Magnitude correlations and criticality in a self-similar model of seismicity

We present an analysis of the statistical relation between subsequent magnitudes for a previously proposed self-similar aftershock rates model of seismicity whose main distinguishing feature arises as a consequence of the dependency of the rates on the magnitude difference between trigger-triggered events. By means of a particular statistical measure we studied the level of magnitude correlations among time-ordered subsequent events for various magnitude thresholds under specific types of time conditioning, explained their provenance through the model and found that the type of null model chosen in the analysis plays a pivotal role in the type of observed correlations. With particular time conditioning between subsequent events, we also analyzed and compared a model catalog to data from Southern California (SC), and found that model and real-world catalogues are consistent with each other within our statistical measure. When comparing a culled SC and the corresponding culled model catalogue under a specific type of time conditioning and magnitude thresholds, correlations do not significantly deviate from zero for the model but are present in the subset SC catalogue; these observed correlations in the SC catalogue we attributed to a process where a fraction of events are missed in the seismic recordings. The former was substantiated when we looked at the culled SC catalog for higher magnitude thresholds and saw no significant correlations, although the amount of data for this already shortened catalog is relatively low. By creating synthetic catalogues between 2 − 26 times the culled model catalogue, we estimated the length of a catalogue needed to begin to observe magnitude correlations at 3σ to be ∼ 15 times the current culled model catalogue ( ∼ 150 years worth of data) while the existence of magnitude correlations can be used in earthquake forecasting, only the time variations in the frequency-magnitude distribution might lead to a significant improvement in forecasting. We also studied the criticality of the self-similar model from the perspective of finite size effects through the introduction of an upper magnitude cut-off in the analysis and established that the model lies in the sub-critical regime for the SC parameters.

Name thesis:degree_name

Master of Science (MSc)

Discipline thesis:degree_discipline

Physics & Astronomy

Grantor dc:publisher.institution

Science

Year dc:date.issued

2019

Author dc:creator

• Zambrano Moreno, Andres Felipe

Advisor dc:contributor.advisor

• Davidsen, Jörn

Committee members dc:contributor.committeemember

• Hobill, David W.
• Jackel, Brian J.
• Dettmer, Jan
• Simon, Ch M.

• Emergence
• Seismicity
• Self-similarity

Licence dc:rights.uri

• https://creativecommons.org/share-your-work/public-domain/cc0

DOI

http://dx.doi.org/10.11575/PRISM/36425

OAI identifier oai:identifier

oai:ucalgary.scholaris.ca:1880/110243