Many regions in the world are protected against flooding by a dike, which may be either natural or artificial. We deal with a model for finding the optimal heights of such a dike in the future. It minimizes the sum of the investments costs for upgrading the dike in the future and the expected costs due to flooding. The model is highly nonlinear, nonconvex, and infinite-dimensional. Despite this...

Diamonds formed during the Proterozoic and Archaean and are in-homogenously distributed in the mantle below Archaean cratons. Kimberlite magmas usually form well within the diamond stability field and physically incorporate seemingly random amounts of diamonds during their ascent through the mantle. The diamond content of a kimberlite magma arriving at the earth’s surface is defined by ascent p...

In March 1996 an intense swarm of volcano-tectonic earthquakes (-3000 felt by local residents, A/max5.1, cumulative moment of 2.7 x 10 •8 N m) beneath Akutan Island in the Aleutian volcanic arc, Alaska, produced extensive ground cracks but no eruption of Akutan volcano. Synthetic aperture radar interferograms that span the time of the swarm reveal complex island-wide deformation: the western pa...

In order to assess the age relations between astra/novae (features with extensive radial fracture-graben systems) and their surroundings, and to determine the duration of their activity, we undertook a photogeologic analysis of Magellan images of 78 astra, 49 dark-parabola craters and 114 clear-halo craters. For seven of these 78 astra it was found that the astrum-forming faulting started befor...

Dike height optimization is of major importance to the Netherlands as a large part of the country lies below sea level and high water levels in rivers can cause floods. A cost-benefit analysis is discussed in Eijgenraam et al. (2010), which is an improvement of the model Van Dantzig (1956) introduced after a devastating flood in the Netherlands in 1953. We consider the extension of this model t...

[1] Large‐scale mass wasting is a natural part of the evolution of volcanic islands, where deformation and indications of flank instability, such as large‐scale faulting and seismic and aseismic slip are common. The Cumbre Vieja volcano on the island of La Palma (Canary Islands) provides an ideal setting to address fundamental questions about the structure, evolution and stability of island vol...

Pseudotachylyte, a fault rock formed through coseismic frictional melting, provides an important record of coseismic mechanics. In particular, injection veins formed at a high angle to the fault surface have been used to estimate rupture directivity, velocity, pulse length, stress and strength drop, as well as slip weakening distance and wall rock sti ness. These studies, however, have generall...

Sahagian et al. (2002a, 2002b) have developed a methodology for determining paleoelevations of highlands using observed vesicularities of lava flows. Since vesicular lavas preserve a record of paleoatmospheric pressure during the time of emplacement, they can be used to directly infer paleoelevations. Their model could act as a powerful tool, particularly in view of the uncertainties induced by...

Felsic magma commonly pools within shallow mushroom-shaped magmatic intrusions, so-called laccoliths or cryptodomes, which can cause both explosive eruptions and collapse of the volcanic edifice. Deformation during laccolith emplacement is primarily considered to occur in the host rock. However, shallowly emplaced laccoliths (cryptodomes) show extensive internal deformation. While deformation o...