WHEN IS SPATIOTEMPORAL COINCIDENCE PURELY COINCIDENTAL? ESTABLISHING THE STATISTICAL SIGNIFICANCE OF OVERLAP BETWEEN GEOLOGIC PHENOMENA

Spatiotemporal coincidence, the overlap between two phenomena in space and time, is a critical observation used to infer causal relationships between lithospheric processes in both the rock record and active systems. For example, the broad association between magmatism and upper-plate deformation in convergent margins has inspired causal models of direct tectonomagmatic links in arcs. However, only rarely has the spatiotemporal correlation of the patterns of geologic phenomena been rigorously demonstrated. Although a statistically significant overlap is a prerequisite for such models, correlation alone cannot necessitate the operation of direct tectonomagmatic links. Classic problems in geometric probability such as Buffon’s Needle indicate that uncorrelated phenomena can intersect at some frequency by random chance alone. Geometric probability can be applied to determine a null hypothesis for spatiotemporal coincidence: an overlap frequency threshold that observations must deviate from to demonstrate that two phenomena are correlated in space and/or time.

A new reconstruction of mid-Cretaceous tectonism in the central Sierra Nevada (CA, USA) coeval with voluminous arc activity shows no consistent overlap in the spatiotemporal patterns of intra-arc deformation and magmatism. Contrary to previous influential models, many of which were developed in the study area, central Sierra arc magmatism did not control the location, intensity, or kinematics of deformation, nor vice versa. To further quantify the significance of overlap between shear zones and intrusions, I compare estimated coincidence frequencies for these features to a simplified geometric probability model based on Buffon’s Needle. The estimated frequency of overlap between these features is consistent with the predicted frequency of random coincidence between uncorrelated phenomena. Analogue models using paper and paint splatter are used to further illustrate the importance of this geostatistical perspective. These analogue demonstrations show that rigorously establishing spatiotemporal correlations between geologic phenomena requires both an appropriate extent and scale of observation before such correlations can be used to infer causative relationships between underlying lithospheric processes.