On the usefulness of waterborne measurement of particle velocity in geoacoustic inversion

Recent advances in sensor design have led to the development of receiving systems whose elements are vector sensors, i.e., sensors that simultaneously measure the acoustic pressure and fluid motion due to the propagation of acoustic energy at the sensor location. As such, arrays of vector sensors can provide more information about the sound field than arrays made of traditional hydrophones, and thus are attractive for various applications including the inversion for environmental properties. The fundamental question addressed by this paper is: does the use of acoustic vector data versus pressure-only data improve the results of an inversion scheme based on waterborne observations and matched field processing? To our knowledge no experimental data are available yet to allow a detailed comparison of performance between standard (pressure-only) arrays and vector sensor arrays for environmental inversions. For a preliminary study we will simulate the inversion of vector sensor data in the South Elba environment for which pressure-only inversion results and ground truth data are available following the Yellow Shark'94 and Blue Planet'07 experiments. Broadband signals received on fully-populated and sparse arrays will be considered

On the use of acoustic particle velocity fields in adjoint-based inversion

Following the recent interest in the use of combined pressure and particle motion sensors in underwater acoustics and signal processing, some general aspects regarding the modeling and multipath phenomenology of acoustic particle velocity fields in shallow water environments have been studied. In this paper we will address a number of issues associated with the incorporation of vector sensor data (pressure and particle velocity) into adjoint-based inversion schemes. Specifically, we will discuss the ability of a semi-automatic adjoint approach to compute the necessary gradient information without the need for an analytic model of the adjoint particle velocity field. Solutions to the forward propagation of acoustic pressure are computed using an implicit finite-difference parabolic equation solver while the particle velocity is calculated locally at each grid point. Some numerical examples of vector sensor inversion results are provided

METEOR : draft protocols on hazard and exposure modelling. Report M6.3/P

The objective of this report is to present the methodology proposed for the production of national level multihazard risk assessments for Tanzania and Nepal. We discuss need to create a relative hazard vulnerability map and then to combine these in a way that allows the hazards to be weighted independently of each other. We present how this approach has been applied in Nepal and Tanzania, and to which hazards and discuss the types of data that are necessary inputs to such an approach. We also define the governing formulae that are the basis for our model and describe how these can be paired with expert elicitation to support decision making in places where data is scarce. We present the data that the model produces and discuss the possible uses for this information. We also discuss ways in which sensitivity testing could be performed to assess the performance of the model, which is further developed in later work. This report (M6.3/P) describes a specific piece of work conducted by British Geological Survey (BGS) as part of the METEOR (Modelling Exposure Through Earth Observation Routines) project, a 3-year project funded by UK Space Agency through their International Partnership Programme, details of which can be located in the Foreword of the report, the project having completed in 2021. The project aimed to provide an innovative solution to disaster risk reduction, through development of an innovative methodology of creating exposure data from Earth Observation (EO) imagery to identify development patterns throughout a country and provide detailed information when combined with population information. Level 1 exposure was developed for all 47 least developed countries on the OECD DAC list, referred to as ODA least-developed countries in the METEOR documentation, with open access to data and protocols for their development. New national detailed exposure and hazard datasets were also generated for the focus countries of Nepal and Tanzania and the impact of multiple hazards assessed for the countries. Training on product development and potential use for Disaster Risk Reduction was performed within these countries with all data made openly available on data platforms for wider use both within country and worldwide. The METEOR project was led by British Geological Survey (BGS) with collaborative partners Oxford Policy Management Limited (OPM), SSBN Limited, The Disaster Management Department, Office of the Prime Minister – Tanzania (DMD), The Global Earthquake Model Foundation (GEM), The Humanitarian OpenStreetMap Team (HOT), ImageCat and the National Society for Earthquake Technology (NSET) – Nepal. The project was broken into collaborative work packages including: Project Management (WP1 – led by BGS), Monitoring and Evaluation (WP2 – led by OPM), EO data for exposure development (WP3 – led by ImageCat), Inputs and Validation (WP4 – led by HOT), Vulnerability and Uncertainty (WP5 - led by GEM), Multiple Hazard Impact (WP6 - led by BGS), Knowledge sharing (WP7 – led by GEM) and Sustainability and capacity building (WP8 – led by ImageCat) with key collaboration throughout by the partners in Nepal (NSET) and Tanzania (DMD)

On dual Schur domain decomposition method for linear first-order transient problems

This paper addresses some numerical and theoretical aspects of dual Schur domain decomposition methods for linear first-order transient partial differential equations. In this work, we consider the trapezoidal family of schemes for integrating the ordinary differential equations (ODEs) for each subdomain and present four different coupling methods, corresponding to different algebraic constraints, for enforcing kinematic continuity on the interface between the subdomains. Method 1 (d-continuity) is based on the conventional approach using continuity of the primary variable and we show that this method is unstable for a lot of commonly used time integrators including the mid-point rule. To alleviate this difficulty, we propose a new Method 2 (Modified d-continuity) and prove its stability for coupling all time integrators in the trapezoidal family (except the forward Euler). Method 3 (v-continuity) is based on enforcing the continuity of the time derivative of the primary variable. However, this constraint introduces a drift in the primary variable on the interface. We present Method 4 (Baumgarte stabilized) which uses Baumgarte stabilization to limit this drift and we derive bounds for the stabilization parameter to ensure stability. Our stability analysis is based on the ``energy'' method, and one of the main contributions of this paper is the extension of the energy method (which was previously introduced in the context of numerical methods for ODEs) to assess the stability of numerical formulations for index-2 differential-algebraic equations (DAEs).Comment: 22 Figures, 49 pages (double spacing using amsart

METEOR : methods for analysing multi-hazards with exposure. Report M6.2/P

The objective of this report is to review methods for analysing multi-hazards with exposure and to propose a methodology for integrating multiple hazards, exposure and vulnerability in Nepal and Tanzania. The report introduces the concepts of fragility curves, damage matrices and physical vulnerability and reviews existing methods for assessing multi-hazard risk. It goes on to test two existing methodologies for multi-hazard assessment, concentrating on integrated risk assessment and relative vulnerability indices before discussing the use of expert elicitation to determine expert weighting of hazards into the hazard assessment. The report shows the hazard footprints generated through the METEOR project for Tanzania before discussing the framework for deriving relative vulnerability indicators and results of integrated risk. This report (M6.2/P) describes a piece of work conducted by British Geological Survey (BGS) as part of the METEOR (Modelling Exposure Through Earth Observation Routines) project, a 3-year project funded by UK Space Agency through their International Partnership Programme, details of which can be located in the Foreword of the report, the project having completed in 2021. The project aimed to provide an innovative solution to disaster risk reduction, through development of an innovative methodology of creating exposure data from Earth Observation (EO) imagery to identify development patterns throughout a country and provide detailed information when combined with population information. Level 1 exposure was developed for all 47 least developed countries on the OECD DAC list, referred to as ODA least-developed countries in the METEOR documentation, with open access to data and protocols for their development. New national detailed exposure and hazard datasets were also generated for the focus countries of Nepal and Tanzania and the impact of multiple hazards assessed for the countries. Training on product development and potential use for Disaster Risk Reduction was performed within these countries with all data made openly available on data platforms for wider use both within country and worldwide. The METEOR project was led by British Geological Survey (BGS) with collaborative partners Oxford Policy Management Limited (OPM), SSBN Limited, The Disaster Management Department, Office of the Prime Minister – Tanzania (DMD), The Global Earthquake Model Foundation (GEM), The Humanitarian OpenStreetMap Team (HOT), ImageCat and the National Society for Earthquake Technology (NSET) – Nepal. The project was broken into collaborative work packages including: Project Management (WP1 – led by BGS), Monitoring and Evaluation (WP2 – led by OPM), EO data for exposure development (WP3 – led by ImageCat), Inputs and Validation (WP4 – led by HOT), Vulnerability and Uncertainty (WP5 - led by GEM), Multiple Hazard Impact (WP6 - led by BGS), Knowledge sharing (WP7 – led by GEM) and Sustainability and capacity building (WP8 – led by ImageCat) with key collaboration throughout by the partners in Nepal (NSET) and Tanzania (DMD)

Limit theorems for weakly subcritical branching processes in random environment

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the process may at the same time be subcritical and, conditioned on nonextinction, 'supercritical'. This so-called weakly subcritical case is considered in this paper. We study the asymptotic survival probability and the size of the population conditioned on non-extinction. Also a functional limit theorem is proven, which makes the conditional supercriticality manifest. A main tool is a new type of functional limit theorems for conditional random walks.Comment: 35 page

Operator-Algebraic Approach to the Yrast Spectrum of Weakly Interacting Trapped Bosons

We present an operator-algebraic approach to deriving the low-lying quasi-degenerate spectrum of weakly interacting trapped N bosons with total angular momentum \hbar L for the case of small L/N, demonstrating that the lowest-lying excitation spectrum is given by 27 g n_3(n_3-1)/34, where g is the strength of the repulsive contact interaction and n_3 the number of excited octupole quanta. Our method provides constraints for these quasi-degenerate many-body states and gives higher excitation energies that depend linearly on N.Comment: 7 pages, one figur

Microscopic Theory of the Reentrant IQHE in the First and Second Excited LLs

We present a microscopic theory for the recently observed reentrant integral quantum Hall effect in the n=1 and n=2 Landau levels. Our energy investigations indicate an alternating sequence of M-electron-bubble and quantum-liquid ground states in a certain range of the partial filling factor of the n-th level. Whereas the quantum-liquid states display the fractional quantum Hall effect, the bubble phases are insulating, and the Hall resistance is thus quantized at integral values of the total filling factor.Comment: 4 pages, 4 figures; minor corrections include

Ballistic electron motion in a random magnetic field

Using a new scheme of the derivation of the non-linear $\sigma$-model we consider the electron motion in a random magnetic field (RMF) in two dimensions. The derivation is based on writing quasiclassical equations and representing their solutions in terms of a functional integral over supermatrices $Q$ with the constraint $Q^2=1$. Contrary to the standard scheme, neither singling out slow modes nor saddle-point approximation are used. The $\sigma$-model obtained is applicable at the length scale down to the electron wavelength. We show that this model differs from the model with a random potential (RP).However, after averaging over fluctuations in the Lyapunov region the standard $\sigma$-model is obtained leading to the conventional localization behavior.Comment: 10 pages, no figures, to be submitted in PRB v2: Section IV is remove