Statistical self‐similarity of hotspot seamount volumes modeled as self‐similar criticality

Tebbens, S. F.; Burroughs, S. M.; Barton, Christopher C.; Naar, David F.

doi:10.1029/2000gl012748

Cited by 10 publications

(19 citation statements)

References 20 publications

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“…We observe that β < 1 leading to 1.5 < q, in agreement with previous published results on earth physics processes in a broad range of scales from laboratory up to geodynamic one [16,17]. For V q = 24 km 3 as estimated for the fitting of Q-exponential (see Figure 2) we lead to V o = 20 km 3 which is similar with the cut off used in [40].…”

Section: Esc Data Analysis and Discussionsupporting

confidence: 78%

“…The power-law frequency volume distribution is the only distribution that does not have a characteristic scale and can be explained in terms of scale invariance, i.e., fractal statistics [11,12,44]. In the frame of non-extensive statistical mechanics approach for seamount volumes bigger than a given one Vo we lead to a power law description of the distribution function and in such a case the cumulative distribution is (> ) ≅ ~ with an exponent = and = ( ) in agreement with the power law empirically used to describe the seamount distribution [40] with β = 0.85 close to that presented in [40]. To have an estimation of Vο we select the volume where the power law approximation of P(>V) takes the value P(>V) = 1 leading to = ( ) .…”

Section: Esc Data Analysis and Discussionmentioning

confidence: 52%

“…In the frame of non-extensive statistical mechanics approach for seamount volumes bigger than a given one V o we lead to a power law description of the distribution function and in such a case the in agreement with the power law empirically used to describe the seamount distribution [40] with β = 0.85 close to that presented in [40]. To have an estimation of V o we select the volume where the power law approximation of P(>V) takes the value P(>V) = 1 leading to V = V q ( 2−q q−1 ) 3 2 .…”

Section: Esc Data Analysis and Discussionmentioning

confidence: 99%

“…Many empirical distribution functions were already proposed in the past decade, mainly based on empirical and not physically justified approaches [6][7][8][9][10]. Among them exponential and power law distributions have been suggested to statistical characterize seamounts volume distributions, based on the argument that power law results when the seamounts organized in terms of self-organized criticality (SOC) [40]. In the context of SOC, [11,12,41] the cumulative frequency volume distribution of seamounts can be well described by the power-law relation P(> V) ∼ = C V −β [41][42][43] in a similar way as in other parameters in volcanic systems [44].…”

Section: Esc Data Analysis and Discussionmentioning

confidence: 99%

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A Non-Extensive Statistical Mechanics View on Easter Island Seamounts Volume Distribution

Vallianatos¹

2018

Geosciences

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Abstract:In the volcanic complex processes, inherent long-range interactions exist suggesting that Non-Extensive Statistical mechanics could be used to describe fundamental properties of the system. Based on the non-extensive Tsallis entropy a frequency-volume distribution function is suggested for the Easter Island-Salas y Gomez seamounts chain. Our results demonstrate the applicability of fundamental principles of Tsallis entropy to derive the cumulative distribution of seamounts volumes. The work suggests that the processes responsible for hotspot seamount formation are complex and the cumulative frequency-volume distribution of seamounts in the Easter Island/Salas y Gomez Chain (ESC) are well-described by a q-exponential function. The analysis leads to a non-extensive index q = 1.54 in agreement with that presented in other geodynamic or laboratory scale effects.

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Section: Esc Data Analysis and Discussionsupporting

confidence: 78%

Section: Esc Data Analysis and Discussionmentioning

confidence: 52%

Section: Esc Data Analysis and Discussionmentioning

confidence: 99%

Section: Esc Data Analysis and Discussionmentioning

confidence: 99%

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A Non-Extensive Statistical Mechanics View on Easter Island Seamounts Volume Distribution

Vallianatos¹

2018

Geosciences

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“…An upper-truncated power law has been shown to describe cumulative distributions associated with several natural systems (11)(12)(13)). An upper-truncated power law, N T (r), has the form where N T (r) is the number of objects with size greater than or equal to r, r T is the truncation size where the upper-truncated power law equals zero, and ␣ is the scaling exponent.…”

Section: Methodsmentioning

confidence: 99%

Wavelet analysis of shoreline change on the Outer Banks of North Carolina: An example of complexity in the marine sciences

Tebbens

Burroughs

Nelson

2002

Proc. Natl. Acad. Sci. U.S.A.

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The horizontal, shore-perpendicular change in shoreline position along the Outer Banks of North Carolina is found to be a self-affine signal. We measure shoreline change by determining the horizontal change in position of the 0.8-m contour sampled from shoreperpendicular profiles spaced at 20-m intervals along the coast. The profiles are obtained from two light detection and ranging surveys performed in September 1997 and September 1998. For six selected sections of coast, wavelet analysis of the shoreline change signal indicates the signal is self-affine with a scaling exponent that varies from 1.2 to 2.1. This self-affine behavior indicates that the shoreline change signal is nonstationary with long-range persistence. A stochastic diffusion model of sediment transport replicates the observed self-affine behavior observed south of Cape Hatteras (scaling exponent between 1.2 and 1.6) whereas a random walk model replicates the signal observed north of Cape Hatteras (scaling exponent Ϸ2.0). Because of the finite nature of the data set, there are limits in space and time to the power law behavior of the system. Characteristics of such systems can be described by upper-truncated power laws, which yield the upper limits of power law behavior. Applying an upper-truncated power law to the data for one section of coast, we find an upper limit of 7 km for the maximum continuous alongshore distance eroding or accreting. For the same section of coast, we find upper limits of 25 m for the maximum shore-perpendicular erosion and 11 m for the maximum shore-perpendicular accretion during the study period.

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Power-law Scaling and Probabilistic Forecasting of Tsunami Runup Heights

Burroughs

Tebbens

2005

Pure appl. geophys.

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A power-law scaling relationship describes tsunami runup heights at ten locations in Japan. Knowledge of the scaling law for tsunamis can be the basis for probabilistic forecasting of the size and number of future events and for estimating probabilities of extremely large events. Using tsunami runup data archived by the U.S. National Geophysical Data Center, we study ten locations where the tsunami record spans at least one order of magnitude in runup height and the temporal record extends back several decades. A power law or upper-truncated power law describes the cumulative frequency-size distribution of tsunami runup heights at all ten locations. Where the record is sufficient to examine shorter time intervals within the record, the scaling relationship for the shorter time intervals is consistent with the scaling relationship for the entire record. The scaling relationship is used to determine recurrence intervals for tsunami runup heights at each location. In addition to the tsunami record used to determine the scaling relationship, at some of the locations a record of large events (>5 m) extends back several centuries. We find that the recurrence intervals of these large events are consistent with the frequency predicted from the more recent record. For tsunami prone locations where a scaling relationship is determined, the predicted recurrence intervals may be useful for planning by coastal engineers and emergency management agencies.

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Statistical self‐similarity of hotspot seamount volumes modeled as self‐similar criticality

Cited by 10 publications

References 20 publications

A Non-Extensive Statistical Mechanics View on Easter Island Seamounts Volume Distribution

A Non-Extensive Statistical Mechanics View on Easter Island Seamounts Volume Distribution

Wavelet analysis of shoreline change on the Outer Banks of North Carolina: An example of complexity in the marine sciences

Power-law Scaling and Probabilistic Forecasting of Tsunami Runup Heights

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