Introduction

The radiometric method, or radiometrics, measures naturally occurring radioactivity in the form of gamma-rays (γ-rays) (Fig. 4.1). Most of this radiation originates from mineral species containing radioactive isotopes of potassium (K), uranium (U) and thorium (Th). Radiometrics is a passive geophysical method because it measures a natural source of energy. Radiometric surveys for mineral exploration are routinely made from the air, on the ground and within drillholes. Airborne radiometrics is particularly common in mineral exploration where the radiometric data are acquired simultaneously with magnetics during airborne surveying, although it would be unusual for a solely radiometric survey to be conducted. Ground radiometric surveys are usually conducted with hand-held instruments, but γ-ray detectors are sometimes mounted on a moving vehicle for larger-scale surveys. Downhole radiometric measurements are limited to γ-logging; downhole surveying as defined in Section 1.2.1 is not possible in radiometrics. Gamma-logging is a common component of multiparameter logging for rapidly and economically measuring in situ physical properties, correlating stratigraphy between drillholes and assisting in the evaluation of uranium deposits. It is also used extensively by the petroleum industry in well-logging.

Historically, the main use of radiometrics in mineral prospecting was detection of anomalies caused by outcropping, highly radioactive, uranium deposits. With improvements in sensor technology and data-processing algorithms, downhole radiometric techniques were developed for estimating the grade of uranium ores intersected by drillholes. The advent of multichannel detectors for airborne surveying, capable of distinguishing radiation from different radioactive elements, the increased sensitivity and resolution of airborne surveying techniques, and the development of new data reduction algorithms have focused airborne radiometrics more toward geological mapping than purely anomaly detection. Newer applications include detecting and mapping areas of hydrothermal alteration and weakly radioactive mineral deposits, e.g. heavy-mineral sands. Renewed interest in the method has also been driven by the requirement to map the materials making up the near-surface. In this context, the radiometric data are usually interpreted in combination with topographic and satellite-borne remote-sensing data. Some applications include regolith mapping for mineral exploration and the mapping of soil types for environmental studies.

In the previous chapter we studied the propagation of rupture in a material that we assumed to be otherwise unbroken, continuous and perfectly elastic outside the fracture. A direct consequence of these assumptions is that the stress and slip rate present inverse square root singularities as we approach the tip of the crack. These two singularities result from approximations that need to be corrected, since no material of finite strength can sustain infinite stresses or slip at an infinite rate. Moreover, homogeneous models cannot explain the nucleation and arrest of rupture nor the super-shear rupture speeds that sometime occur in earthquake ruptures. To avoid these problems we need to introduce heterogeneities into the medium. These will explain the beginning of the fracture process and its arrest and will also eliminate the singularities of stress and slip rate at the rupture edge.

The cohesive zone

We start with a study of the singularities at the edge of a propagating fracture. In order that the values of the stress and slip rate near the rupture front be finite it is necessary to introduce a transition zone where the material behaves inelastically. Barenblatt (1959a, b, 1962) proposed that the stresses immediately ahead of the fracture front should be regularized by the action of cohesive forces, which hold together the material while it is in the process of being broken. These forces are distributed in the vicinity of the rupture front and may be considered as a material property. They are analogous to the attractive or cohesive forces exerted on a liquid molecule by neighboring molecules which explains their name. The transition zone where these forces act is called the cohesive zone and its dimension d must be small compared with the size of the fracture (Fig. 11.1). At the front of the cohesive zone the opposite sides at the edge of the crack are smoothly joined and the stresses remain finite. Let us consider a very simple model of a cohesive zone of length d where the cohesive stresses are constant and equal to σc, which is a compressive stress that opposes the opening of the cohesive zone. Generally, the cohesive stress σc is larger than the acting stress σ0 (Fig. 11.1). Behind the cohesive zone, at distance d from the tip, the tensional stresses drop to zero.

Introduction

The seismic method is an active form of geophysical surveying that uses elastic waves to investigate the subsurface. The waves are created by a source and propagate through the subsurface before being recorded by detectors that measure deformation of the ground (Fig. 6.1). The deformation of the ground as a function of time since the waves were created comprises a time series, which is called a seismic trace. The passing of a seismic wave appears as a deflection of the trace, referred to as an arrival or an event. The path of the waves from source to detector is controlled by the elastic properties of the material through which they travel. Discontinuities in the elastic properties deflect and divide the seismic waves so that the detectors record a series of waves that have taken different paths through the subsurface. It is by identifying these different arrivals and analysing their travel times and amplitudes that the nature of the subsurface can be inferred.

Most seismic surveys use sources and detectors located on, or near, the Earth’s surface. Surface seismic surveys are of two types. Surveys that particularly exploit waves reflected at elastic discontinuities are known as seismic reflection surveys, whilst those based on waves deflected so as to travel parallel to the discontinuities are known as seismic refraction surveys. Of all the geophysical methods, seismic reflection surveys provide the most detailed information about the subsurface, albeit at the greatest cost (see Fig. 1.3). Reflection survey data are displayed in a pseudosection/pseudovolume form where the travel times of the seismic waves provide an approximate indication of depth; but accurate time-to-depth conversion is difficult. Refraction surveys provide less detailed information, detecting only major changes in elastic properties, although the positions of these boundaries can usually be accurately determined.