Extended Kramers-Moyal analysis applied to optical trapping

The Kramers-Moyal analysis is a well established approach to analyze stochastic time series from complex systems. If the sampling interval of a measured time series is too low, systematic errors occur in the analysis results. These errors are labeled as finite time effects in the literature. In the present article, we present some new insights about these effects and discuss the limitations of a previously published method to estimate Kramers-Moyal coefficients at the presence of finite time effects. To increase the reliability of this method and to avoid misinterpretations, we extend it by the computation of error estimates for estimated parameters using a Monte Carlo error propagation technique. Finally, the extended method is applied to a data set of an optical trapping experiment yielding estimations of the forces acting on a Brownian particle trapped by optical tweezers. We find an increased Markov-Einstein time scale of the order of the relaxation time of the process which can be traced back to memory effects caused by the interaction of the particle and the fluid. Above the Markov-Einstein time scale, the process can be very well described by the classical overdamped Markov model for Brownian motion.Comment: 14 pages, 18 figure

The First Second of Volcanic Eruptions from the Erebus Volcano Lava Lake, Antarctica—Energies, Pressures, Seismology, and Infrasound

[1] We describe a multiparameter experiment at Erebus volcano, Antarctica, employing Doppler radar, video, acoustic, and seismic observations to estimate the detailed energy budget of large (up to 40 m-diameter) bubble bursts from a persistent phonolite lava lake. These explosions are readily studied from the crater rim at ranges of less than 500 m and present an ideal opportunity to constrain the dynamics and mechanism of magmatic bubble bursts that can drive Strombolian and Hawaiian eruptions. We estimate the energy budget of the first second of a typical Erebus explosion as a function of time and energy type. We constrain gas pressures and forces using an analytic model for the expansion of a gas bubble above a conduit that incorporates conduit geometry and magma and gas parameters. The model, consistent with video and radar observations, invokes a spherical bulging surface with a base diameter equal to that of the lava lake. The model has no ad hoc free parameters, and geometrical calculations predict zenith height, velocity, and acceleration during shell expansion. During explosions, the energy contained in hot overpressured gas bubbles is freed and partitioned into other energy types, where by far the greatest nonthermal energy component is the kinetic and gravitational potential energy of the accelerated magma shell (\u3e109 J). Seismic source energy created by explosions is estimated from radar measurements and is consistent with source energy determined from seismic observations. For the generation of the infrasonic signal, a dual mechanism incorporating a terminally disrupted slug is proposed, which clarifies previous models and provides good fits to observed infrasonic pressures. A new and straightforward method is presented for determining gas volumes from slug explosions at volcanoes from remote infrasound recordings

A TV-Gaussian prior for infinite-dimensional Bayesian inverse problems and its numerical implementations

Many scientific and engineering problems require to perform Bayesian inferences in function spaces, in which the unknowns are of infinite dimension. In such problems, choosing an appropriate prior distribution is an important task. In particular we consider problems where the function to infer is subject to sharp jumps which render the commonly used Gaussian measures unsuitable. On the other hand, the so-called total variation (TV) prior can only be defined in a finite dimensional setting, and does not lead to a well-defined posterior measure in function spaces. In this work we present a TV-Gaussian (TG) prior to address such problems, where the TV term is used to detect sharp jumps of the function, and the Gaussian distribution is used as a reference measure so that it results in a well-defined posterior measure in the function space. We also present an efficient Markov Chain Monte Carlo (MCMC) algorithm to draw samples from the posterior distribution of the TG prior. With numerical examples we demonstrate the performance of the TG prior and the efficiency of the proposed MCMC algorithm

Near-surface environmentally forced changes in the Ross Ice Shelf observed with ambient seismic noise

Author Posting. © American Geophysical Union, 2018. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 45 (2018): 11,187-11,196, doi:10.1029/2018GL079665.Continuous seismic observations across the Ross Ice Shelf reveal ubiquitous ambient resonances at frequencies >5 Hz. These firn‐trapped surface wave signals arise through wind and snow bedform interactions coupled with very low velocity structures. Progressive and long‐term spectral changes are associated with surface snow redistribution by wind and with a January 2016 regional melt event. Modeling demonstrates high spectral sensitivity to near‐surface (top several meters) elastic parameters. We propose that spectral peak changes arise from surface snow redistribution in wind events and to velocity drops reflecting snow lattice weakening near 0°C for the melt event. Percolation‐related refrozen layers and layer thinning may also contribute to long‐term spectral changes after the melt event. Single‐station observations are inverted for elastic structure for multiple stations across the ice shelf. High‐frequency ambient noise seismology presents opportunities for continuous assessment of near‐surface ice shelf or other firn environments.NSF Office of Polar Programs Grant Number: PLR-11425182019-04-1

Tsunami and infragravity waves impacting Antarctic ice shelves

Author Posting. © American Geophysical Union, 2017. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 122 (2017): 5786–5801, doi:10.1002/2017JC012913.The responses of the Ross Ice Shelf (RIS) to the 16 September 2015 8.3 (Mw) Chilean earthquake tsunami (>75 s period) and to oceanic infragravity (IG) waves (50–300 s period) were recorded by a broadband seismic array deployed on the RIS from November 2014 to November 2016. Here we show that tsunami and IG-generated signals within the RIS propagate at gravity wave speeds (∼70 m/s) as water-ice coupled flexural-gravity waves. IG band signals show measureable attenuation away from the shelf front. The response of the RIS to Chilean tsunami arrivals is compared with modeled tsunami forcing to assess ice shelf flexural-gravity wave excitation by very long period (VLP; >300 s) gravity waves. Displacements across the RIS are affected by gravity wave incident direction, bathymetry under and north of the shelf, and water layer and ice shelf thicknesses. Horizontal displacements are typically about 10 times larger than vertical displacements, producing dynamical extensional motions that may facilitate expansion of existing fractures. VLP excitation is continuously observed throughout the year, with horizontal displacements highest during the austral winter with amplitudes exceeding 20 cm. Because VLP flexural-gravity waves exhibit no discernable attenuation, this energy must propagate to the grounding zone. Both IG and VLP band flexural-gravity waves excite mechanical perturbations of the RIS that likely promote tabular iceberg calving, consequently affecting ice shelf evolution. Understanding these ocean-excited mechanical interactions is important to determine their effect on ice shelf stability to reduce uncertainty in the magnitude and rate of global sea level rise.NSF Grant Numbers: PLR 1246151, PLR-1246416, PLR-1142518, 1141916, 1142126; National Oceanic and Atmospheric Administration (NOAA); Incorporated Research Institutions for Seismology (IRIS) through the PASSCAL Instrument Center at New Mexico Tech.; National Science Foundation under Cooperative Agreement Grant Number: EAR-1261681; DOE National Nuclear Security Administration2018-01-2

Shear velocity structure of central Antarctica from teleseismic Rayleigh waves

第2回極域科学シンポジウム/第31回極域地学シンポジウム 11月16日（水） 国立国語研究

The waveform correlation event detection system project, Phase I: Issues in prototype development and testing

A study using long-period seismic data showed that seismic events can be detected and located based on correlations of processed waveform profiles with the profile expected for an event. In this technique both time and space are discretized and events are found by forming profiles and calculating correlations for all time-distance points. events are declared at points with large correlations. In the first phase of the Waveform Correlation Event Detection System (WCEDS) Project at Sandia Labs we have developed a prototype automatic event detection system based on Shearer`s work which shows promise for treaty monitoring applications. Many modifications have been made to meet the requirements of the monitoring environment. A new full matrix multiplication has been developed which can reduce the number of computations needed for the data correlation by as much as two orders of magnitude for large grids. New methodology has also been developed to deal with the problems caused by false correlations (sidelobes) generated during the correlation process. When an event has been detected, masking matrices are set up which will mask all correlation sidelobes due to the event, allowing other events with intermingled phases to be found. This process is repeated until a detection threshold is reached. The system was tested on one hour of Incorporated Research Institutions for Seismology (IRIS) broadband data and built all 4 of the events listed in the National Earthquake Information Center (NEIC) Preliminary Determination of Epicenters (PDE) which were observable by the IRIS network. A continuous execution scheme has been developed for the system but has not yet been implemented. Improvements to the efficiency of the code are in various stages of development. Many refinements would have to be made to the system before it could be used as part of an actual monitoring system, but at this stage we know of no clear barriers which would prevent an eventual implementation of the system