Practical exercises

Some structural geological exercises performed by geologists are presented in this chapter. Many of the practical problems are related to the orientation of planes, lines or principal stress directions. We have chosen to pay particular attention to the Mohr circle, used for analysing stress as well as strain, and to the use of orientation diagrams that allow the geologist to visualize structural data in 3D. Fractured outcrops and seismological data are presented under the form of exercises that help the geologist to document the state of stress associated with past or present geodynamic processes. The chapter ends with a very classic exercise based on the principle of Archimedes.

Inferring rheology and geometry of subsurface structures by adjoint-based inversion of principal stress directions

SUMMARY Imaging subsurface structures, such as salt domes, magma reservoirs or subducting plates, is a major challenge in geophysics. Seismic imaging methods are, so far, the most precise methods to open a window into the Earth. However, the methods may not yield the exact depth or size of the imaged feature and may become distorted by phenomena such as seismic anisotropy, fluid flow, or compositional variations. A useful complementary method is therefore to simulate the mechanical behaviour of rocks on large timescales, and compare model predictions with observations. Recent studies have used the (non-linear) Stokes equations and geometries from seismic studies in combination with an adjoint-based approach to invert for rheological parameters that are consistent with surface observations such as GPS velocities. Nevertheless, it would be useful to use other surface observations, such as principal stress directions, as constraints as well. Here, we derive the adjoint formulation for the case that principal stress directions are used as observables with respect to rheological parameters. Both an algebraic and a discretized derivation of the adjoint equations are described. This thus enables the usage of two data fields - surface velocities and stress directions - as a misfit for the inversion. We test the performance of the inversion for principal stress directions on simplified 3-D test cases. Finally, we demonstrate how the adjoint approach can be used to compute 3-D geodynamic sensitivity kernels, which highlight the areas in the model domain that have the largest impact on the misfit value of a particular point. This provides a simple, yet powerful, way to visualize which parts of the model domain are of key importance if changing rheological constants.

Time-Dependent Stresses From Fluid Extraction and Diffusion With Applications to Induced Seismicity

Over recent decades, it has become clear that the extraction of fluids from underground reservoirs can be linked to seismicity and aseismic deformation around producing fields. Using a simple model with uniform fluid extraction from a reservoir, Segall (1989, “Earthquakes Triggered by Fluid Extraction,” Geology, 17(10), pp. 942–946) illustrated how poroelastic stresses resulting from fluid withdrawal may be consistent with earthquake focal mechanisms surrounding some producing fields. Since these stress fields depend on the spatial gradient of the change in pore fluid content within the reservoir, both quantitative and qualitative predictions of the stress changes surrounding a reservoir may be considerably affected by assumptions in the geometry and hydraulic properties of the producing zone. Here, we expand upon the work of Segall (1989, “Earthquakes Triggered by Fluid Extraction,” Geology, 17, pp. 942–946 and 1985, “Stress and Subsidence Resulting From Subsurface Fluid Withdrawal in the Epicentral Region of the 1983 Coalinga Earthquake,” J. Geophys. Res. Solid Earth, 90, pp. 6801–6816) to provide a quantitative analysis of the surrounding stresses resulting from fluid extraction and diffusion in a horizontal reservoir. In particular, when considering the diffusion of fluids, the spatial pattern and magnitude of imposed stresses is controlled by the ratio between the volumetric rate of fluid extraction and the reservoir diffusivity. Moreover, the effective reservoir length expands over time along with the diffusion front, predicting a time-dependent rotation of the induced principal stresses from relative tension to compression along the ends of the producing zone. This reversal in perturbed principal stress directions may manifest as a rotation in earthquake focal mechanisms or varied sensitivity to poroelastic triggering, depending upon the criticality of the pre-existing stress state and fault orientations, which may explain inferred rotations in principal stress directions associated with some induced seismicity.

Influence of inherited structural domains and their particular strain distributions on the Roer Valley Graben evolution from inversion to extension

After their first development in the middle Mesozoic, the overall NW-SE striking border fault systems of the Roer Valley Graben were reactivated as reverse faults under Late Cretaceous compression (inversion) and reactivated again as normal faults under Cenozoic extension. In Flanders (northern Belgium), a new geological model was created for the western border fault system of the Roer Valley Graben. After carefully evaluating the new geological model, this study shows the presence of two structural domains in this fault system with distinctly different strain distributions during both Late Cretaceous compression and Cenozoic extension. A southern domain is characterized by narrow ( 10 km) distributed faulting. The total normal and reverse throw in the two domains was estimated to be similar during both tectonic phases. The repeated similarities in strain distribution during both compression and extension stresses the importance of inherited structural domains on the inversion/rifting kinematics besides more obvious factors such as stress directions. The faults in both domains strike NW-SE, but the change in geometry between them takes place across the oblique WNW-ESE striking Grote Brogel fault. Also in other parts of the Roer Valley Graben, WNW-ESE striking faults are associated with major geometrical changes (left-stepping patterns) in its border fault system. This study thereby demonstrates the presence of different long-lived structural domains in the Roer Valley Graben, each having their particular strain distributions that are related to the presence of non-colinear faults.