Exploration Geophysics - Volume 33, Issue 3-4, 2002

In this paper, we treat a 3-D cased borehole model, to investigate theoretically and numerically the effects of an outermost boundary on borehole waves, and to discuss borehole wave penetration in a radial direction. The closed form solution for this model, numerical estimates of full waveforms, and excitation spectra are presented. We show that, when the radius of the simulated formation is greater than 1.5 m, the outermost boundary has little influence on borehole waveforms, for sourcereceiver spacings between 1.0 m and 1.5 m and at typical logging frequencies. When the radius of the outermost boundary is less than 0.5 m the influence of the outermost boundary cannot be neglected.

In order to absorb energy at the outermost boundary, a solid absorption material is better than a fluid one. Even if the first or second boundary is not cemented, the effect of the outermost boundary on borehole waveforms cannot be totally neglected in a typical sonic logging environment if the outermost boundary radius is less than 0.5 m. At low frequencies (for example, for a source centre frequency less than 3 kHz), these effects are negligible.

The numerical analysis also illustrates that low-frequency mode waves, such as Stoneley waves in an open borehole, have a radial penetration less than 10 cm, which implies that formation information such as permeability determined by such mode waves is limited to a very shallow zone around the borehole.

A magnetotelluric (MT) survey was conducted across the Narmoda-Son lineament to delineate zones of weakness along the Khandwa-Indore traverse, Madhya Pradesh, Central India. This survey was taken after two strong earthquakes at Jabalpur and Pandhana, of magnitudes 6.4 and 6.0, came in quick succession. One 100 km long profile from Borgaon to Barwaha was chosen, with a station spacing of about 8 to 10 km. MT signals were recorded, within the period range from 0.25 seconds to 4096 seconds, with a Metronix MMS 02E system. These MT signals are capable of mapping the variation in electrical conductivity of the subsurface to a depth of 200 km. A two-dimensional Rapid Relaxation Inversion (RRI) algorithm was used for modelling. Rotational invariant pairs, viz. (ρD, φD), (ρB, φB) and (ρC, φC), and transverse electric (TE) and transverse magnetic (TM) mode pairs (ρTE, φTE), (ρTM, φTM) were used to generate 2D models. Combined qualitative and quantitative interpretations are highlighted.

A highly conducting body is present in the lower crust and uppermost mantle, and it is present in all five models. These conducting rocks in the lower crust and the uppermost mantle may be responsible for the high heat flow in this study area. Rifting of the continent is a prominent signature in all these models. Sharp changes in electrical conductivity at a depth of about 110 to 120 km may be the signature of the lithosphere-asthenosphere boundary. Two-dimensional models generated from the rotationinvariant parameters show broadly the same important features as depicted by TE and TM mode models. Rotation-invariant phases (ΦD, ΦB, ΦC) and apparent resistivities (ρD, ρB, ρC) show the major zones of weakness along the traverse. Pandhana, the location of the epicentre of one recent earthquake in central India, is right over one of the zones of weakness. Static shifts can be used to locate fractures, fissures, and lineaments.

Complete Bouguer corrections have been computed over the Australian mainland and Tasmania on a 9 arc-second grid (∼250 m spatial resolution) from version 2 of the GEODATA digital elevation model (DEM) of Australia. These include the Bouguer plate correction to the geoid (mean sea level) and the planar terrain correction residual to this plate out to a radius of 50 km (beyond Hammer zone M). A constant topographic density of 2670 kg.m^-3 has been used for both correction terms. The terrain corrections were computed using a planar two-dimensional fast Fourier transform (FFT) algorithm.

Review of the magnetic properties and field responses of a Tasmanian dolerite sheet suggests that the magnetic field is controlled by variations in remanent magnetisation. There is general correlation between magnetic susceptibility and crystal size and texture through the intrusion, but no correlation between susceptibility and nature of the magnetic field. As the natural remanence and modern field vectors are crudely aligned, the effective contrast of the intrusion is the vector sum, which is equivalent to a susceptibility of about 0.07 SI. Intruded rocks are non-magnetic. Variations within the intrusion are explained in terms of oxide-rich horizons (which have equivalent susceptibilities up to 0.15 SI) and reversely magnetised sections.

Statistical methods for removing noise from multichannel spectra are now routinely applied in gamma-ray spectrometry. The two methods in common use are the Noise Adjusted Singular Value Decomposition (NASVD) method and the Maximum Noise Fraction (MNF) method. These methods use a principal component (PC) type analysis to extract the dominant spectral shapes from a dataset. These PCs are used to reconstruct spectra that have most of the original signal, but little of the noise. The NASVD and MNF methods differ mainly in how they normalise the input spectra for noise before spectral component analysis. The purpose of this paper is to evaluate these methods in terms of both the accuracy and precision of the resultant noise-reduced spectra.

We develop a methodology based on the use of a synthetic spectra dataset where the true spectrum channel count rates (in the absence of noise) are known. Because the true values are known, by repeatedly processing the same synthetic data using different synthesised noise we derive estimates of both the precision and accuracy of the processed data.

Our tests using synthetic data show that the NASVD and MNF methods produce almost identical results. This suggests that the differences in the way the methods normalise for noise are not of great significance. However, the MNF method produces results that are fractionally better in terms of both precision and accuracy. This may be a function of the robustness of the numerical algorithms we used to implement these methods.