Kinematic artifacts in prestack depth migration.

Strong refraction of waves in the migration velocity model introduces kinematic artifacts¿coherent events not corresponding to actual reflectors¿into the image volumes produced by prestack depth migration applied to individual data bins. Because individual bins are migrated independently, the migration has no access to the bin component of slowness. This loss of slowness information permits events to migrate along multiple incident-reflected ray pairs, thus introducing spurious coherent events into the image volume. This pathology occurs for all common binning strategies, including common-source, common-offset, and common-scattering angle. Since the artifacts move out with bin parameter, their effect on the final stacked image is minimal, provided that the migration velocity model is kinematically correct. However, common-image gathers may exhibit energetic primary events with substantial residual moveout, even with the kinematically accurate migration velocity model

Preconditioners based on windowed Fourier frames applied to elliptic partial differential equations

We investigate the application of windowed Fourier frames to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is close to a multiplication, where the multiplication factor is given by the symbol of the PDO evaluated at the wave number and central position of the windowed plane wave. This can be exploited in a preconditioning method for use in iterative inversion. For domains with periodic boundary conditions we find that the condition number with the preconditioning becomes bounded and the iteration converges well. For problems with a Dirichlet boundary condition, some large and small singular values remain. However the iterative inversion still appears to converge well

Modelling and inversion of seismic data in anisotropic elastic media

Seismic data is modeled in the high frequency limit We consider general anisotropic media and our method is also valid in the case of multipathing caustics The data is modeled in two ways First using the Kirchho approximation where the medium is assumed to be piecewise smooth and reection and transmission occurs at the interface Secondly the data is modeled using the Born approximation in other words by a linearization in the medium parameters The main result is a characterisation of seismic data We construct a Fourier integral operator and a reectivity function which is a function of subsurface position and scattering angle and azimuth such that the data is given by the invertible ourier integral operator acting on the reectivity function Using this new transformation of seismic data to subsurface position angle coor dinates we obtain the following results on the problem of reconstructing the medium coecients Given the medium above the interface in the Kirchho approximation one can reconstruct the position of the interface and the angular dependent reection coecients on the interface We also obtain a criterium to determine whether the medium above the interface the background medium in the Born approximation is correctly chosen These results are new in medium with caustics In the Born approximation the singular medium perturbation can be reconstructe

On the modeling and inversion of seismic data

In this thesis we investigate some mathematical questions related to the inversion of seismic data. In Chapter 2 we review results in the literature and give some new results on wave equations with coefficients that are just bounded and measurable. We show that these equations have unique solutions and we investigate the dependence on the coefficients. We also discuss solutions in case the coefficients have a discontinuity along a smooth surface. In Chapters 3 and 4 we discuss seismic imaging using high-frequency techniques (microlocal analysis). In particular we discuss the case that multipathing (the formation of caustics) occurs. In Chapter 3 we construct an operator that maps data to an angle-dependent reflectivity function, for elastic media. This makes it possible to reconstruct the position of a reflector and the reflection coefficients, given a smooth approximation to the medium coefficients. It also gives a criterion to determine the smooth part of the medium (velocity analysis), even in the case of caustics. In Chapter 4 we investigate the linearized inverse scattering problem for acoustic media. We consider the case where the so called traveltime injectivity condition is violated. We show that generically the inversion is still possible, but that in certain special cases this is no longer the case. We also give some examples

Long-term air pollution exposure, genome-wide DNA methylation and lung function in the lifelines cohort study

BACKGROUND: Long-term air pollution exposure is negatively associated with lung function, yet the mechanisms underlying this association are not fully clear. Differential DNA methylation may explain this association. OBJECTIVES: Our main aim was to study the association between long-term air pollution exposure and DNA methylation. METHODS: We performed a genome-wide methylation study using robust linear regression models in 1,017 subjects from the LifeLines cohort study to analyze the association between exposure to nitrogen dioxide (NO2) and particulate matter (PM2.5, fine particulate ma