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This paper revisits and extends the adjoint theory for glacial isostatic adjustment (GIA) of Crawford et al. (2018). Rotational feedbacks are now incorporated, and the application of the second-order adjoint method is described for the first time. The first-order adjoint method provides an efficient means for computing sensitivity kernels for a chosen objective functional, while the second-order adjoint method provides second-derivative information in the form of Hessian kernels. These latter kernels are required by efficient Newton-type optimization schemes and within methods for quantifying uncertainty for non-linear inverse problems. Most importantly, the entire theory has been reformulated so as to simplify its implementation by others within the GIA community. In particular, the rate-formulation for the GIA forward problem introduced by Crawford et al. (2018) has been replaced with the conventional equations for modelling GIA in laterally heterogeneous earth models. The implementation of the first- and second-order adjoint problems should be relatively easy within both existing and new GIA codes, with only the inclusions of more general force terms being required. [ABSTRACT FROM AUTHOR]

PurposeThe aim of this study was to elicit utilities for radioactive iodine-refractory differentiated thyroid cancer (RR-DTC) and evaluate the impact of treatment response and toxicities on quality of life.Patients and methodsRR-DTC health states were developed based on data from a previous qualitative study and iterative review by clinical experts. Following piloting, health states underwent valuation by 100 members of the UK public during time trade-off interviews. Mean utilities and descriptive distribution statistics were calculated, and a logistic regression analysis was conducted.ResultsThe demographic characteristics of the study sample were generally reflective of the UK population. Clear differentiation in valuation between health states was observed. No response/stable disease had an adjusted utility value of 0.87, with a corresponding gain of +0.04 following a treatment response and a decline of -0.35 for disease progression. Adverse events were associated with utility decrements between -0.47 (grade III diarrhea) and -0.05 (grade I/II alopecia).ConclusionThe trade-off interviews derived utility weights show clear differentiation between RR-DTC health states in response to treatment. The values reported in this study are suitable for cost-effectiveness evaluations for new treatments in RR-DTC.

A key initial step in geophysical imaging is to devise an effective means of mapping the sensitivity of an observation to the model parameters, that is to compute its Fréchet derivatives or sensitivity kernel. In the absence of any simplifying assumptions and when faced with a large number of free parameters, the adjoint method can be an effective and efficient approach to calculating Fréchet derivatives and requires just two numerical simulations. In the Glacial Isostatic Adjustment problem, these consist of a forward simulation driven by changes in ice mass and an adjoint simulation driven by fictitious loads that are applied at the observation sites. The theoretical basis for this approach has seen considerable development over the last decade. Here, we present the final elements needed to image 3-D mantle viscosity using a dataset of palaeo sea-level observations. Developments include the calculation of viscosity Fréchet derivatives (i.e. sensitivity kernels) for relative sea-level observations, a modification to the numerical implementation of the forward and adjoint problem that permits application to 3-D viscosity structure, and a recalibration of initial sea level that ensures the forward simulation honours present-day topography. In the process of addressing these items, we build intuition concerning how absolute sea-level and relative sea-level observations sense Earth's viscosity structure and the physical processes involved. We discuss examples for potential observations located in the near field (Andenes, Norway), far field (Seychelles), and edge of the forebulge of the Laurentide ice sheet (Barbados). Examination of these kernels: (1) reveals why 1-D estimates of mantle viscosity from far-field relative sea-level observations can be biased; (2) hints at why an appropriate differential relative sea-level observation can provide a better constraint on local mantle viscosity and (3) demonstrates that sea-level observations have non-negligible 3-D sensitivity to deep mantle viscosity structure, which is counter to the intuition gained from 1-D radial viscosity Fréchet derivatives. Finally, we explore the influence of lateral variations in viscosity on relative sea-level observations in the Amundsen Sea Embayment and at Barbados. These predictions are based on a new global 3-D viscosity inference derived from the shear-wave speeds of GLAD-M25 and an inverse calibration scheme that ensures compatibility with certain fundamental geophysical observations. Use of the 3-D viscosity inference leads to: (1) generally greater complexity within the kernel; (2) an increase in sensitivity and presence of shorter length-scale features within lower viscosity regions; (3) a zeroing out of the sensitivity kernel within high-viscosity regions where elastic deformation dominates and (4) shifting of sensitivity at a given depth towards distal regions of weaker viscosity. The tools and intuition built here provide the necessary framework to explore inversions for 3-D mantle viscosity based on palaeo sea-level data. [ABSTRACT FROM AUTHOR]