Practical VTI approximations: a systematic anatomy

Transverse isotropy (TI) with a vertical symmetry axis (VTI) often provides an appropriate earth model for prestack imaging of steep-dip reflection seismic data. Exact P-wave and SV-wave phase velocities in VTI media are described by complicated equations requiring four independent parameters. Estimating appropriate multiparameter earth models can be difficult and time-consuming, so it is often useful to replace the exact VTI equations with simpler approximations requiring fewer parameters. The accuracy limits of different previously published VTI approximations are not always clear, nor is it always obvious how these different approximations relate to each other. Here I present a systematic framework for deriving a variety of useful VTI approximations. I develop first a sequence of well-defined approximations to the exact P-wave and SV-wave phase velocities. In doing so, I show how the useful but physically questionable heuristic of setting shear velocities identically to zero can be replaced with a more precise and quantifiable approximation. The key here to deriving accurate approximations is to replace the stiffness a₁₃ with an appropriate factorization in terms of velocity parameters. Two different specific parameter choices lead to the P-wave approximations of Alkhalifah (Geophysics 63 (1998) 623) and Schoenberg and de Hoop (Geophysics 65 (2000) 919), but there are actually an infinite number of reasonable parametrizations possible. Further approximations then lead to a variety of other useful phase velocity expressions, including those of Thomsen (Geophysics 51 (1986) 1954), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Harlan (Stanford Exploration Project Report 89 (1995) 145), and Stopin (Stopin, A., 2001. Comparison of v(θ) equations in TI medium. 9th International Workshop on Seismic Anisotropy). Each P-wave phase velocity approximation derived this way can be paired naturally with a corresponding SV-wave approximation. Each P-wave or SV-wave phase velocity approximation can then be converted into an equivalent dispersion relation in terms of horizontal and vertical slownesses. A simple heuristic substitution also allows each phase velocity approximation to be converted into an explicit group velocity approximation. From these, in turn, travel time or moveout approximations can also be derived. The group velocity and travel time approximations derived this way include ones previously used by Byun et al. (Geophysics 54 (1989) 1564), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Tsvankin and Thomsen (Geophysics 59 (1994) 1290), Harlan (89 (1995) 145), and Zhang and Uren (Zhang, F. and Uren, N., 2001. Approximate explicit ray velocity functions and travel times for P-waves in TI media. 71st Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, 106–109).     

Failure Mode and Spatial Distribution of Damage in Rothbach Sandstone in the Brittle-ductile Transition

— To elucidate the spatial complexity of damage and evolution of localized failure in the transitional regime from brittle faulting to cataclastic ductile flow in a porous sandstone, we performed a series of triaxial compression experiments on Rothbach sandstone (20% porosity). Quantitative microstructural analysis and X-ray computed tomography (CT) imaging were conducted on deformed samples. Localized failure was observed in samples at effective pressures ranging from 5 MPa to 130 MPa. In the brittle faulting regime, dilating shear bands were observed. The CT images and stereological measurements reveal the geometric complexity and spatial heterogeneity of damage in the failed samples. In the transitional regime (at effective pressures between 45 MPa and 130 MPa), compacting shear bands at high angles and compaction bands perpendicular to the maximum compression direction were observed. The laboratory results suggest that these complex localized features can be pervasive in sandstone formations, not just limited to the very porous aeolian sandstone in which they were first documented. The microstructural observations are in qualitative agreement with theoretical predictions of bifurcation analyses, except for the occurrence of compaction bands in the sample deformed at effective pressure of 130 MPa. The bifurcation analysis with the constitutive model used in this paper is nonadequate to predict compaction band formation, may be due to the neglect of bedding anisotropy of the rock and multiple yield mechanisms in the constitutive model.     

Characterisation of the 1997 Vulcanian explosions of Soufrière Hills Volcano,Montserrat, by video analysis

The activity of Convention at Montserrat Soufrière Hills Volcano, Montserrat, during the period 1995–1999 included numerous violent explosions. Two major cycles of Vulcanian explosions occurred in 1997: a first of 13 explosions between 4 and 12 August and a second of 75 between 22 September and 21 October. The explosions were short-lived events lasting a few tens of seconds during which partial fountain collapse generated pyroclastic surges and pyroclastic flows, and buoyant plumes ascended 3–15 km into the atmosphere. Each explosion discharged on average 3×10⁵ m³ (dense-rock equivalent, DRE) of magma, draining the conduit to depths of 1–2 km. The paper focuses on the first few seconds of three explosions of the 75 that occurred in September/October 1997: 6 October 1997 at 17:50, 7 October 1997 at 16:02 and 9 October 1997 at 12:32. Physical parameters such as exit velocities, magmatic water contents and magma pressures at fragmentation are estimated by following and modelling the ascent of individual momentum-dominated finger jets visible on videos during the initial stages of each explosion. The model treats each finger jet as an incompressible flow sustained by a steady flux of gas and particles during the few seconds of ascent, and produces results that compare favourably with those using a multiphase compressible code run using similar eruptive parameters. Each explosion reveals a progressive increase in eruptive intensity with time, jet exit velocities increasing from 40 m s^–1 at the beginning of the explosion up to 140 m s^–1 after a few seconds. Modelling suggests that the first magma to exit was largely degassed, whereas that discharged after a few seconds contained up to 2 wt% water. Magma overpressures up to ~10 MPa are estimated to have existed in the conduit immediately prior to each explosion. Progressive increases in jet exit velocity with time over the first few seconds of each explosion provide direct evidence for strong pre-eruptive gradients in water content and magma pressure in the upper reaches (probably 100–500 m) of the conduit. Fountain collapse occurred during the first 10–20 s of each explosion because the discharging jets had bulk densities up to 100 times that of the atmosphere and were unable to entrain enough air to become buoyant. Such high eruptive densities were due to the presence of partially degassed magma in the conduit.Editorial responsibility: A. Woods     

Indoor Radon Radioactivity at the University of Brunei Darussalam

— Indoor radon radioactivity in the rooms on the ground floor and first floor of the Physics Department, Faculty of Science, Universiti Brunei Darussalam was measured using a system that consists of an air filter pump, ZnS detector, photomultiplier tube and counter. Ground floor rooms' radon radioactivity was found to be about three times higher than that of the first floor. The maximum ground floor indoor radioactivity is only 0.39 Bqm^?3, a value relatively low and safe compared to the mean outdoor radon concentration of 1.41 Bqm^?3 measured (HU and TAN, 2000). The main source of radon emanation originates from the ground soil rather than the building materials.     

Fishery Water Releases to the Lower Pool of the Volgograd Hydroelectric Power Plant

Conditions of fish reproduction in the Volga–Caspian Basin depending on the hydrological regime in the Volga lower reaches, transformed by water withdrawals and regulatory impact of reservoirs are considered.     

Towards non-linear inversion for characterization of time-lapse phenomena through numerical modelling

We compare two geophysical survey measurements of the same type made at different times in order to characterize the change in the geological medium during the elapsed time. The aim of this study is to develop a strategy using a full non-linear inversion algorithm as the interpretation tool. In this way, not only the location and the form of the changes are recovered, but also the changes in the material parameters of the geological medium can be estimated. In order to solve this fully non-linear problem, the so-called ‘multiplicative regularized contrast source inversion’ (MR-CSI) method is employed. The unique property of this iterative method is that it does not solve the forward problem at each iterative step. This makes it possible to use the non-linear inversion algorithm for large-scale computation problems. The numerical results show that by taking into account the non-linear nature of the problem, interpretation of the time-lapse data can be significantly improved, compared with that obtained using linear inversion.     

Mars in depth

P Lognonné, T Spohn and D Giardini describe the state of knowledge of Mars' interior and make the case for deep seismology to address the unanswered questions.     

Dark skies action

Helen Walker and Paul Murdin report on the Royal Astronomical Society's involvement in government action to protect dark skies.     

A review of the physics and ecological implications of the thermal bar circulation

Following recent applications of numerical modelling and remote sensing to the thermal bar phenomenon, this paper seeks to review the current state of knowledge on the effect of its circulation on lacustrine plankton ecosystems. After summarising the literature on thermal bar hydrodynamics, a thorough review is made of all plankton observations taken in the presence of a thermal bar. Two distinct plankton growth regimes are found, one with production favoured throughout the inshore region and another with a maximum in plankton biomass near the position of the thermal bar. Possible explanations for the observed distributions are then discussed, with reference to numerical modelling studies, and the scope for future study of this interdisciplinary topic is outlined.