For the first time, nanometer resolution techniques both in situ and ex situ were compared in order to study calcite dissolution under stress. The obtained results enabled identification of the relative importance of pressure solution driven by normal load and free surface dissolution driven by strain energy. It is found that pressure solution of calcite crystals at the grain scale occurred by two different mechanisms. Diffusion of the dissolved solid took place either at a rough calcite/indenter interface, or through cracks that propagated from the contact toward the less stressed part of the crystal. It is also found that strain rates are mostly a function of the active process, i.e., pressure solution associated or not with cracks, rather than being influenced by stress variations. Strain rates obtained in this study are in agreement with published data of experimental calcite and carbonate dissolution under stress.
We wish to address the concerns raised by Bulnes et al. regarding the magnetic dipole and the associated magnetic current density. These entities are mathematical constructs for calculating electromagnetic fields.
Green’s functions for radar waves propagating in heterogeneous 2.5D media might be calculated in the frequency domain using a hybrid method. The model is defined in the Cartesian coordinate system, and its electromagnetic properties might vary in the [Formula: see text]- and [Formula: see text]-directions, but not in the [Formula: see text]-direction. Wave propagation in the [Formula: see text]- and [Formula: see text]-directions is simulated with the finite-difference method, and wave propagation in the [Formula: see text]-direction is simulated with an analytic function. The absorbing boundaries on the finite-difference grid are perfectly matched layers that have been modified to make them compatible with the hybrid method. The accuracy of these numerical Green’s functions is assessed by comparing them with independently calculated Green’s functions. For a homogeneous model, the magnitude errors range from [Formula: see text] through 0.44%, and the phase errors range from [Formula: see text] through 4.86%. For a layered model, the magnitude errors range from [Formula: see text] through 2.06%, and the phase errors range from [Formula: see text] through 2.73%. These numerical Green’s functions might be used for forward modeling and full waveform inversion.
Uniaxial compression tests were conducted on bioclastic sand and crushed calcite crystals. Mechanical and chemical processes were investigated to better quantify petrophysical properties of carbonates and their evolution with burial or during fault zone processes. The grain size was in the range 63–500 μ m, and the samples were saturated with water in equilibrium with carbonate, glycol, decane, or air. During loading, effective stress was increased to 32 MPa. Mechanical compaction processes (i.e., grain rearrangement, crushing) could be separated from chemical processes (i.e., pressure solution, subcritical crack growth). P and S waves monitored during the tests showed low velocity in samples saturated with reactive fluids. This suggested that chemical reactions at grain contacts reduced the grain framework stiffness. Creep tests were also carried out on bioclastic sand at effective stress of 10, 20, and 30 MPa. No creep was observed in samples saturated with nonreactive fluids. For all the samples saturated with reactive fluids, strain as a function of time was described by a power law of time with a single exponent close to 0.23. Parameters controlling creep rate were, in order of importance, grain size, effective stress, and water saturation. Microstructural observations showed that compaction of bioclastic carbonate sand occurred both mechanically and chemically. Crack propagation probably contributed to mechanical compaction and enhanced chemical compaction during creep. Experimental compaction showed that compaction of carbonates should be modeled as a function of both mechanical and chemical processes, also at relatively shallow depth and low temperature.
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