An algorithm is proposed for the reconstruction of a sparse spike train from an incomplete set of its Fourier components. It is shown that as little as 20–25 percent of the Fourier spectrum is sufficient in practice for a high‐quality reconstruction. The method employs linear programming to minimize the [Formula: see text]‐norm of the output, because minimization of this norm favors solutions with isolated spikes. Given a wavelet, this technique can be used to perform deconvolution of noisy seismograms when the desired output is a sparse spike series. Relative reliability of the data is assessed in the frequency domain, and only the reliable spectral data are included in the calculation of the spike series. Equations for the unknown spike amplitudes are solved to an accuracy compatible with the uncertainties in the reliable data. In examples with 10 percent random noise, the output is superior to that obtained using conventional least‐squares techniques.
In an effort to reduce costs and increase revenues at mines, there is a strong incentive to develop highresolution techniques both for near-mine exploration and for delineation of known orebodies. To investigate the potential of high-frequency EM techniques for exploration and delineation of massive sulfide orebodies, radio frequency electromagnetic (RFEM) and ground-penetrating radar (GPR) surveys were conducted in boreholes through the McConnell massive nickel-copper sulfide body near Sudbury, Ontario, from 1993Ontario, from -1996 Crosshole RFEM data were acquired with a JW-4 electric dipole system between two boreholes on section 2720W. Ten frequencies between 0.5 and 5.0 MHz were recorded. Radio signals propagated through the Sudbury Breccia over ranges of at least 150 m at all frequencies. The resulting radio absorption tomogram clearly imaged the McConnell deposit over 110 m downdip. Signal was extinguished when either antenna entered the sulfide body. However, the expected radio shadow did not eventuate when transmitter and receiver were on opposite sides of the deposit. Two-dimensional modeling suggested that diffraction around the edges of the sulfide body could not account for the observed field amplitudes. It was concluded at the time that the sulfide body is discontinuous; according to modeling, a gap as small as 5 m could have explained the observations. Subsequent investigations by INCO established that pick-up in the metal-cored downhole cables was actually responsible for the elevated signal levels.Both single-hole reflection profiles and crosshole measurements were acquired using RAMAC borehole radar systems, operating at 60 MHz. Detection of radar reflections from the sulfide contact was problematic. One coherent reflection was observed from the hanging-wall contact in single-hole reflection mode. This reflection could be traced about 25 m uphole from the contact. In addition to unfavorable survey geometry, factors which may have suppressed reflections included host rock heterogeneity, disseminated sulfides, and contact irregularity.Velocity and absorption tomograms were generated in the Sudbury Breccia host rock from the crosshole radar. Radar velocity was variable, averaging 125 m/µs, while absorption was typically 0.8 dB/m at 60 MHz. Kirchhoffstyle 2-D migration of later arrivals in the crosshole radargrams defined reflective zones that roughly parallel the inferred edge of the sulfide body.The McConnell high-frequency EM surveys established that radio tomography and simple radio shadowing are potentially valuable for near-and in-mine exploration and orebody delineation in the Sudbury Breccia. The effectiveness of borehole radar in this particular environment is less certain.
A procedure has been developed to perform automatic inversion of HLEM frequency soundings by the method of Backus and Gilbert (BG). Using a linearized iterative scheme, a layered conductivity is constructed satisfying the available soundings to an accuracy consistent with the observational uncertainties. Subsequently, in order to investigate the resolving power of the data and hence (hopefully) to determine the broad scale features which are common to all conductivity models which satisfy the data, BG average conductivities are computed for the constructed model at a number of depths. In examples with both synthetic data and field data these averages proved to be identical (except for random error) to the corresponding average conductivities computed for a number of different models satisfying the same data. The additional models for this analysis were generated by maximizing or minimizing the conductivities of individual layers in the original constructed model using linear programming techniques. On the basis of these empirical results, in conjunction with the uniqueness theorem for HLEM soundings, it is concluded that BG average conductivities computed for a particular constructed model will often provide a valid characterization of the true ground conductivity over a depth range governed by survey parameters.
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