Statistical Variability and Tokunaga Branching of Aftershock Sequences Utilizing BASS Model Simulations

Yoder, Mark R.; Aalsburg, J. van; Turcotte, Donald L.; Abaimov, Sergey G.; Rundle, John B.

doi:10.1007/s00024-011-0411-2

Cited by 15 publications

(10 citation statements)

References 53 publications

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“…The Tokunaga model (2) completely specifies a combinatorial tree shape (up to a permutation of side branch attachment within a given branch) with only two parameters (a, c), hence suggesting a conventional modeling paradigm. The empirical validity of the Tokunaga constraints (2) has been strongly confirmed for a variety of river networks at different geographic locations [10,[35][36][37][38], as well as in other types of data represented by trees, including botanical trees [39], the veins of botanical leaves [26,27], clusters of dynamically limited aggregation [39,40], percolation and forest-fire model clusters [41,42], earthquake aftershock sequences [14,15,19], tree representation of symmetric random walks [43], and hierarchical clustering [44]. The conditions (2), however, lack a theoretical justification.…”

Section: Introductionmentioning

confidence: 88%

“…Tree-shaped fractal formations, from the namesake botanical trees to river tributary networks to the systems of canyons and mountain crests that define the Earth topography, have always fascinated the great minds (e.g., [1]) providing inspiration in science, art, and architecture [2,3]. A quantitative understanding of the branching patterns is instrumental in hydrology [4][5][6][7][8][9], geomorphology [10,11], statistical seismology [12][13][14][15][16][17][18][19], statistical physics of fracture [20][21][22], vascular analysis [23], brain studies [24], ecology [25], biology [26], and beyond, en-couraging further rigorous treatment. This study establishes equivalence between the Tokunaga self-similaritya widely recognized algebraic parameterization of a selfsimilar tree -and a measure-theoretic invariance of a tree distribution with respect to a depth shift.…”

Section: Introductionmentioning

confidence: 99%

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Tokunaga self-similarity arises naturally from time invariance

Kovchegov

Zaliapin

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The Tokunaga condition is an algebraic rule that provides a detailed description of the branching structure in a self-similar tree. Despite a solid empirical validation and practical convenience, the Tokunaga condition lacks a theoretical justification. Such a justification is suggested in this work. We define a geometric branching processes G(s) that generates self-similar rooted trees. The main result establishes the equivalence between the invariance of G(s) with respect to a time shift and a one-parametric version of the Tokunaga condition. In the parameter region where the process satisfies the Tokunaga condition (and hence is time invariant), G(s) enjoys many of the symmetries observed in a critical binary Galton-Watson branching process and reproduce the latter for a particular parameter value.

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Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Tokunaga self-similarity arises naturally from time invariance

Kovchegov

Zaliapin

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In this case, the magnitude of the main shock of the Northridge sequence, 6.69, is taken as m p for the first generation of aftershocks and m min is taken as 4.5, which is the rounded lowest magnitude of the ground motions in the database used to calibrate the prediction equations in Section 4. According to the literature, typical values for California are selected for the empirical parameters in Equations to ( b d = 1, ∆m * = 1.3, τ 0 = 0.001 day, p = 1.25, d = 4 m, q = 1.35). V S30 is assumed to be 326.19 m/second according to PEER NGA‐West2 database .…”

Section: Example: a Replay Of 1994 Northridge Ms‐as Sequencementioning

confidence: 99%

“…Aftershock sequences of earthquake characteristics (ie, locations, times, and magnitudes) can be generated using the BASS model developed by Turcotte et al In the BASS model, a main shock acts as a seed and triggers first‐generation (or primary) aftershocks. Each first‐generation aftershock can also act as a seed and trigger second‐generation aftershocks and so forth.…”

Section: Model To Generate Aftershock Sequences Of Earthquake Charactmentioning

confidence: 99%

Stochastic procedure for the simulation of synthetic main shock‐aftershock ground motion sequences

Gardoni

2018

Earthq Engng Struct Dyn

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Summary According to the current seismic codes, structures are designed to resist the first damaging earthquake during their service life. However, after a strong main shock, a structure may still face damaging aftershocks. The main shock‐aftershock sequence may result in major damage and eventually the collapse of a structure. Current studies on seismic hazard mainly focus on the modeling and simulation of main shocks. This paper proposes a 3‐step procedure to generate main shock‐aftershock sequences of pairs of horizontal components of a ground motion at a site of interest. The first step generates ground motions for the main shock using either a source‐based or site‐based model. The second step generates sequences of aftershocks' magnitudes, locations, and times of occurrence using either a fault‐based or seismicity‐based model. The third step simulates pairs of ground motion components using a new empirical model proposed in this paper. We develop prediction equations for the controlling parameters of a ground motion model, where the predictors are the site condition and the aftershock characteristics from the second step. The coefficients in the prediction equations and the correlation between the model parameters (of the 2 horizontal components of 1 record and of several records in 1 sequence) are estimated using a database of aftershock accelerograms. A backward stepwise deletion method is used to simplify the initial candidate prediction equations and avoid overfitting the data. The procedure, based on easily identifiable engineering parameters, is a useful tool to incorporate effects of aftershocks into seismic analysis and design.

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“…In addition, BASS simulations generate aftershock statistics in agreement with simulations (Yoder et al, 2013). The BASS model limit eliminates the dependence on a specified minimum magnitude aftershock m min .…”

Section: Epidemic-type Aftershock Sequence Modelsmentioning

confidence: 99%