S U M M A R YDisplacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space R 3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.Key words: Geomechanics; Kinematics of crustal and mantle deformation.
I N T RO D U C T I O NCrustal deformations associated with earthquakes, volcanoes, landslides and human activities can be observed at a high level of detail using modern geodetic techniques, including synthetic aperture radar interferometry (InSAR) and GPS (Segall 1997;Bürgmann et al. 2000). These deformation data are often analysed using modelling techniques that are typically very computationally intense. The primary objective of such modelling is to understand the underlying processes through indirect imaging of the so-called sources, such as seismogenic faults, magma chambers and other reservoirs. The position and geometry of these sources, as well as the slip or the forces acting on them, are typically regarded as the source parameters. The source parameters, in other words, the outputs of the implemented modelling, are relevant to earthquake aftershock studies, the assessment of volcanic eruption precursors, tsunami modelling and many other applications (Feigl et al. 2002).The majority of methods that are applied for crustal deformation modelling are based on the theory of elasticity in general and the concept of dislocations in particular (Segall 2010). Elastic dislocation theory concerns the state of deformations in a strained solid body that is subject to the action of a dislocation embedded inside it (Love 1944). The Volterra model (Volterra 1907) describes a dislocation as a surface of displacement discontinuity with a uniform distribution of the slip throughout. The edges of the Volterra dislocation, also known as ...