Generalized earthquake frequency-magnitude distribution described by asymmetric Laplace mixture modelling

Mignan, A.1,2

2019-11

10.1093/gji/ggz373

GEOPHYSICAL JOURNAL INTERNATIONAL   影响因子和分区

0956-540X

1365-246X

The complete part of the earthquake frequency-magnitude distribution, above the completeness magnitude m(c), is well described by the Gutenberg-Richter law. On the other hand, incomplete data does not follow any specific law, since the shape of the frequency-magnitude distribution below max(m(c)) is function of m(c) heterogeneities that depend on the seismic network spatiotemporal configuration. This paper attempts to solve this problem by presenting an asymmetric Laplace mixture model, defined as the weighted sum of Laplace (or double exponential) distribution components of constant m(c), where the inverse scale parameter of the exponential function is the detection parameter. below m(c), and the Gutenberg-Richter beta-value above m(c). Using a variant of the Expectation-Maximization algorithm, the mixture model confirms the ontology proposed by Mignan [2012, https://doi.org/10.1029/2012JB009347], which states that the shape of the earthquake frequency-magnitude distribution shifts from angular (in log-linear space) in a homogeneous space-time volume of constant m(c) to rounded in a heterogeneous volume corresponding to the union of smaller homogeneous volumes. The performance of the proposed mixture model is analysed, with encouraging results obtained in simulations and in eight real earthquake catalogues that represent different seismic network spatial configurations. We find that k = kappa/ln(10) approximate to 3 in most earthquake catalogues (compared to b = beta/ln(10) approximate to 1), suggesting a common detection capability of different seismic networks. Although simpler algorithms may be preferred on pragmatic grounds to estimate m(c) and the b-value, other methods so far fail to model the angular distributions observed in homogeneous space-time volumes. Mixture modelling is a promising strategy to model the full earthquake magnitude range, hence potentially increasing seismicity data availability tenfold, since ca. 90 per cent of earthquake catalogue events are below max(m(c)).

Probability distributions Statistical methods Statistical seismology

SCI ; EI

英语

通讯

Geochemistry & Geophysics

Geochemistry & Geophysics

WOS:000491050200044

OXFORD UNIV PRESS

20194207552671

Angular distribution ; Exponential functions ; Image segmentation ; Inverse problems ; Laplace transforms ; Maximum principle ; Mixtures ; Probability distributions ; Scales (weighing instruments) ; Statistical methods

Seismology:484 ; Mathematics:921 ; Mathematical Transformations:921.3 ; Probability Theory:922.1 ; Mathematical Statistics:922.2 ; Special Purpose Instruments:943.3

GEOSCIENCES

Web of Science

1.Swiss Fed Inst Technol, Sonneggstr 5, CH-8092 Zurich, Switzerland
2.Southern Univ Sci & Technol, Acad Adv Interdisciplinary Studies, Inst Risk Anal Predict & Management, Shenzhen 518055, Peoples R China

Mignan, A.. Generalized earthquake frequency-magnitude distribution described by asymmetric Laplace mixture modelling[J]. GEOPHYSICAL JOURNAL INTERNATIONAL,2019,219(2):1348-1364.

Mignan, A..(2019).Generalized earthquake frequency-magnitude distribution described by asymmetric Laplace mixture modelling.GEOPHYSICAL JOURNAL INTERNATIONAL,219(2),1348-1364.

Mignan, A.."Generalized earthquake frequency-magnitude distribution described by asymmetric Laplace mixture modelling".GEOPHYSICAL JOURNAL INTERNATIONAL 219.2(2019):1348-1364.