Crosshole radar tomography is a useful tool in diverse investigations in geology, hydrogeology, and engineering. Conventional tomograms provided by standard ray-based techniques have limited resolution, primarily because only a fraction of the information contained in the radar data i.e., thefirst-arrivaltimesandmaximumfirst-cycleamplitudesis included in the inversion. To increase the resolution of radar tomograms,wehavedevelopedaversatilefull-waveforminversion scheme that is based on a finite-difference time-domain solution of Maxwell’s equations. This scheme largely accountsforthe3Dnatureofradar-wavepropagationandincludes an efficient method for extracting the source wavelet from the radar data.After demonstrating the potential of the newschemeontworealisticsyntheticdatasets,weapplyitto two crosshole field data sets acquired in very different geologic/hydrogeologic environments. These are the first applications of full-waveform tomography to observed crosshole radar data.The resolution of all full-waveform tomograms is showntobemarkedlysuperiortothatoftheassociatedraytomograms. Small subsurface features a fraction of the dominant radar wavelength and boundaries between distinct geological/hydrological units are sharply imaged in the fullwaveformtomograms.

Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data

Multichannel Analysis of Surface Waves (MASW) analysis is an efficient tool to obtain the vertical shear-wave profile. One of the key steps in the MASW method is to generate an image of dispersive energy in the frequency-velocity domain, so dispersion curves can be determined by picking peaks of dispersion energy. In this paper, we propose to image Rayleigh-wave dispersive energy by high-resolution linear Radon transform (LRT). The shot gather is first transformed along the time direction to the frequency domain and then the Rayleigh-wave dispersive energy can be imaged by high-resolution LRT using a weighted preconditioned conjugate gradient algorithm. Synthetic data with a set of linear events are presented to show the process of generating dispersive energy. Results of synthetic and real-world examples demonstrate that, compared with the slant stacking algorithm, high-resolution LRT can improve the resolution of images of dispersion energy by more than 50%.

Rayleigh-wave dispersive energy imaging using a high-resolution linear radon transform

Crosshole radar techniques are important tools for a wide range of geoscientific and engineering investigations. Unfortunately, the resolution of crosshole radar images may be limited by inadequacies of the ray tomographic methods that are commonly used in inverting the data. Since ray methods are based on high-frequency approximations and only account for a small fraction of the information contained in the radar traces, they are restricted to resolving relatively large-scale features. As a consequence, the true potential of crosshole radar techniques has yet to be realized. To address this issue, we introduce a full-waveform inversion scheme that is based on a finite-difference time-domain solution of Maxwell's equations. We benchmark our new scheme on synthetic crosshole data generated from suites of increasingly complex models. The full-waveform tomographic images accurately reconstruct the following: (1) the locations, sizes, and electrical properties of isolated subwavelength objects embedded in homogeneous media; (2) the locations and sizes of adjacent subwavelength objects embedded in homogeneous media; (3) abrupt media boundaries and average and stochastic electrical property variations of heterogeneous layered models; and (4) the locations, sizes, and electrical conductivities of water-filled tunnels and closely spaced subwavelength pipes embedded in heterogeneous layered models. The new scheme is shown to be remarkably robust to the presence of uncorrelated noise in the radar data. Several limitations of the full-waveform tomographic inversion are also identified. For typical crosshole acquisition geometries and parameters, small resistive bodies and small closely spaced dielectric objects may be difficult to resolve. Furthermore, electrical property contrasts may be underestimated. Nevertheless, the full-waveform inversions usually provide substantially better results than those supplied by traditional ray methods.

Full-Waveform Inversion of Crosshole Radar Data Based on 2-D Finite-Difference Time-Domain Solutions of Maxwell's Equations

A space containing electric currents may be regarded as a field where energy is transform ed a t certain points into the electric and magnetic kinds by means of batteries, dynamos, thermoelectric actions, and so on, while in other parts of the field this energy is again transformed into heat, work done by electromagnetic forces, or any form of energy yielded by currents. Formerly a current was regarded as something travelling along a conductor, attention being chiefly directed to the conductor, and the energy which appeared at any part of the circuit, if considered at all, was supposed to be conveyed thither through the conductor by the current. But the existence of induced currents and of electromagnetic actions at a distance from a primary circuit from which they draw their energy, have led us, under the guidance of Faraday and Maxwell, to look upon the medium surrounding the conductor as playing a very important part in the development of the phenomena. If we believe in the continuity of the motion of energy, that is, if we believe that when it disappears at one point and reappears at another, it must have passed through the intervening space, we are forced .to conclude that the surrounding medium contains at least a part of the energy, and that it is capable of transferring it from point to point. Upon this basis Maxwell has investigated what energy is contained in the medium, and. he has given expressions which assign to each art of the field a quantity of energy depending on the electromotive and magnetic intensities, and on the nature of the matter at that part l regard to its specific inductive capacity and magnetic permeability. These expressions account, as far as we know, for the whole energy. According to Maxwell’s theory currents consist essentially in a certain distribution of energy in and around a conductor, accompanied by transformation and consequent movement of energy through the field.

http://rspl.royalsocietypublishing.org/content/36/228-231/186.full.pdf

On the Transfer of Energy in the Electromagnetic Field.

Providing a balance between principles and practice, this state-of-the-art overview of geophysical methods takes readers from the basic physical phenomena, through the acquisition and processing of data, to the creation of geological models of the subsurface and data interpretation to find hidden mineral deposits. Detailed descriptions of all the commonly used geophysical methods are given, including gravity, magnetic, radiometric, electrical, electromagnetic and seismic methods. Each technique is described in a consistent way and without complex mathematics. Emphasising extraction of maximum geological information from geophysical data, the book also explains petrophysics, data modelling and common interpretation pitfalls. Packed with full-colour figures, also available online, the text is supported by selected examples from around the world, including all the major deposit types. Designed for advanced undergraduate and graduate courses in minerals geoscience, this is also a valuable reference for professionals in the mining industry wishing to make greater use of geophysical methods. In 2015, Dentith and Mudge won the ASEG Lindsay Ingall Memorial Award for their combined effort in promoting geophysics to the wider community with the publication of this title.

Geophysics for the Mineral Exploration Geoscientist

New derivations for the conventional linear and parabolic [tau]-p transforms in the classic continuous function domain provide useful insight into the discrete [tau]-p transformations. For the filtering of unwanted waves such as multiples, the derivation of the [tau]-p transform should define the inverse transform first, and then compute the forward transform. The forward transform usually requires a p-direction deconvolution to improve the resolution in that direction. It aids the wave filtering by improving the separation of events in the [tau]-p domain. The p-direction deconvolution is required for both the linear and curvilinear [tau]-p transformations for aperture-limited data. It essentially compensates for the finite length of the array. For the parabolic [tau]-p transform, the deconvolution is required even if the input data have an infinite aperture. For sampled data, the derived [tau]-p transform formulas are identical to the DRT equations obtained by other researchers. Numerical examples are presented to demonstrate event focusing in [tau]-p space after deconvolution.

Linear and parabolic [tau]-p transforms revisited

Automated lithology prediction from PGNAA and other geophysical logs

By means of the inverse Fourier transform, we introduce an easy way to design convolutional differentiators. Such convolutional spatial differentiators may be used for the pseudo-spectral solution of the scalar wave equation. The tapered differentiators have the same form as a high-order finite difference (FD) operator, and share some of the advantages of both the conventional FD and Fourier methods. The differentiators have been implemented for 2-D zero-offset and common-source seismic modeling. Results using filters with as few as five points are acceptable; longer operators (e.g., 15 points) yield results of comparable quality to seismograms obtained with the Fourier method, but with considerable savings in computer time. Accuracy of the convolutional differentiator approach is appreciably better than that of the fourth-order FD method. The method can readily be extended to elastic wave field modeling.

Seismic scalar wave equation modeling by a convolutional differentiator

Delineation of sulphide ore-zones by borehole radar tomography at Hellyer Mine, Australia

A new nonlinear filter for wave-equation extrapolation-based multiple suppression is designed in the f-k domain. The realization of the new filter in the f-k domain is an extension of the conventional f-k dip filter. However, the new demultiple filter is superior to the conventional f-k dip filter in the sense that the multiple reject zones are determined automatically (based on the information of the input original data and the multiple model traces obtained by the waveextrapolation method) rather than by prior information on multiple moveout (dip) range. Therefore, it can easily cope with situations such as aliasing and the mixture of energy from multiples and primaries in the same quadrant. The new filter is smooth on the boundary of the reject area. Numerical examples demonstrate that the new filter is equivalent to the conventional f-k dip filter in multiple suppression for simple situations. However, when the multiples and primaries are mixed in the same quadrant and have only slight difference in dip, the new filter offers significant advantages over the conventional technique.

Binzhong Zhou

Papers

Linear and parabolic [tau]-p transforms revisited

Automated lithology prediction from PGNAA and other geophysical logs

Seismic scalar wave equation modeling by a convolutional differentiator

Delineation of sulphide ore-zones by borehole radar tomography at Hellyer Mine, Australia

Wave‐equation extrapolation‐based multiple attenuation: 2-D filtering in the f-k domain