocity waveguides from the measured data by analyzing the amplitude and energy behavior within the data. For transmitters present within the waveguide, high amplitude elongated wave-trains are detected for receivers straddling the waveguide depth range, with significantly larger amplitudes than on receivers outside the low-velocity layer, whereas transmitters outside the waveguide show an energy minimum for receivers within the waveguide.

Full-waveform inversion of GPR data in frequency-domain

A new full-waveform inversion scheme is developed to obtain high-resolution images of cross-hole ground penetrating radar (GPR) data. The inversion is formulated as a non-linear least squares problem which minimizes errors between synthetic and observed data. The full-waveform modeling is implemented in frequency domain using the finite-difference (FDFD) solution of Maxwell equation. Here, we are using an iterative gradient method (Gauss-Newton) where the gradient is determined by using the forward vector wavefield and the backward-propagated vectorial residual wavefield. The algorithm inverts sequentially from low to high frequencies and permittivity and conductivity distributions can be obtained simultaneously. Preliminary inversion results of a synthetic example for a homogeneous background model with embedded high contrast parameters anomalies show that the permittivity result is comparable with time domain full-waveform inversion that uses an expanding bandwidth for increasing iterations.