Particle relabelling transformations in elastodynamics

The motion of a self-gravitating hyperelastic body is described through a time-dependent mapping from a reference body into physical space, and its material properties are determined by a referential density and strain-energy function defined relative to the reference body. Points within the reference body do not have a direct physical meaning, but instead act as particle labels that could be assigned in different ways. We use Hamilton’s principle to determine how the referential density and strain-energy functions transform when the particle labels are changed, and describe an associated “particle relabelling symmetry”. We apply these results to linearised elastic wave propagation, and discuss their implications for seismological inverse problems. In particular, we show that the effects of boundary topography on elastic wave propagation can be mapped exactly into volumetric heterogeneity while preserving the form of the equations of motion. Several numerical calculations are presented to illustrate our results.O.C. is supported through a NERC PhD studentship.This is the final version of the article. It first appeared from Oxford University Press via http://dx.doi.org/10.1093/gji/ggw03

Forward and inverse modelling of post-seismic deformation

We consider a new approach to both the forward and inverse problems in post-seismic deformation. We present a method for forward modelling post-seismic deformation in a self-gravitating, heterogeneous and compressible earth with a variety of linear and nonlinear rheologies. We further demonstrate how the adjoint method can be applied to the inverse problem both to invert for rheological structure and to calculate the sensitivity of a given surface measurement to changes in rheology or time-dependence of the source. Both the forward and inverse aspects are illustrated with several numerical examples implemented in a spherically symmetric earth model.Natural Environment Research Council, British Antarctic Surve

Intrinsic non-uniqueness of the acoustic full waveform inverse problem

SUMMARY In the context of seismic imaging, full waveform inversion (FWI) is increasingly popular. Because of its lower numerical cost, the acoustic approximation is often used, especially at the exploration geophysics scale, both for tests and for real data. Moreover, some research domains such as helioseismology face true acoustic media for which FWI can be useful. In this work, an argument that combines particle relabelling and homogenization is used to show that the general acoustic inverse problem based on band-limited data is intrinsically non-unique. It follows that the results of such inversions should be interpreted with caution. To illustrate these ideas, we consider 2-D numerical FWI examples based on a Gauss–Newton iterative inversion scheme and demonstrate effects of this non-uniqueness in the local optimization context.</jats:p

Sensitivity kernels for body tides on laterally heterogeneous planets based on adjoint methods

SUMMARY We apply the adjoint method to efficiently calculate the linearized sensitivity of body tide observations to perturbations in density, elastic/anelastic moduli and boundary topography. This theory is implemented practically within the context of normal mode coupling calculations, with an advantage of this approach being that much of the necessary technical machinery is present in existing coupling codes. A range of example sensitivity kernels are calculated relative to both spherically symmetric and laterally heterogeneous background models. These results reaffirm the conclusions of earlier studies that the M2 body tide is strongly sensitive to spherical harmonic degree-2 density variations at the base of the mantle. Moreover, it is found that the sensitivity kernels are only weakly dependent on the background model, and hence linearized methods are likely to be effective within inversions of body tide observations.NSF grant EAR-192386

Anelasticity across seismic to tidal timescales: a self-consistent approach

In a pioneering study, Wahr & Bergen developed the widely adopted, pseudo-normal mode framework for predicting the impact of anelastic effects on the Earth's body tides. Lau $\textit{et al.}$ have recently derived an extended normal mode treatment of the problem (as well as a minor variant of the theory known as the direct solution method) that makes full use of theoretical developments in free oscillation seismology spanning the last quarter century and that avoids a series of assumptions and approximations adopted in the traditional theory for predicting anelastic effects. There are two noteworthy differences between these two theories: (1) the traditional theory only considers perturbations to the eigenmodes of an elastic Earth, whereas the new theory augments this set of modes to include the relaxation modes that arise in anelastic behaviour; and (2) the traditional theory approximates the complex perturbation to the tidal Love number as a scaled version of the complex perturbation to the elastic moduli, whereas the new theory computes the full complex perturbation to each eigenmode. In this study, we highlight the above differences using a series of synthetic calculations, and demonstrate that the traditional theory can introduce significant error in predictions of the complex perturbation to the Love numbers due to anelasticity and the related predictions of tidal lag angles. For the simplified Earth models we adopt, the computed lag angles differ by ∼20 per cent. The assumptions in the traditional theory have important implications for previous studies that use model predictions to correct observables for body tide signals or that analyse observations of body tide deformation to infer mantle anelastic structure. Finally, we also highlight the fundamental difference between apparent attenuation (i.e. attenuation inferred from observations or predicted using the above theories) and intrinsic attenuation (i.e. the material property investigated through experiments), where both are often expressed in terms of lag angles or $\textit{Q}$$^{-1}$. In particular, we demonstrate the potentially significant (factor of two or more) bias introduced in estimates of $\textit{Q}$$^{-1}$ and its frequency dependence in studies that have treated $\textit{Q}$$^{-1}$ determined from tidal phase lags or measured experimentally as being equal. The observed or theoretically predicted lag angle (or apparent $\textit{Q}$$^{-1}$) differs from the intrinsic, material property due to inertia, self-gravity and effects associated with the energy budget. By accounting for these differences we derive, for a special case, an expression that accurately maps apparent attenuation predicted using the extended normal mode formalism of Lau $\textit{et al.}$ into intrinsic attenuation. The theory allows for more generalized mappings which may be used to robustly connect observations and predictions of tidal lag angles to results from laboratory experiments of mantle materials.This work was supported by NSF EAR-1464024, NSF EAR-1215061, and Harvard University

Quantitative and qualitative differences in subcutaneous adipose tissue stores across lipodystrophy types shown by magnetic resonance imaging

BACKGROUND: Lipodystrophies are characterized by redistributed subcutaneous fat stores. We previously quantified subcutaneous fat by magnetic resonance imaging (MRI) in the legs of two patients with familial partial lipodystrophy subtypes 2 and 3 (FPLD2 and FPLD3, respectively). We now extend the MRI analysis across the whole body of patients with different forms of lipodystrophy. METHODS: We studied five subcutaneous fat stores (supraclavicular, abdominal, gluteal, thigh and calf) and the abdominal visceral fat stores in 10, 2, 1, 1 and 2 female subjects with, respectively, FPLD2, FPLD3, HIV-related partial lipodystrophy (HIVPL), acquired partial lipodystrophy (APL), congenital generalized lipodystrophy (CGL) and in six normal control subjects. RESULTS: Compared with normal controls, FPLD2 subjects had significantly increased supraclavicular fat, with decreased abdominal, gluteal, thigh and calf subcutaneous fat. FPLD3 subjects had increased supraclavicular and abdominal subcutaneous fat, with less severe reductions in gluteal, thigh and calf fat compared to FPLD2 subjects. The repartitioning of fat in the HIVPL subject closely resembled that of FPLD3 subjects. APL and CGL subjects had reduced upper body, gluteal and thigh subcutaneous fat; the APL subject had increased, while CGL subjects had decreased subcutaneous calf fat. Visceral fat was markedly increased in FPLD2 and APL subjects. CONCLUSION: Semi-automated MRI-based adipose tissue quantification indicates differences between various lipodystrophy types in these studied clinical cases and is a potentially useful tool for extended quantitative phenomic analysis of genetic metabolic disorders. Further studies with a larger sample size are essential for confirming these preliminary findings

Dimensional accuracy of Electron Beam Melting (EBM) additive manufacture with regard to weight optimized truss structures

The Electron Beam (EBM) additive manufacturing process is well suited to fabricating complex structural designs in Ti–6Al–4V because of the design freedoms it offers combined with strong and consistent material properties. However it has been observed that complications may arise when manufacturing truss-like structures (such as those produced via structural topology optimization) in the form of undersized features on the finished part. The issue appears to affect truss members that are not aligned with the vertical build direction, with an apparent lack of material on the negative surfaces. This effect appears to worsen with a greater angle between the truss member and the build direction, even with the use of support structures. This investigation has characterized and measured the dimensional errors that result from this issue through 3D scanning techniques. Process modifications have then been made which result in significant improvements in dimensional accuracy. This investigation highlights the importance of heat management at features with negative surfaces to yield parts that are dimensionally accurate without introducing excessive internal melt defects in the form of voids and porosity

How the other half lives: CRISPR-Cas's influence on bacteriophages

CRISPR-Cas is a genetic adaptive immune system unique to prokaryotic cells used to combat phage and plasmid threats. The host cell adapts by incorporating DNA sequences from invading phages or plasmids into its CRISPR locus as spacers. These spacers are expressed as mobile surveillance RNAs that direct CRISPR-associated (Cas) proteins to protect against subsequent attack by the same phages or plasmids. The threat from mobile genetic elements inevitably shapes the CRISPR loci of archaea and bacteria, and simultaneously the CRISPR-Cas immune system drives evolution of these invaders. Here we highlight our recent work, as well as that of others, that seeks to understand phage mechanisms of CRISPR-Cas evasion and conditions for population coexistence of phages with CRISPR-protected prokaryotes.Comment: 24 pages, 8 figure