Abstract - One of E.M. Anderson’s major contributions to geology was his numerical analysis of stresses induced by inflating and deflating sub-surface bodies such as magma reservoirs. This analysis led to still-widely cited explanations for different types of sub-volcanic intrusion, such as cone-sheets and ring-dykes. Ring-dykes are steeply-inclined arcuate sheet-intrusions whose emplacement occurs along ring-fractures of tensile and/or shear mode in the overlying roof. Anderson predicted that ring-fractures initially formed during reservoir deflation should be inclined outward from the centre of the magma reservoir roof, as a consequence of similarly-inclined maximum compressive stress trajectories. These ring-fractures accommodate initial subsidence of the reservoir roof and, potentially, the formation of a volcanic depression at the Earth’s surface. This process was termed “cauldron subsidence” and is today usually known as caldera subsidence.
At many calderas, however, ring fractures accommodating caldera subsidence are observed to dip inward rather than outward. This has led to the formulation of alternative numerical analyses of reservoir deflation that predict initial roof failure along inward-dipping ring-fractures, and even to the suggestion of mechanisms for caldera subsidence other than reservoir deflation. These alternative numerical analyses conflict with evidence from analogue models of caldera subsidence which predict the initial occurrence of outward dipping ring faults and later appearance of inward dipping ring faults. More recently, direct observation of small-scale caldera collapses has strongly supported the analogue model evidence. Since we attribute the uncertainties in numerical predictions for ring fault orientation to their inability to reproduce the large discontinuous strains typical of caldera subsidence, we have used the Distinct Element Method (DEM) software, PFC-2D, to create numerical models that explicitly replicate reservoir deflation and associated gravity-driven failure and subsidence of a reservoir roof.
Our models show that generally, and in broad agreement with Anderson’s predictions, the ring fractures causing ultimate failure of the roof are outward-inclined. Inward-inclined fractures also form, however, as observed in analogue models and nature. The DEM models produce several ‘end-member’ structural styles of subsidence, although individual model realizations typically display some aspects of different ‘end-members’. Our models show how certain geometric and material properties interact to produce different styles of subsidence. Strength (cohesion) and the thickness/diameter ratio of the roof exert the strongest influences, whilst the roof’s Young’s Modulus and the reservoir’s shape impart secondary influences. The model results include some structural forms that match the classic concepts of cauldron subsidence as predicted by Anderson and fellow workers, but also other forms that differ markedly. Our results provide new quantitative perspectives on the genesis of caldera subsidence structures and the extent to which related faulting conforms to predictions of Andersonian stress analysis, as a function of geometric and material properties.
Abstract of talk given to:
Anderson Conference: Stress controls on faulting, fracturing and igneous intrusion in the Earth's crust, Glasgow, Scotland, September 2010.