Physics

Coupling of rupture processes in solids with waves also propagating in fluids is a prominent phenomenon arising during tectonic earthquakes. It is executed here in a single `monolithic' model which can asymptotically capture both damageable solids (rocks) and (visco-)elastic fluids (outer core or oceans). Both ruptures on pre-existing lithospheric faults and a birth of new faults in compact rocks are covered by this model, together with emission and propagation of seismic waves, including, e.g., reflection of S-waves and refraction of P-waves on the solid-fluid interfaces. A robust, energy conserving, and convergent staggered FEM discretisation is devised. Using a rather simplified variant of such models for rupture, three computational experiments documenting the applicability of this approach are presented. Some extensions of the model towards more realistic geophysical modelling are outlined, too.

Particularly in the presence of a hydrothermal system, many volcanoes output large quantities of heat through the transport of water from deep within the edifice to the surface. Thus, heat flux is a prime tool for evaluating volcanic activity and unrest. We review the volcanic unrest at La Soufrière de Guadeloupe (French West Indies) using an airborne thermal camera survey, and in-situ measurements of temperature and flow rate through temperature probes, Pitot-tube and MultiGAS measurements. We deduce mass and heat fluxes for the fumarolic, ground and thermal spring outputs and follow these over a period spanning 2000--2020. Our results are compared with published data and we performed a retrospective analysis of the temporal variations in heat flux over this period using the literature data. We find that the heat emitted by the volcano is 36.5 +/- 7.9 MW, of which the fumarolic heat flux is dominant at 28.3 +/- 6.8 MW. Given a total heated area of 26780 m2, this equates to a heat flux density of 627 +/- 94 W/m2, which is amongst the highest established for worldwide volcanoes with hydrothermal systems, particularly for dome volcanoes. A major change at La Soufrière de Guadeloupe, however, is the development of a widespread region of ground heating at the summit where heat output has increased from 0.2 +/- 0.1 MW in 2010 to 5.7 +/- 0.9 MW in 2020. This change is concurrent with accelerating unrest at the volcano, and the emergence of two new high-flux fumaroles in recent years. Our findings highlight the importance of continued and enhanced surveillance and research strategies at La Soufrière de Guadeloupe, the results of which can be used to better understand hydrothermal volcanism the world over.

We have seen many developments in Marchenko equation-based methods for internal multiple attenuation in the past years. Starting from a wave-equation based method that required a smooth velocity model, there are now Marchenko equation-based methods that do not require any model information or user-input. In principle, these methods accurately predict internal multiples. Therefore, the role of the adaptive filter has changed for these methods. Rather than needing an aggressive adaptive filter to compensate for inaccurate internal multiple predictions, only a conservative adaptive filter is needed to compensate for minor amplitude and/or phase errors in the internal multiple predictions caused by imperfect acquisition and preprocessing of the input data. We demonstate that a conservative adaptive filter can be used to improve the attenuation of internal multiples when applying a Marchenko multiple elimination (MME) method to a 2D line of streamer data. In addition, we suggest that an adaptive filter can be used as a feedback mechanism to improve the preprocessing of the input data.

We examine the precursory behavior of geoelectric signals before large earthquakes by means of an algorithm including an alarm-based model and binary classification. This algorithm, introduced originally by Chen and Chen [Nat. Hazards., 84, 2016], is improved by removing a time parameter for coarse-graining of earthquake occurrences, as well as by extending the single station method into a joint stations method. We also determine the optimal frequency bands of earthquake-related geoelectric signals with the highest signal-to-noise ratio. Using significance tests, we also provide evidence of an underlying seismoelectric relationship. It is appropriate for machine learning to extract this underlying relationship, which could be used to quantify probabilistic forecasts of impending earthquakes, and to get closer to operational earthquake prediction.

Geologic shear fractures such as faults and slip surfaces involve marked friction along the discontinuities as they are subjected to significant confining pressures. This friction plays a critical role in the growth of these shear fractures, as revealed by the fracture mechanics theory of Palmer and Rice decades ago. In this paper, we develop a novel phase-field model of shear fracture in pressure-sensitive geomaterials, honoring the role of friction in the fracture propagation mechanism. Building on a recently proposed phase-field method for frictional interfaces, we formulate a set of governing equations for different contact conditions (or lack thereof) in which frictional energy dissipation emerges in the crack driving force during slip. We then derive the degradation function and the threshold fracture energy of the phase-field model such that the stress-strain behavior is insensitive to the length parameter for phase-field regularization. This derivation procedure extends a methodology used in recent phase-field models of cohesive tensile fracture to shear fracture in frictional materials in which peak and residual strengths coexist and evolve by confining pressure. The resulting phase-field formulation is demonstrably consistent with the theory of Palmer and Rice. Numerical examples showcase that the proposed phase-field model is a physically sound and numerically efficient method for simulating shear fracture processes in geologic materials, such as faulting and slip surface growth.

The interconnectivity of the porous space is an important characteristic in the study of porous media and their transport properties. Hence we propose a way to quantify it and relate it with the intrinsic permeability of rocks. We propose a measure of connectivity based on geometric and topological information of pore-throat network, which are models built from microtomographic images, and we obtain an analytical method to compute that property. The method is expanded to handle rocks that present a higher degree of heterogenity in the porous space, which characterization requires images from different resolutions (multiscale analysis). Trying to expand the methodology beyond the scope of images, we also propose a new interpretation for the experiment that generates the mercury intrusion curve and calculate the permeability. The methodology was applied to images of 11 rocks, 3 sandstone and 8 carbonate rock samples, and to the experimental mercury intrusion curve of 4 tight gas sand rock samples. We observe as result the existence of a correlation between the experimental and the predicted values. The notions of connectivity developed in this work seek above all to characterize a porous material before a typical macroscopic phenomenology.

Electrical conductivity is one of the most commonly used geophysical method for reservoir and environmental studies. Its main interest lies in its sensitivity to key properties of storage and transport in porous media. Its quantitative use therefore depends on the efficiency of the petrophysical relationship to link them. In this work, we develop a new physically based model for estimating electrical conductivity of saturated porous media. The model is derived assuming that the porous media is represented by a bundle of tortuous capillary tubes with a fractal pore-size distribution. The model is expressed in terms of the porosity, electrical conductivity of the pore liquid and the microstructural parameters of porous media. It takes into account the interface properties between minerals and pore water by introducing a surface conductivity. Expressions for the formation factor and hydraulic tortuosity are also obtained from the model derivation. The model is then successfully compared with published data and performs better than previous models. The proposed approach also permits to relate the electrical conductivity to other transport properties such as the hydraulic conductivity.

Among the different contributions generating self-potential, the streaming potential is of particular interest in hydrogeology for its sensitivity to water flow. Estimating water flux in porous media using streaming potential data relies on our capacity to understand, model, and upscale the electrokinetic coupling at the mineral-solution interface. Different approaches have been proposed to predict streaming potential generation in porous media. One of these approaches is the flux averaging which is based on determining the excess charge which is effectively dragged in the medium by water flow. In this study, we develop a physically-based analytical model to predict the effective excess charge in saturated porous media using a flux-averaging approach in a bundle of capillary tubes with a fractal pore-size distribution. The proposed model allows the determination of the effective excess charge as a function of pore water ionic concentration and hydrogeological parameters like porosity, permeability and tortuosity. The new model has been successfully tested against different set of experimental data from the literature. One of the main findings of this study is the mechanistic explanation to the empirical dependence between the effective excess charge and the permeability that has been found by several researchers. The proposed model also highlights the link to other lithological properties and it is able to reproduce the evolution of effective excess charge with electrolyte concentrations.

The Hessian matrix plays an important role in correct interpretation of the multiple scattered wave fields inside the FWI frame work. Due to the high computational costs, the computation of the Hessian matrix is not feasible. Consequently, FWI produces overburden related artifacts inside the target zone model, due to the lack of the exact Hessian matrix. We have shown here that Marchenko-based target-oriented Full Waveform Inversion can compensate the need of Hessian matrix inversion by reducing the non-linearity due to overburden effects. This is achieved by exploiting Marchenko-based target replacement to remove the overburden response and its interactions with the target zone from residuals and inserting the response of the updated target zone into the response of the entire medium. We have also shown that this method is more robust with respect to prior information than the standard gradient FWI. Similarly to standard Marchenko imaging, the proposed method only requires knowledge of the direct arrival time from a focusing point to the surface and the reflection response of the medium.

Seismic observations of a slowdown in P wave velocity at the base of Earth's outer core suggest the presence of a stably-stratified region known as the F-layer. This raises an important question: how can light elements that drive the geodynamo pass through the stably-stratified layer without disturbing it? We consider the F-layer as a slurry containing solid particles dispersed within the liquid iron alloy that snow under gravity towards the inner core. We present a regime diagram showing how the dynamics of the slurry F-layer change upon varying the key parameters: Péclet number ( Pe ), the ratio between advection and chemical diffusion; Stefan number ( St ), the ratio between sensible and latent heat; and Lewis number ( Le ), the ratio between thermal and chemical diffusivity. We obtain four regimes corresponding to stable, partially stable, unstable and no slurries. No slurry is found when the heat flow at the base of the layer exceeds the heat flow at the top, while a stably-stratified slurry arises when advection overcomes thermal diffusion ( Pe≳Le ) that exists over a wide range of parameters relevant to the Earth's core. Our results estimate that a stably-stratified F-layer gives a maximum inner-core boundary (ICB) body wave density jump of Δ ρ bod ≤534 kg m −3 which is compatible with the lower end of the seismic observations where 280≤Δ ρ bod ≤1,100 kg m −3 is reported in the literature. With high thermal conductivity the model predicts an inner core age between 0.6 and 1.2 Ga , which is consistent with other core evolution models. Our results suggest that a slurry model with high core conductivity predicts geophysical properties of the F-layer and core that are consistent with independent seismic and geodynamic calculations.