Seismic moment tensors and estimated uncertainties in southern Alaska

Abstract

We present a moment tensor catalog of 106 earthquakes in southern Alaska, and we perform a conceptually based uncertainty analysis for 21 of them. For each earthquake, we use both body waves and surface waves to do a grid search over double couple moment tensors and source depths in order to find the minimum of the misfit function. Our uncertainty parameter or, rather, our confidence parameter is the average value of the curve 𝒫0.3em(V), where 𝒫0.3em(V) is the posterior probability as a function of the fractional volume V of moment tensor space surrounding the minimum misfit moment tensor. As a supplemental means for characterizing and visualizing uncertainties, we generate moment tensor samples of the posterior probability. We perform a series of inversion tests to quantify the impact of certain decisions made within moment tensor inversions and to make comparisons with existing catalogs. For example, using an L1 norm in the misfit function provides more reliable solutions than an L2 norm, especially in cases when all available waveforms are used. Using body waves in addition to surface waves, as well as using more stations, leads to the most accurate moment tensor solutions.

Hamiltonian Monte Carlo Inversion of Seismic Sources in Complex Media

“…With the focus of this work being on Hamiltonian Monte Carlo as a method for source inversion, we admittedly paid less attention to other aspects of the problem that may not be less important. These include the quantification of forward modeling and observational uncertainties, as performed, for instance, by Mustać and Tkalčić (), Silwal and Tape (), Staehler and Sigloch (, ), Vackár et al (), and Wéber ().…”

Estimation of Full Moment Tensors, Including Uncertainties, for Nuclear Explosions, Volcanic Events, and Earthquakes

“…For our moment tensor inversions, we use the “cut‐and‐paste” code of Zhao and Helmberger (), Zhu and Helmberger (), and Zhu and Ben‐Zion (), with some modifications. Our misfit function is given by where Φ p ( M ) is the L1 misfit of polarities, Φ w ( M ) is the L1 misfit of waveform differences (e.g., Silwal & Tape, ), N p is the number of polarities used, and m is a weight factor to balance the contributions of polarity differences and waveform differences. We also use an efficient grid search over moment tensor space, described below.…”

“…The area under the confidence curve is the confidence parameter . The confidence curve is constructed from two functions and (Silwal & Tape, , Figure 4). The number is the fractional volume of the set of moment tensors within angular distance ω of M 0 , and is the probability associated with that same set.…”

“…A depth search was performed in Silwal and Tape () using the double‐couple constraint; we fix those depths for our full moment tensor inversions.…”

“…Following Tape and Tape (), we represent moment tensor uncertainties in the form of a confidence curve that expresses the concentration of probability in moment tensor space near M 0 . We build upon three recent studies: Tape and Tape (), which established the theory for confidence curves; Silwal and Tape (), which estimated confidence curves for double‐couple moment tensors; and Alvizuri and Tape (), which estimated a catalog of full moment tensors for volcanic events. In our examination of earthquakes and nuclear explosions from the Nevada Test Site (NTS), we use the same 29 events as in Ford et al ().…”