In volcano-tectonic regions, dyke propagation from shallow magmatic chambers is often controlled by the interaction of the local and regional stress fields. The variations of the stress fields result from a combination of factors including the regional tectonic stress, the geometry of pressurized magma chambers, the layering and the pre-existing discontinuities (e.g. fractures). In this contribution, we describe and apply a new multiparametric inversion technique based on geomechanics that can invert for both the far field stress attributes and the internal pressure of magma chambers or stocks, constrained by observed dyke or eruptive fissure orientations. This technique is based on the superposition principle and uses linear elastic models that can be solved using many types of numerical methods. For practical reasons, we chose a 3D boundary element method (BEM) for a heterogeneous elastic half-space, where magma chambers are modelled as pressurized cavities. To verify this approach, the BEM solution has been validated against the known 3D analytical solution of a pressurized cylindrical cavity. Then the effectiveness of this technique and its practical use is demonstrated through application to natural examples of dyke network development around two different volcanic systems, the Spanish Peaks (USA) and the Galapagos Islands (Ecuador). Results demonstrate that regional stress characteristics as well as the internal pressure of magma chambers can be estimated from observed radial and circumferential dyke patterns and some knowledge of magma chamber geometry.

The Franconian Platform of SE Germany and the underlying Permian and Triassic rocks that developed from latest Permian to Triassic time were affected by multiple compressional and extensional events that created a complex fracture, fault and stylolite network. We reconstructed the spatio-temporal variations of post-Triassic palaeostress fields in the Franconian Platform and Triassic strata using fault-slip and tectonic stylolite inversion. Our highly resolved stress inversion enables us to demonstrate a cyclic stress evolution from the stress regime of normal faulting to thrusting, strike-slip and back to normal faulting. Five main stress fields correlating with two stress cycles are determined for Late Jurassic to Cenozoic time. The first cycle consists of: (SF1) an initially NE–SW-directed horizontal extension during Late Jurassic to Early Cretaceous time; (SF2) NNE–SSW-directed horizontal compression with an early set of tectonic stylolites prior to the development of reverse and thrust faults; and (SF3) a strike-slip-dominated setting with (N)NE–(S)SW horizontal compression representing a first relaxation. The second cycle comprises (SF4) NW–SE-directed horizontal extension during Oligocene–Miocene time; and (SF5) a second strike-slip-dominated regime with WNW–ESE to NW–SE horizontal compression during the Alpine shortening, creating the youngest set of tectonic stylolites. In addition, we consider the transitional stages between thrusting and a strike-slip regime as a snapshot in the process of intraplate tectonics.

The Fanshi Basin is one of the NE–SW-striking depocentres formed along the northern segment of the fault-bounded Shanxi rift. In order to understand the crustal driving stresses that led to the basin formation and development, a palaeostress analysis of a large quantity of fault-slip data collected mainly at the boundaries of the basin was accomplished. The stress inversion of these data revealed three stress regimes. The oldest SR1 was a Neogene stress regime giving rise to a strike-slip deformation with NE–SW contraction and NW–SE extension. SR1 activated the large faults trending NNE–NE, i.e. (sub)parallel to the main strike of the Shanxi rift, as right-lateral strike-slip faults. It was subjected to the Shanxi rift before the activation of the Fanshi Basin boundary fault, i.e. the Fanshi (or Wutai) fault, as a normal fault. The next is a short-lived NE–SW extensional stress regime SR2 in early Pleistocene time, which shows the inception of the basin’s extension. A strong NW–SE to NNW–SSE extensional stress regime SR3 has governed the northern segment of the Shanxi rift since late Pleistocene time and is the present-day extension. It gave rise to the current half-graben geometry of the Fanshi Basin by activating the Fanshi (or Wutai) fault as a normal fault in the southern part of the graben. Because of the dominance of the NW–SE to NNW–SSE extension, which is perpendicular to the NE–SW extension, mutual permutations between σ3 and σ2 due to inherited fault patterns might have occurred while the crustal stresses in the Fanshi Basin changed from the SR1 to SR3 stress regimes.