A confidence parameter for seismic moment tensors

Tape, Walter; Tape, Carl

doi:10.1093/gji/ggw057

Cited by 14 publications

(22 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The confidence curve for − M 0 is always a 180° rotation of the confidence curve for M 0 [ Tape and Tape , ]. Since in this example the confidence curve for M 0 resembles a Γ (Figure f), then the confidence curve for − M 0 resembles a backward L. And since

𝒫_{AV}

for M 0 was 0.95,

𝒫_{AV}

for − M 0 is only 0.05.…”

Section: Discussionmentioning

confidence: 93%

“…The normalized eigenvalues are therefore

Λ = (1, 0, - 1) / \sqrt{2}

, and the fractional volume curve

\overset{V}{true} (ω)

takes the shape of a mesa. (The curve will change for full moment tensors or for a different choice of Λ [ Tape and Tape , ]. )…”

Section: Discussionmentioning

confidence: 99%

“…The confidence curve

𝒫 (V)

in Figure f is shaped like a Γ for a high‐quality event, and it is close to the 45°line for a low‐quality event. The slope of

𝒫 (V)

at the origin is related to the probability density at the best fitting moment tensor, and the area under the curve

𝒫 (V)

provides the average confidence [ Tape and Tape , ]. Results for 21 events are presented in Silwal [] and summarized in Table .…”

Section: Discussionmentioning

confidence: 99%

“…Our confidence curve

𝒫 (V)

is from Tape and Tape []. The curve depends on a reference moment tensor, which will usually be the moment tensor M 0 with lowest misfit (or highest probability density).…”

Section: Estimation Of Uncertaintiesmentioning

confidence: 99%

“…Its derivative

{\overset{V}{true}}^{'} (ω)

has a mesa‐like shape. Values of

{\overset{V}{true}}^{'} (ω)

are tabulated in Appendix A of Tape and Tape [].…”

Section: Estimation Of Uncertaintiesmentioning

confidence: 99%

See 4 more Smart Citations

Seismic moment tensors and estimated uncertainties in southern Alaska

Silwal

Tape

2016

JGR Solid Earth

Self Cite

View full text Add to dashboard Cite

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.

show abstract

𝒫_{AV}

for M 0 was 0.95,

𝒫_{AV}

for − M 0 is only 0.05.…”

Section: Discussionmentioning

confidence: 93%

“…The normalized eigenvalues are therefore

Λ = (1, 0, - 1) / \sqrt{2}

, and the fractional volume curve

\overset{V}{true} (ω)

takes the shape of a mesa. (The curve will change for full moment tensors or for a different choice of Λ [ Tape and Tape , ]. )…”

Section: Discussionmentioning

confidence: 99%

“…The confidence curve

𝒫 (V)

in Figure f is shaped like a Γ for a high‐quality event, and it is close to the 45°line for a low‐quality event. The slope of

𝒫 (V)

at the origin is related to the probability density at the best fitting moment tensor, and the area under the curve

𝒫 (V)

provides the average confidence [ Tape and Tape , ]. Results for 21 events are presented in Silwal [] and summarized in Table .…”

Section: Discussionmentioning

confidence: 99%

“…Our confidence curve

𝒫 (V)

is from Tape and Tape []. The curve depends on a reference moment tensor, which will usually be the moment tensor M 0 with lowest misfit (or highest probability density).…”

Section: Estimation Of Uncertaintiesmentioning

confidence: 99%

“…Its derivative

{\overset{V}{true}}^{'} (ω)

has a mesa‐like shape. Values of

{\overset{V}{true}}^{'} (ω)

are tabulated in Appendix A of Tape and Tape [].…”

Section: Estimation Of Uncertaintiesmentioning

confidence: 99%

See 3 more Smart Citations

Seismic moment tensors and estimated uncertainties in southern Alaska

Silwal

Tape

2016

JGR Solid Earth

Self Cite

View full text Add to dashboard Cite

show abstract

Source mechanism of a lower crust earthquake beneath the Himalayas and its possible relation to metamorphism

Alvizuri

Hetényi

2019

Tectonophysics

View full text Add to dashboard Cite

The nature of deep-crustal, intermediate and deep-focus earthquakes and their relation to metamorphic reactions is a topic of debate. Here we seek to better understand a possible link between the earthquake process and metamorphism by analyzing the mechanism of ongoing deep-crustal earthquakes. We focus on a region in the Himalayas with observed seismicity at depths expected to experience active eclogite-facies metamorphism and dehydration reactions. There are few permanent seismic stations in the region, therefore we use waveform data from a temporary seismic array deployment. We find two earthquakes with magnitude and station coverage adequate for moment tensor inversion. For a given earthquake we estimate its seismic full moment tensors (and magnitude) together with uncertainties using all available waveforms. For the largest earthquake (Mw 3.7) we obtain a best-fitting moment tensor and uncertainties that show a double-couple with a tensional crack component. In the context of geological records that document similar processes, and of laboratory experiments conducted at spatial scales that are 5-6 orders of magnitude smaller, this mechanism may be related to dehydration-driven stress changes triggering slight crack opening, and ambient stresses favoring slip along a fault.

show abstract

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

et al. 2018

Self Cite

View full text Add to dashboard Cite

A seismic moment tensor is a 3 × 3 symmetric matrix that provides a compact representation of a seismic source. We develop an algorithm to estimate moment tensors and their uncertainties from observed seismic data. For a given event, the algorithm performs a grid search over the six‐dimensional space of moment tensors by generating synthetic waveforms for each moment tensor and then evaluating a misfit function between the observed and synthetic waveforms. “The” moment tensor M0 for the event is then the moment tensor with minimum misfit. To describe the uncertainty associated with M0, we first convert the misfit function to a probability function. The uncertainty, or rather the confidence, is then given by the “confidence curve” 𝒫false(Vfalse), where 𝒫false(Vfalse) is the probability that the true moment tensor for the event lies within a certain neighborhood of M that has fractional volume V. The area under the confidence curve provides a single, abbreviated “confidence parameter” for M0. We apply the method to data from events in different regions and tectonic settings: 17 nuclear explosions and 12 earthquakes at the Nevada Test Site, 63 small (Mw<2.5) events at Uturuncu volcano in Bolivia, and 21 moderate (Mw>4) earthquakes in the southern Alaska subduction zone. Characterization of moment tensor uncertainties puts us in better position to discriminate among moment tensor source types and to assign physical processes to the events.

show abstract

A confidence parameter for seismic moment tensors

Cited by 14 publications

References 10 publications

Seismic moment tensors and estimated uncertainties in southern Alaska

Seismic moment tensors and estimated uncertainties in southern Alaska

Source mechanism of a lower crust earthquake beneath the Himalayas and its possible relation to metamorphism

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

Contact Info

Product

Resources

About