R. C. Bailey

Crosshole seismic tomography

Many tomographic interpretations of crosshole seismic traveltimes have approximated the raypaths with straight lines connecting the source and receiver. This approximation is valid where the velocity does not vary greatly, but in many regions of interest velocity variations of 10–20 percent or more are observed, causing significant ray curvature. Other work has taken this nonlinear effect into account, but there do not appear to be many cases of demonstrated success in its application to the crosshole seismic problem. We present here an iterative inversion scheme based on two‐dimensional ray tracing and its successful application to field data. The interpretation method iteratively ray traces and then updates the velocity model. Within each iteration, the differences between the data and the current model traveltimes obtained by ray tracing are related to the unknown velocity perturbations through a system of linear equations. A damped least‐squares method solves for the velocity perturbations which updat...

Analytic investigations of the effects of near-surface three-dimensional galvanic scatterers on MT tensor decompositions

An outcropping hemispherical inhomogeneity embedded in a two‐dimensional (2-D) earth is used to model the effects of three‐dimensional (3-D) near‐surface electromagnetic (EM) “static” distortion. Analytical solutions are first derived for the galvanic electric and magnetic scattering operators of the heterogeneity. To represent the local distortion by 3-D structures of fields which were produced by a large‐scale 2-D structure, these 3-D scattering operators are applied to 2-D electric and magnetic fields derived by numerical modeling to synthesize an MT data set. Synthetic noise is also included in the data. These synthetic data are used to study the parameters recovered by several published methods for decomposing or parameterizing the measured MT impedance tensor. The stability of these parameters in the presence of noise is also examined. The parameterizations studied include the conventional 2-D parameterization (Swift, 1967), Eggers’s (1982) and Spitz’s (1985) eigenstate formulations, LaTorraca et al...

Inversion of the geomagnetic induction problem

An algorithm has been found for inverting the problem of geomagnetic induction in a concentrically stratified Earth. It determines the (radial) conductivity distribution from the frequency spectrum of the ratio of internal to external magnetic potentials of any surface harmonic mode. The derivation combines the magnetic induction equation with the principle of causality in the form of an integral constraint on the frequency spectrum. This algorithm generates a single solution for the conductivity. This solution is here proved unique if the conductivity is a bounded, real analytic function with no zeros. Suggestions are made regarding the numerical application of the algorithm to real data.

Conductivity anomalies: lower crust or asthenosphere?

Abstract The indication from surface measurements of a zone of relatively high conductivity (resistivity

Gravity-driven continental overflow and Archaean tectonics

Whether modern tectonic processes differ substantially from those in Archaean times (>2,500 Myr ago) remains controversial. One view is that Archaean tectonic processes were some combination of modern ones, occurring faster or more shallowly because of the larger heat output of the early Earth, but others have proposed that significantly different processes operated. Here I argue that gravitational spreading of Archaean continents would have caused them continuously and pervasively to ‘overflow’ onto adjacent ocean basins, and that this process would have naturally ceased at the end of the Archaean era. Because modern continental crust is believed to be ductile rather than brittle below a depth corresponding to a temperature of about 350–400 °C (ref. 3), it seems likely that such a ductile zone was universally present within the hotter Archaean continental crust. If the mean geothermal gradient of the continents had exceeded ∼25–30 °C km−1 , then the resulting ductile zone would have caused continental overflow to occur, and such a process can account for many of the distinctive peculiarities observed in the Archaean geological record. The cessation of continental overflow corresponds naturally to the stabilizing ‘cratonization’ which marked the end of the Archaean era, with its timing dependent on the evolution of both the geothermal gradient in the continents and the depth of the ocean basins.

An instrument for measuring complex magnetic susceptibility of soils

To improve the success of electromagnetic induction (EMI) metal detectors in identifying anti-personnel land mines buried in slightly ferromagnetic natural soils, we need to know what range of soil physical properties must be dealt with. We have therefore built a laboratory instrument for measuring complex magnetic susceptibility in inch-sized samples over a frequency range from 100 Hz to ~ 70 kHz with errors of a few percent of the sample susceptibility in a sample of ~1 milli-SIU volume susceptibility, (i.e. ~30 micro-SIU). The instrument is a symmetrical, six coil, induction spectrometer. A pair of transmitter coils in Helmholtz configuration generates a uniform magnetic field over the sample region. The magnetic moment induced in the sample is detected (mainly) by a pair of receiver coils which are closer to the sample than the transmitter pair and also (nearly) in Helmholtz configuration, so as to provide uniform sensitivity over the whole sample region. The coupling of the main receiver pair to the transmitter pair is annulled with a second pair of coils (called the reference receiver pair) situated outside the transmitter pair. The transmitter coils are energized with a wideband current. Data acquisition is by a PC computer with a 192 kHz, 24 bit, 2 channel sound card using software in written in MatLab. Although our instrument is still a prototype and its design continues to evolve, we have measured susceptibility spectra of some samples from de-mining projects in areas where false alarms are a problem and have found dispersive susceptibilities.

Implications of iceberg dynamics for iceberg stability estimation

Abstract Methods of estimating when an iceberg is likely to become unstable and roll over are potentially useful (e.g. in iceberg towing). Iceberg stability assessment and prediction can be done using surveys of the underwater geometry of the iceberg; this however is is not fast enough to be ideal for working conditions. Real-time monitoring of the dynamic response of icebergs to ocean wave excitation can be used as the basis of three alternative stability assessment methods which work in real time. An iceberg becomes unstable to rolling when its resonant rolling frequency diminishes to zero, typically as a result of changes in geometry produced by ablation. The first assessment method is based on the Weeks-Mellor iceberg stability criterion, and translates to a requirement that f r √ W g be small compared with unity, where W and fr are observed iceberg width and roll frequency, and g is the acceleration of gravity. Secondly, the time evolution of the roll frequency may be used to predict time remaining to capsize, without knowledge of iceberg geometry. Thirdly, the development of higher harmonics of the fundamental roll frequency in the motion is diagnostic of incipient rollover. Finally, the dependence of roll frequency and higher harmonic development on towing force may make possible estimates of the maximum stable tow force.

A closer look at deep crustal reflections

Since acquisition of the first crustal-scale seismic reflection sections, Earth scientists have been intrigued by images of the inaccessibly deep parts of the crust. The pattern of discontinuous subhorizontal reflections at 20–40 km depths has evoked hypotheses as diverse as depositional layering, mafic sills/intrusive layering, shear zones, and fluidfilled fractures. It is clearly important to develop interpretational criteria to relate geological evolution to seismic images. A valid approach, practiced in seismic programs worldwide, is to study regions where the geological history is well understood. For example, the lower crust of the Basin and Range Province has a history of repeated recent mafic underplating, detectable seismically in high refraction velocities and widespread subhorizontal reflections. Such images observed in other extended regions may be interpreted in a similar fashion.

Predictive filter calculation of primary fields in a fixed-wing time-domain AEM system

High-altitude data are used to calibrate a least-squares recursion filter that estimates the continually changing primary field of an airborne electromagnetic (AEM) system. The coupling changes in fixed-wing towed-bird systems generate “geometry noise” that in the on-time can be much larger than the ground secondary response. The LSQ filter accurately predicts the high-altitude primary field of a fixed-wing system. The filter is then applied to survey-altitude data to estimate the primary field for subsequent subtraction. After removing the primary field, a spatially consistent difference is detected over a range of delay times, as would be expected from geologic responses. A map of decay constants is produced for the survey area using the data corrected by the predicted primary field. Comparing these time constants with those computed from the conventional method, the maximum decay constant detectable was seven times larger. Thus, the new process can characterize conductors that are seven times more cond...

Dynamical analysis of continental overflow

Abstract Recent field and laboratory studies indicate that the viscosity of the middle and lower continental crust may be 10 18 Pa s or less in regions of high heat flow. Such strikingly low viscosities must strongly facilitate gravitational collapse of overthickened crust (thicker than would be possible without lateral tectonic support). In such areas, the ductile zone is so weak that lateral flow in it can relax all lateral pressure gradients in a geologically short time. The ductile or “fluid” zone is, for geological purposes, a fluid in hydrostatic equilibrium, floating a brittle cap of upper crust above it. A continent built in this way can collapse by overflow onto adjacent ocean basins if the continental elevation exceeds a critical threshold related to the mean geothermal gradient. This model permits relatively simple identification of the terms of the energy budget of gravitational collapse. Here I show that the budget is likely to be dominated by the balance between liberated gravitational energy (a source) and normal fault friction (a sink). Examination of this budget provides a stability criterion for gravitational collapse by continental overflow onto ocean basins: that crustal elevation above the ocean basin beyond an amount between a third and a half of the brittle cap thickness should drive a propagating overflow front.