F.H. Cornet

Effects of topography on the interpretation of the deformation field of prominent volcanoes—Application to Etna

We have investigated the effects of topography on the surface-deformation field of volcanoes. Our study provides limits to the use of classical half-space models. Considering axisymmetrical volcanoes, we show that interpreting ground-surface displacements with half-space models can lead to erroneous estimations of the shape of the deformation source. When the average slope of the flanks of a volcano exceeds 20°, tilting in the summit area is reversed to that expected for a flat surface. Thus, neglecting topography may lead to misinterpreting an inflation of the source as a deflation. Comparisons of Mogis model with a three-dimensional model shows that ignoring topography may lead to an overestimate of the source-volume change by as much as 50% for a slope of 30°. This comparison also shows that the depths calculated by using Mogis solution for prominent volcanoes should be considered as depths from the summit of the edifices. Finally, we illustrate these topographic effects by analyzing the deformation field measured by radar interferometry at Mount Etna during its 1991–1993 eruption. A three-dimensional modeling calculation shows that the flattening of the deflation field near the volcanos summit is probably a topographic effect.

Collection and three‐dimensional modeling of GPS and tilt data at Merapi volcano, Java

We study here the deformations associated with the November 1996 to March 1997 eruption period at Mount Merapi (Central Java), one of the most active volcanoes in Indonesia. This activity period includes a vertical explosion on January 17 and an increase of the lava dome volume by about 3×106 m3. Two Global Positioning System (GPS) campaigns have been carried out on a six-benchmark network at the beginning and at the end of the period. Relative displacements with respect to the reference point show an average subsidence of 6.5 cm. A multicomponent tilt station installed on the southeast flank, 3 km from the summit, recorded a tilt of 11.1 ± 0.7 μrad in the tangential direction and 0.9 ± 0.4 μrad in the radial direction. These data are interpreted using a three-dimensional (3-D) elastic model based on the mixed boundary element method and a near-neighbor Monte Carlo inversion. Interpretation of tilt data requires an accurate mesh for discretizing the 3-D topography. The final result supports a horizontal elliptic magma source located 8.5 ± 0.4 km below the summit and 2 ± 0.4 km to the east of it. In particular, the data cannot be consistent with the location of a magma chamber determined from seismic activity analysis (i.e., 2 km below the summit). The computed depth depends strongly on the source shape and cannot be constrained properly because of the small amount of data. The computed deflation of 11 ± 2×106 m3 is about 3 times larger than the observed increase in the lava dome volume. This difference is attributed to rock avalanches and pyroclastic flows on the flanks of the volcano.

Three‐dimensional modeling of the 1983–1984 eruption at Piton de la Fournaise Volcano, Réunion Island

Displacement vectors on 125 points over a 6-km 2 area were calculated [Zlotnicki et al., 1990] for Piton de la Fournaise volcano, Reunion Island, from photogrammetric surveys conducted in September 1981 and again in September 1984. An eruptive crisis with two episodes occurred during the 3 years between the surveys. We modeled the displacements from the photogrammetric surveys using a three-dimensional mixed boundary element method. The model shows that both eruptive episodes were fed by a single dike oriented 165° from north. As the dike approached the ground surface, it divided into segments that rotated into an en echelon pattern. The model that best fits all observations suggests that the stress state within the volcano is quasi-isotropic such that horizontal stresses equal the overburden. These high horizontal stresses are incompatible with an elastic edifice loaded merely by gravitational forces. However, they may be attributed to the cumulative effect of repeated dike intrusions.

Evidence of thermally induced borehole elongation: a case study at Soultz, France

Abstract When they occur, borehole breakouts are considered strong markers of principal stress directions at depth. An innovative processing method for automatically identifying breakouts from ultrasonic borehole wall images has been developed. It has been applied to data sets from two deep, sub-vertical wells (GPK1 and GPK2) at the Soultz geothermal site in eastern France. In well GPK1, below 3 km depth, compression breakouts, with a 95°±7° azimuth, increasingly occur with depth. They result from time dependent compression failure at sub-critical stress levels and are indicators of the minimum horizontal principal stress orientation. However, in the uppermost logged section of well GPK2 (1.6– 2.9 km depth), continuous borehole elongations share roughly the same azimuth with so called drilling-induced fractures (164°±18° and 175°±17° azimuth, respectively). Both features concomitantly vanish with depth, together with the amplitude of the thermal perturbation induced by drilling. It is proposed that these latter borehole elongations result from a pervasive, cooling-induced, tensile micro-cracking process prior to macroscopic failure localization. They are termed thermal elongations and are indicators of the maximum horizontal principal stress orientation. Had a simple logging caliper tool been used for this work, these thermal elongations might have been confused with classical compression breakouts. A simple criterion for differentiating compression breakouts from thermal elongation is proposed.

15 – The HTPF and the Integrated Stress Determination Methods

Publisher Summary The applicability of the hydraulic fracturing stress determination method is dependent on the validity of a few constraining conditions: (1) the borehole must be parallel to a principal stress direction; (2) the rock must exhibit a linearly isotropic elastic response up to fracture initiation; and (3) the tensile strength of the rock must be isotropic. The interstitial fluid pressure field is axisymmetric with respect to the borehole axis and that its influence on both the stress field and on the fracturing process is properly taken into account. The Hydraulic Tests on Preexisting Fractures (HTPF) stress determination method has been developed for eliminating these restrictive conditions. It is based on the determination of the normal stress supported by a number of preexisting fracture planes with known orientation

Evaluation of hydromechanical coupling in a granite rock mass from a high-volume, high-pressure injection experiment: Le Mayet de Montagne, France

Abstract An injection experiment was conducted to investigate the pressure domain within which hydromechanical coupling significantly influences the hydrologic behavior of a rock mass. The study site is located in the village of Le Mayet de Montagne in central France, where the local granitic terrain has been extensively characterized. The test well is 840 m deep, with an open-hole diameter of about 16 cm. A heat-pulse flowmeter was initially used to delineate the natural fluid circulation in the well and water was then injected from the surface through a tube anchored on an inflatable packer set at a depth of 275 m. This packer location was chosen in order to reach a depth where the minimum principal stress shifts from vertical to horizontal, thereby avoiding extraneous surface effects. The injection rate was progressively increased from 20 to 780 L/min while fluid velocity in the well was simultaneously recorded as a function of depth with flowmeters; corresponding well-head pressures gradually increased from 0.3 to 6.4 MPa. Fluid-intake zones were identified and their transmissivities were monitored as a function of varying effective stress. When pore pressure remained less than about 2/3 of the minimum principal stress, the hydrologic system responded linearly and Darcys Law applied. However, as pore pressure approached or exceeded the minimum principal stress magnitude, several new fluid-intake zones emerged. Meanwhile, other intervals exhibited either slight enhancements or reductions in transmissivity apparently due to changes in the far-field pressure conditions. The borehole was capable of supporting hydraulic pressures nearly equal to the magnitude of the far-field maximum principal stress. Results show that transmissive fractures form a dynamic and interdependent network; individual fracture zones cannot be adequately modeled as independent equivalent continua once hydromechanical coupling becomes significant.

Integrated stress determination by joint inversion of hydraulic tests and focal mechanisms

An inversion method, based on a genetic algorithm, is proposed for interpreting jointly various kinds of stress data in order to overcome the limitation, in number and quality, of each data set. The method has been applied to results from hydraulic tests in boreholes and to focal mechanisms of induced seismicity observed within the same depth interval. The regional stress field is described by two symmetrical tensors. The first one represents the stress at a given depth and the second one the vertical stress gradient. Results indicate that one of the principal directions is vertical. They are consistent with all but one of the hydraulic tests considered in the inversion and with about 70% of the focal mechanisms. This inversion confirms previous results suggesting that, for the scale of these induced microseismic events, the regional stress field cannot be determined solely from an inversion of the fault plane solutions.

Thermal anomaly near the Aigio fault, Gulf of Corinth, Greece, maybe due to convection below the fault

A thermal profile has been measured in a 1000 m deep borehole intersecting the active Aigio fault, Corinth Rift, Greece. The heat flow is 53 mW/m 2 , indicating that the rifting process has no effect in heat flow. The temperature near the fault is higher than expected from a pure conductive model. This discrepancy is not due to fluid flow above the fault as shown by the long term monitoring of downhole pressure. Neither can it be attributed to the fault slip since the Aigio fault is a minor normal fault of the rift, with no very recent earthquake. We propose that the anomaly is due to the convection within the karst that constitutes the footwall. Numerical simulations give a correct estimate for the recorded temperature increase. This is an extreme case of thermal disturbance induced near a fault by local fluid circulation. The occurrence of convection outside geothermal area is very rare.

Stresses in Rock and Rock Masses

Publisher Summary In continuum mechanics, some aspects of rock mechanics may be dealt with very efficiently without referring to stresses. Rocks, and even more so, rock masses, are neither continuous nor purely solid and one may question the validity of applying concepts of continuum mechanics to such materials. Because rocks are heterogeneous and, most of the time, polyphasic, the concept of stress refers, in rock mechanics, to mean forces per unit area. When the rock is assimilated to a continuum material, the elementary representative volume is the smallest volume for which there is equivalence between the idealized continuum material and the real rock. This equivalence principle may be illustrated by considering a simple porous material. This material is made up of a single material matrix and a single fluid completely filling the pore space assumed to be fully interconnected.

In‐situ stress fields and focal mechanism solutions in central France

Focal mechanisms of 31 Central France earthquakes (mb= 2.9-4.4) were evaluated to determine if slip is compatible with stress field determinations conducted at four nearby sites. The coherent picture that results indicates that the regional stress fields can be inferred by linear extrapolation of in-situ measurements performed between 400–1000 m depths. Furthermore, the results show that in spite of rather constant principal stress directions from one site to the next (100 km apart), principal stress amplitudes vary significantly. For the domain investigated (200×200 km²), the size of the homogeneous stress field regions appears to be fairly small (about 100×100 km²). In addition, within these regions, important local stress perturbations as identified by extremely inconsistent focal mechanisms, are present. Thus only by integrating different data types is it possible to map properly the regional stress field. This mapping provides means to identify the homogeneous regions as well as to highlight zones of local stress perturbations, most likely indicative of active faulting.