Presentation by Nicholas van der Elst
The power of positive statistics: extracting complete seismicity models from incomplete catalogs
Abstract:
Earthquake catalogs provide the core data of statistical seismology but are typically incomplete records of the earthquakes that occur. Incomplete detection results from sparse network coverage and saturation of the network during periods of high activity. Robust statistics require a catalog completeness model, but these models are non-unique and introduce additional uncertainty.
Here I present a framework for statistical seismology that focuses on the intervals between pairs of earthquakes where the second is larger than the first. This approach replaces the assumption of uniform completeness with the softer assumption that completeness is non-decreasing in the quiet periods between any two earthquakes. Each detected earthquake provides a reference time and magnitude above which we are likely to detect a subsequent earthquake. By restricting our measurements to the ‘next larger earthquake’ we get a population that is virtually immune to incompleteness bias.
Positive statistics open a window into the first moments of an aftershock sequence, where the magnitude and temporal distributions of the aftershocks may encode the stress conditions and perhaps give clues to how the sequence will play out. Unbiased rate measurements show 1/t rate scaling down to the time of the earliest recorded aftershocks (Omori parameter c ~ 0), with implications for the distribution of fault strength and proximity to failure under rate-state friction. Unbiased magnitude statistics show that the b-value evolves with time over some aftershock sequences, leaving them ‘front-loaded’ with large aftershocks (or foreshocks). The data suggest that both aftershock size and timing may be influenced by the local stress to strength ratio, with implications for forecasting in the first hours and days of a sequence.
Zoom link:
https://columbiauniversity.zoom.us/j/96846952250?pwd=X8VYhnMcGBLfFj2r7Glzs5a3gsRmsa.1
