Location and Mechanism of Very Long Period Tremor During the 2008 Eruption of Okmok Volcano from Interstation Arrival Times

We describe continuous, very long period (VLP) tremor that occurred during the 2008 eruption of Okmok Volcano, Alaska. Due to its low frequency content in band from the 0.2–0.4 Hz, the wave field of the VLP tremor is relatively free of path effects. From continuous recordings of the VLP tremor on 2 three-component broadband and 3 single-component short‐period instruments, we devise a method to locate the epicenter of the tremor based on interstation arrival times computed with cross correlation. We find the epicenter since the vertical and radial components of the VLP tremor wave field are dominated by Rayleigh waves and the time shifts are related to lateral propagation. Over the 4 h period studied, this procedure yields a location NNW of Cone D, close to the new cone built over the course of the eruption. Similar analysis using the transverse horizontal components from the 2 three‐component broadband instruments yields strong constraints on the source mechanism of the VLP tremor. We observe an anomalous interstation arrival time due to the existence of a nodal plane in the Love wave radiation pattern. The orientation of a compensated linear vector dipole (CLVD) source estimated from the transverse components closely aligns with the regional maximum horizontal stress direction. The depth of the CLVD source is constrained by matching the vertical components to the Rayleigh wave radiation pattern at all five stations. We find the VLP tremor source depth to be 2 km BSL, positioned between the magma chamber at Okmok (\u3e3 km BSL) and the surface

Infrasonic Ambient Noise Interferometry From Correlations of Microbaroms

We show that microbaroms, continuous infrasound fluctuations resulting from the interaction of the ocean with the atmosphere, have long-range correlation properties that make it possible to estimate the impulse response between two microphones from passive recordings. The processing is analogous to methods employed in the emerging field of ambient noise seismology, where the random noise source is the ocean coupling with the solid Earth (microseisms) instead of the atmosphere (microbaroms). We find that timedependent temperature fields and temperature inversions determine the character of infrasonic impulse responses at Fourpeaked Volcano in Alaska. Applications include imaging and monitoring the gross structure of the Earth’s atmospheric boundary layer

Perturbational and nonperturbational inversion of Rayleigh-wave velocities

The inversion of Rayleigh-wave dispersion curves is a classic geophysical inverse problem. We have developed a set of MATLAB codes that performs forward modeling and inversion of Rayleigh-wave phase or group velocity measurements. We describe two different methods of inversion: a perturbational method based on finite elements and a nonperturbational method based on the recently developed Dix-type relation for Rayleigh waves. In practice, the nonperturbational method can be used to provide a good starting model that can be iteratively improved with the perturbational method. Although the perturbational method is well-known, we solve the forward problem using an eigenvalue/eigenvector solver instead of the conventional approach of root finding. Features of the codes include the ability to handle any mix of phase or group velocity measurements, combinations of modes of any order, the presence of a surface water layer, computation of partial derivatives due to changes in material properties and layer boundaries, and the implementation of an automatic grid of layers that is optimally suited for the depth sensitivity of Rayleigh waves

Nonperturbational surface-wave inversion: A Dix-type relation for surface waves

We extend the approach underlying the well-known Dix equation in reflection seismology to surface waves. Within the context of surface wave inversion, the Dix-type relation we derive for surface waves allows accurate depth profiles of shear-wave velocity to be constructed directly from phase velocity data, in contrast to perturbational methods. The depth profiles can subsequently be used as an initial model for nonlinear inversion. We provide examples of the Dix-type relation for under-parameterized and over-parameterized cases. In the under-parameterized case, we use the theory to estimate crustal thickness, crustal shear-wave velocity, and mantle shear-wave velocity across the Western U.S. from phase velocity maps measured at 8-, 20-, and 40-s periods. By adopting a thin-layer formalism and an over-parameterized model, we show how a regularized inversion based on the Dix-type relation yields smooth depth profiles of shear-wave velocity. In the process, we quantitatively demonstrate the depth sensitivity of surface-wave phase velocity as a function of frequency and the accuracy of the Dix-type relation. We apply the over-parameterized approach to a near-surface data set within the frequency band from 5 to 40 Hz and find overall agreement between the inverted model and the result of full nonlinear inversion

Utility Cost of Formal Privacy for Releasing National Employer-Employee Statistics

National statistical agencies around the world publish tabular summaries based on combined employer-employee (ER-EE) data. The privacy of both individuals and business establishments that feature in these data are protected by law in most countries. These data are currently released using a variety of statistical disclosure limitation (SDL) techniques that do not reveal the exact characteristics of particular employers and employees, but lack provable privacy guarantees limiting inferential disclosures. In this work, we present novel algorithms for releasing tabular summaries of linked ER-EE data with formal, provable guarantees of privacy. We show that state-of-the-art differentially private algorithms add too much noise for the output to be useful. Instead, we identify the privacy requirements mandated by current interpretations of the relevant laws, and formalize them using the Pufferfish framework. We then develop new privacy definitions that are customized to ER-EE data and satisfy the statutory privacy requirements. We implement the experiments in this paper on production data gathered by the U.S. Census Bureau. An empirical evaluation of utility for these data shows that for reasonable values of the privacy-loss parameter ϵ≥1, the additive error introduced by our provably private algorithms is comparable, and in some cases better, than the error introduced by existing SDL techniques that have no provable privacy guarantees. For some complex queries currently published, however, our algorithms do not have utility comparable to the existing traditiona

Causal Instrument Corrections for Short-Period and Broadband Seismometers

Of all the filters applied to recordings of seismic waves, which include source, path, and site effects, the one we know most precisely is the instrument filter. Therefore, it behooves seismologists to accurately remove the effect of the instrument from raw seismograms. Applying instrument corrections allows analysis of the seismogram in terms of physical units (e.g., displacement or particle velocity of the Earth’s surface) instead of the output of the instrument (e.g., digital counts). The instrument correction can be considered the most fundamental processing step in seismology since it relates the raw data to an observable quantity of interest to seismologists. Complicating matters is the fact that, in practice, the term “instrument correction” refers to more than simply the seismometer. The instrument correction compensates for the complete recording system including the seismometer, telemetry, digitizer, and any anti‐alias filters

A comparison of methods to estimate seismic phase delays: numerical examples for coda wave interferometry

Time-shift estimation between arrivals in two seismic traces before and after a velocity perturbation is a crucial step in many seismic methods. The accuracy of the estimated velocity perturbation location and amplitude depend on this time shift. Windowed cross-correlation and trace stretching are two techniques commonly used to estimate local time shifts in seismic signals. In the work presented here we implement Dynamic Time Warping (DTW) to estimate the warping function – a vector of local time shifts that globally minimizes the misfit between two seismic traces. We compare all three methods using acoustic numerical experiments. We show that DTW is comparable to or better than the other two methods when the velocity perturbation is homogeneous and the signal-to-noise ratio is high. When the signal-to-noise ratio is low, we find that DTW and windowed cross-correlation are more accurate than the stretching method. Finally, we show that the DTW algorithm has good time resolution when identifying small differences in the seismic traces for a model with an isolated velocity perturbation. These results impact current methods that utilize not only time shifts between (multiply) scattered waves, but also amplitude and decoherence measurements