Asymptotic wave-splitting in anisotropic linear acoustics

Linear acoustic wave-splitting is an often used tool in describing sound-wave propagation through earth's subsurface. Earth's subsurface is in general anisotropic due to the presence of water-filled porous rocks. Due to the complexity and the implicitness of the wave-splitting solutions in anisotropic media, wave-splitting in seismic experiments is often modeled as isotropic. With the present paper, we have derived a simple wave-splitting procedure for an instantaneously reacting anisotropic media that includes spatial variation in depth, yielding both a traditional (approximate) and a `true amplitude' wave-field decomposition. One of the main advantages of the method presented here is that it gives an explicit asymptotic representation of the linear acoustic-admittance operator to all orders of smoothness for the smooth, positive definite anisotropic material parameters considered here. Once the admittance operator is known we obtain an explicit asymptotic wave-splitting solution.Comment: 20 page

Linearized inverse scattering based on seismic Reverse Time Migration

In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse-time migration (RTM). In the process, the explicit evaluation of the so-called normal operator is avoided, while other differential and pseudodifferential operator factors are introduced. We prove that, under certain conditions, the transform yields a partial inverse, and support this with numerical simulations. In addition, we explain the recently discussed 'low-frequency artifacts' in RTM, which are naturally removed by the new method

The effect of the use of T and V pronouns in Dutch HR communication

In an online experiment among native speakers of Dutch we measured addressees' responses to emails written in the informal pronoun T or the formal pronoun V in HR communication. 172 participants (61 male, mean age 37 years) read either the V-versions or the T-versions of two invitation emails and two rejection emails by four different fictitious recruiters. After each email, participants had to score their appreciation of the company and the recruiter on five different scales each, such as The recruiter who wrote this email seems … [scale from friendly to unfriendly]. We hypothesized that (i) the V-pronoun would be more appreciated in letters of rejection, and the T-pronoun in letters of invitation, and (ii) older people would appreciate the V-pronoun more than the T-pronoun, and the other way around for younger people. Although neither of these hypotheses was supported, we did find a small effect of pronoun: Emails written in V were more highly appreciated than emails in T, irrespective of type of email (invitation or rejection), and irrespective of the participant's age, gender, and level of education. At the same time, we observed differences in the strength of this effect across different scales

Source-Indexed Migration Velocity Analysis with Global Passive Data

The reverse-time migration of global seismic data generated by free-surface multiples is regularly used to constrain the crustal structure, but its accuracy is to a large extent determined by the accuracy of the 3-D background velocity model used for wave propagation. To this improve the velocity model and hence the accuracy of the migrated image, we wish to apply the technique of migration velocity analysis (MVA) to global passive data. Applications of MVA in the active setting typically focus on o ffset- or angle-gather annihilation, a process that takes advantage of data redundancy to form an extended image, and then applies an annihilation operator to determine the success of image formation. Due to the nature of regional-scale passive seismic arrays, it is unlikely that the data in most of these studies will be su cient to form an extended image volume for use in annihilation-based MVA. In order to make use of the sparse and irregular array design of these arrays, we turn towards a shot-pro le moveout scheme for migration velocity analysis introduced by Xie and Yang (2008). In the place of extended image annihilation, we determine the success of the migration velocity model by using a weighted image correlation power norm. We compare pairs of images formed by migrating each teleseismic source by image cross-correlation in the depth direction. We look for a suitable background model by penalizing the amount of correlation power away from zero depth shift. The total weighted correlation power between source-pro le images is then used as the error function and optimized via conjugate gradient. We present the method and a proof-of-concept with 2-D synthetic data

Convergence Rates for Learning Linear Operators from Noisy Data

This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear operator. Assuming that the operator is diagonalizable in a known basis, this work solves the equivalent inverse problem of estimating the operator's eigenvalues given the data. Adopting a Bayesian approach, the theoretical analysis establishes posterior contraction rates in the infinite data limit with Gaussian priors that are not directly linked to the forward map of the inverse problem. The main results also include learning-theoretic generalization error guarantees for a wide range of distribution shifts. These convergence rates quantify the effects of data smoothness and true eigenvalue decay or growth, for compact or unbounded operators, respectively, on sample complexity. Numerical evidence supports the theory in diagonal and non-diagonal settings.Comment: To appear in SIAM/ASA Journal on Uncertainty Quantification (JUQ); 34 pages, 5 figures, 2 table