Rashomon at the Sound

This is a presentation I gave last week at the Crescent Annual Meeting in Seattle. Thanks to my coauthor Brian Sherrod.

This is the latest installment of a sort of hobby project I've been working on with Brian over the past decade or so. My goal here is to try to think broadly about what paleoseismic data really represent and how they can be interpreted in a larger context---moving outside the trench.

The idea of relating geological data topologically has been gestating in my head for a long time, and to me is perhaps the most compelling part of the analysis. Geological data are often sequential, with an explicit ordering for some set of data that may be otherwise floating in its context. Stratigraphy at a spatial point is basically purely this---the relative ages of the beds and cross-cutting relationships displayed in the outcrop (be they structural, erosional or intrusive) are well defined (and given good exposure, can be exact and unambiguous); the absolute ages of anything are rarely well known, and time for any specific feature to form is as often as not a time span more than a moment. Geology is based around these relative ages. The nature of these relationships continues across space, but correlations are often hard to make and ambiguous, leading to multiple competing interpretations.

The structure of these relationships is topological. It can be defined as a graph, because rock units that are in contact are adjacent; the entire edifice is the collection of the units and their relations (contact types or relative ages or whatever) with adjacent units. If we want to think about events (deposition, faulting, individual earthquakes) this still applies---the connections of the rock unit graph (the edges) become the vertices of the event graph.

Dealing with ambiguous correlations, or events, or whatever is tricky. This means that there are multiple competing, mutually--exclusive graphs, or that there is some other format (like probabilistic connectivity) that needs to be used. Enumerating the possibilities from even a small graph with probabilistic connections leads to a combinatoric chain reaction, a meltdown. It is interesting that the probabilistic connections are not independent---that one connection means that some others are feasible and some are not.

Given the ubiquity of graphs in modern mathematics and computer science, and therefore in the technological air that we breathe, I'm sure that the sorts of problems that I'm encountering have been dealt with many times before---probably every time my phone connects to a website or I get a route planned with google maps. So figuring out how to solve any given problem is really about figuring out exactly what I want the solution to look like---a single best fit, or ruling out some possibilities, or something probabilistic and perhaps Bayesian.

We'll see where it goes! Maybe nowhere as it's not really my 9--5 right now. Perhaps that is really dependent on figuring out what can be meaningfully or gainfully extracted from this web of possibilities.