How do we understand and visualize uncertainty?

Geophysicists are often concerned with reconstructing subsurface properties using observations collected at or near the surface. For example, in seismic migration, we attempt to reconstruct subsurface geometry from surface seismic recordings, and in potential field inversion, observations are used to map electrical conductivity or density variations in geologic layers. The procedure of inferring information from indirect observations is called an inverse problem by mathematicians, and such problems are common in many areas of the physical sciences. The inverse problem of inferring the subsurface using surface observations has a corresponding forward problem, which consists of determining the data that would be recorded for a given subsurface configuration. In the seismic case, forward modeling involves a method for calculating a synthetic seismogram, for gravity data it consists of a computer code to compute gravity fields from an assumed subsurface density model. Note that forward modeling often involves assumptions about the appropriate physical relationship between unknowns (at depth) and observations on the surface, and all attempts to solve the problem at hand are limited by the accuracy of those assumptions. In the broadest sense then, exploration geophysicists have been engaged in inversion since the dawn of the profession and indeed algorithms often applied in processing centers can all be viewed as procedures to invert geophysical data

Seismic anisotropy of Precambrian lithosphere : Insights from Rayleigh wave tomography of the eastern Superior Craton

The seismic data used in this study are freely available from the CNDC (Canadian National Data Centre for Earthquake Seismology and Nuclear Explosion Monitoring) and IRIS DMC (Data Management Center) via their data request tools. The Leverhulme Trust (grant RPG-2013-332) and National Science Foundation are acknowledged for financial support. L.P. is supported by Janet Watson Imperial College Department Scholarship and the Romanian Government Research Grant NUCLEU. F.D. is supported by NSERC through the Discovery Grants and Canada Research Chairs program. We also thank two anonymous reviewers and the Associate Editor for insightful comments that helped improve the manuscript.Peer reviewedPublisher PD

Scattering amplitude of a single fracture under uniaxial stress

Remotely sensing the properties of fractures has applications ranging from exploration geophysics to hazard monitoring. Newly developed capabilities to measure the in-plane component of dense laser-based ultrasound wave fields allow us to test the applicability of a linear slip model to describe fracture properties. In particular, we estimate the diameter, and the normal and tangential compliance of a fracture from the measured scattering amplitudes of P and S waves in the laboratory. Finally, we show that the normal compliance decreases linearly with increasing uniaxial static stress in the plane of the fracture, but that our measurements of the SV scattered field do not show significant changes in the tangential complianc

Bivariate genetic modelling of the response to an oral glucose tolerance challenge: A gene x environment interaction approach

AIMS/HYPOTHESIS: Twin and family studies have shown the importance of genetic factors influencing fasting and 2 h glucose and insulin levels. However, the genetics of the physiological response to a glucose load has not been thoroughly investigated. METHODS: We studied 580 monozygotic and 1,937 dizygotic British female twins from the Twins UK Registry. The effects of genetic and environmental factors on fasting and 2 h glucose and insulin levels were estimated using univariate genetic modelling. Bivariate model fitting was used to investigate the glucose and insulin responses to a glucose load, i.e. an OGTT. RESULTS: The genetic effect on fasting and 2 h glucose and insulin levels ranged between 40% and 56% after adjustment for age and BMI. Exposure to a glucose load resulted in the emergence of novel genetic effects on 2 h glucose independent of the fasting level, accounting for about 55% of its heritability. For 2 h insulin, the effect of the same genes that already influenced fasting insulin was amplified by about 30%. CONCLUSIONS/INTERPRETATION: Exposure to a glucose challenge uncovers new genetic variance for glucose and amplifies the effects of genes that already influence the fasting insulin level. Finding the genes acting on 2 h glucose independently of fasting glucose may offer new aetiological insight into the risk of cardiovascular events and death from all causes

Identifying sets of acceptable solutions to non-linear, geophysical inverse problems which have complicated misfit functions

International audienceA goal of geophysical inversion is to identify all models which give an acceptable misfit between predicted and observed data. However, because of the complexity of Earth structure, the non-linearity of physical processes in the Earth, and the insufficiency of geophysical data, many geophysical inverse problems may have a large number of distinct, acceptable solutions. These problems may be characterized by a complicated surface for the misfit function in the solution parameter space. For exploring such a surface, direct inversion and simple random search methods are often inadequate. However, directed search methods such as the genetic algorithm can be configured to balance convergent and random processes to find large sets of solutions that span the acceptable regions of complicated misfit surfaces

The interaction of socioeconomic position and type 2 diabetes mellitus family history:A cross-sectional analysis of the Lifelines Cohort and Biobank Study

Background Low socioeconomic position (SEP) and family history of type 2 diabetes mellitus (T2DM) contribute to increased T2DM risk, but it is unclear whether they exacerbate each other's effect. This study examined whether SEP reinforces the association of T2DM family history with T2DM, and whether behavioural and clinical risk factors can explain this reinforcement. Methods We used cross-sectional data on 51 725 participants from Lifelines. SEP was measured as educational level and was self-reported, just as family history of T2DM. T2DM was diagnosed based on measured fasting plasma glucose and glycated haemoglobin, combined with self-reported disease and recorded medication use. We assessed interaction on the additive scale by calculating the relative excess risk due to interaction (RERI). Results ORs of T2DM were highest for males (4.37; 95% CI 3.47 to 5.51) and females (7.77; 5.71 to 10.56) with the combination of low SEP and a family history of T2DM. The RERIs of low SEP and a family history of T2DM were 0.64 (-0.33 to 1.62) for males and 3.07 (1.53 to 4.60) for females. Adjustment for behavioural and clinical risk factors attenuated associations and interactions, but risks remained increased. Conclusion Low SEP and family history of T2DM are associated with T2DM, but they also exacerbate each other's impact in females but not in males. Behavioural and clinical risk factors partly explain these gender differences, as well as the associations underlying the interaction in females. The exacerbation by low SEP of T2DM risks in T2DM families deserves attention in prevention and community care

Fast-food environments and BMI changes in the Dutch adult general population:the Lifelines cohort

OBJECTIVE: This study investigated cross-sectional and longitudinal associations of fast-food outlet exposure with BMI and BMI change, as well as moderation by age and genetic predisposition.METHODS: This study used Lifelines' baseline (n = 141,973) and 4-year follow-up (n = 103,050) data. Participant residential addresses were linked to a register with fast-food outlet locations (Nationwide Information System of Workplaces [Dutch: Landelijk Informatiesysteem van Arbeidsplaatsen, LISA]) using geocoding, and the number of fast-food outlets within 1 km was computed. BMI was measured objectively. A weighted BMI genetic risk score was computed, representing overall genetic predisposition toward elevated BMI, based on 941 single-nucleotide polymorphisms genome-wide significantly associated with BMI for a subsample with genetic data (BMI: n = 44,996; BMI change: n = 36,684). Multivariable multilevel linear regression analyses and exposure-moderator interactions were tested.RESULTS: Participants with ≥1 fast-food outlet within 1 km had a higher BMI (B [95% CI]: 0.17 [0.09 to 0.25]), and those with ≥2 fast-food outlets within 1 km increased more in BMI (B [95% CI]: 0.06 [0.02 to 0.09]) than participants with no fast-food outlets within 1 km. Effect sizes on baseline BMI were largest among young adults (age 18-29 years; B [95% CI]: 0.35 [0.10 to 0.59]) and especially young adults with a medium (B [95% CI]: 0.57 [-0.02 to 1.16]) or high genetic risk score (B [95% CI]: 0.46 [-0.24 to 1.16]).CONCLUSIONS: Fast-food outlet exposure was identified as a potentially important determinant of BMI and BMI change. Young adults, especially those with a medium or high genetic predisposition, had a higher BMI when exposed to fast-food outlets.</p

The Interaction of Genetic Predisposition and Socioeconomic Position With Type 2 Diabetes Mellitus:Cross-Sectional and Longitudinal Analyses From the Lifelines Cohort and Biobank Study

OBJECTIVE: A strong genetic predisposition for type 2 diabetes mellitus (T2DM) may aggravate the negative effects of low socioeconomic position (SEP) in the etiology of the disorder. This study aimed to examine cross-sectional and longitudinal associations and interactions of a genetic risk score (GRS) and SEP with T2DM, and to investigate whether clinical and behavioral risk factors can explain these associations and interactions. METHODS: We used data from 13,027 genotyped participants from the Lifelines study. The GRS was based on single-nucleotide polymorphisms (SNPs) genome-wide associated with T2DM and was categorized into tertiles. SEP was measured as educational level. T2DM was based on biological markers, recorded medication use, and self-reports. Cross-sectional and longitudinal associations, and interactions, between the GRS and SEP on T2DM were examined. RESULTS: The combination of a high GRS and low SEP had the strongest association with T2DM in cross-sectional (OR: 3.84; 95% CI: 2.28, 6.46) and longitudinal analyses (HR: 2.71; 1.39, 5.27), compared to a low GRS and high SEP. Interaction between a high GRS and a low SEP was observed in cross-sectional (relative excess risk due to interaction: 1.85; 0.65, 3.05) but not in longitudinal analyses. Clinical and behavioral risk factors mostly explained the observed associations and interactions. CONCLUSIONS: A high GRS combined with a low SEP provides the highest risk for T2DM. These factors also exacerbated each other's impact cross-sectionally but not longitudinally. Preventive measures should target individual and contextual factors of this high-risk group to reduce the risk of T2DM