Out‐of‐plane geometrical spreading in anisotropic media

Two-dimensional seismic processing is successful in media with little structural and velocity variation in the direction perpendicular to the plane defined by the acquisition direction and the vertical axis. If the subsurface is anisotropic, an additional limitation is that this plane is a plane of symmetry. Kinematic ray propagation can be considered as a two-dimensional process in this type of medium. However, two-dimensional processing in a true-amplitude sense requires out-of-plane amplitude corrections in addition to compensation for in-plane amplitude variation. We provide formulae for the out-of-plane geometrical spreading for P- and S-waves in transversely isotropic and orthorhombic media. These are extensions of well-known isotropic formulae.
For isotropic and transversely isotropic media, the ray propagation is independent of the azimuthal angle. The azimuthal direction is defined with respect to a possibly tilted axis of symmetry. The out-of-plane spreading correction can then be calculated by integrating quantities which describe in-plane kinematics along in-plane rays. If, in addition, the medium varies only along the vertical direction and has a vertical axis of symmetry, no ray tracing need be carried out. All quantities affecting the out-of-plane geometrical spreading can be derived from traveltime information available at the observation surface.
Orthorhombic media possess no rotational symmetry and the out-of-plane geometrical spreading includes parameters which, even in principle, are not invertible from in-plane experiments. The exact and approximate formulae derived for P- and S-waves are nevertheless useful for modelling purposes.     

Modelling the compliance of crustal rock—I. Response of shear-wave splitting to differential stress

We show that seismic shear waves may be used to monitor the in situ stress state of deep inaccessible rocks in the crust. The most widespread manifestation of the stress-related behaviour of seismic waves is the shear-wave splitting (shear-wave birefringence) observed in almost all rocks, where the polarizations of the leading split shear waves are usually subparallel to the direction of the local maximum horizontal stress. It has been recognized that such shear-wave splitting is typically the result of propagation through distributions of stress-aligned fluid-filled microcracks and pores, known as extensive-dilatancy anisotropy or EDA. This paper provides a quantitative basis for the EDA hypothesis. We model the evolution of anisotropic distributions of microcracks in triaxial differential stress, where the driving mechanism is fluid migration along pressure gradients between neighbouring microcracks and pores at different orientations to the stress field. This leads to a non-linear anisotropic poroelasticity (APE) model for the stress-sensitive behaviour of fluid-saturated microcracked rocks. A companion paper shows that APE modelling matches a range of observed phenomena and is a good approximation to the equation of state of a stressed fluid-saturated rock mass.     

The mean transmission properties of a fault with imperfect facial contact

A model of a fault where the two faces do not exactly conform is characterized by a distribution of approximately circular contacts; elsewhere, the faces are stress-free. This contrasts with most earlier models, which have assumed the contact geometry to be equivalent to a plane distribution of approximately circular cracks. The contact regions in the present model are taken to be sparsely distributed, and averaged interface conditions are derived that are accurate to second order. At lowest order they agree with established formulae for the normal stiffness of non-conforming surfaces. These averaged, or mean, conditions are expected to hold at wavelengths long compared with the radii and spacing distance of the contact points. Unsurprisingly, they are equivalent to the continuity conditions for a thin elastic layer whose properties are given here in terms of the parameters of the contact surface.     

A laser-ablation ICP-MS study of Apollo 15 low-titanium olivine-normative and quartz-normative mare basalts

Apollo 15 low-Ti mare basalts have traditionally been subdivided into olivine- and quartz-normative basalt types, based on their different SiO₂, FeO, and TiO₂ whole-rock compositions. Previous studies have reconciled this compositional diversity by considering the olivine- and quartz-normative basalts as originating from different lunar mantle source regions. To provide new information on the compositions of Apollo 15 low-Ti mare basalt parental magmas, we report a study of major and trace-element compositions of whole rocks, pyroxenes, and other phases in the olivine-normative basalts 15016 and 15555 and quartz-normative basalts 15475 and 15499. Results show similar rare-earth-element patterns in pyroxenes from all four basalts. The estimated equilibrium parental-melt compositions from the trace-element compositions of pyroxenes are similar for 15016, 15555 and 15499. Additionally, an independent set of trace-element distribution coefficients has been determined from measured pyroxene and mesostasis compositions in sample 15499. These data suggest that fractional crystallization may be a viable alternative to compositional differences in the mantle source to explain the 25% difference in whole-rock TiO₂, and corresponding differences in SiO₂ and FeO between the Apollo 15 olivine- and quartz-normative basalts. In this model, the older (3.35 Ga) quartz-normative basalts, with lower TiO₂ experienced olivine, chromite, and Cr-ulvöspinel fractionation at ‘crustal levels’ in magma chambers or dikes, followed by limited near-surface mineral fractionation, within the lava flows. In contrast, the younger (3.25 Ga) olivine-normative basalts experienced only limited magmatic differentiation at ‘crustal-levels’, but extensive near-surface mineral fractionation to produce their evolved mineral compositions. A two-stage mineral-fractionation model is consistent with textural and mineralogical observations, as well as the mineral trace-element constraints developed by this study.     

Order parameter coupling in leucite: a calorimetric study

The thermal anomalies associated with the Ia3d → I4₁/acd → I4₁/a transition sequence of phase transitions in leucite have been studied by differential scanning calorimetry and interpreted with Landau theory. Both transitions are close to the tricritical point. The coupling between the two transitions is biquadratic, and reduces the stability of the I4₁/a phase.     

Shear‐wave splitting and earthquake forecasting

Seismic shear‐wave splitting (SWS) monitors the low‐level deformation of fluid‐saturated microcracked rock. We report evidence of systematic SWS changes, recorded above small earthquakes, monitoring the accumulation of stress before earthquakes that allows the time and magnitude of impending large earthquakes to be stress‐forecast. The effects have been seen with hindsight before some 15 earthquakes ranging in magnitude from an M1.7 seismic swarm event in Iceland to the Ms7.7 Chi‐Chi Earthquake in Taiwan, including a successfully stress‐forecast of a M5.0 earthquake in SW Iceland. Characteristic increases in SWS time‐delays are observed before large earthquakes, which abruptly change to deceases shortly before the earthquake occurs. There is a linear relationship between magnitudes and logarithms of durations of both increases and decreases in SWS time‐delays before large impending earthquakes. However, suitably persistent swarms of small earthquakes are too scarce for routine stress‐forecasting. Reliable forecasting requires controlled‐source cross‐hole seismics between neighbouring boreholes in stress‐monitoring sites (SMS). It would be possible to stress‐forecast damaging earthquakes worldwide by a global network of SMS in real time.     

Children's Geographies: Tracing The Evolution and Involution of a Concept

This essay traces the evolution of children's geographies as a concept through three phases. First, in the early 1970s as a beginning impression influenced heavily by developmental and environmental psychology. Second, beginning around 1990, children's geographies cohered politically as geographers focused on young people's identity through feminism and Marxism, and global policy initiatives on children's rights. The third phase, covering the last couple of decades, coming from issues of political identity, challenges what we think we know about young people and their geographies, and also advocates a set of loose theories about the ways young people create and re‐create spaces and themselves. Cognate disciplines coming to geography for insights about children and their worlds characterize this current phase. To offset this seeming linear progression the essay also notes an involution of the concept that defies clear categories and sequences, but suggests the fluidity of tensions and accommodations that comprises children's geographies.