05.05. Mathematical geophysics

Annals of Geophysics (ISSN: 1593-5213; from 2010, 2037-416X) is a bimonthly international journal, which publishes scientific papers in the field of geophysics sensu lato. It derives from Annali di Geofisica (ISSN: 0365-2556), which commenced publication in January 1948 as a quarterly periodical devoted to general geophysics, seismology, Earth magnetism, and atmospheric studies....

In this note, we study the distribution of earthquake numbers in both worldwide and regional catalogs: in the Global Centroid Moment Tensor catalog, from 1980 to 2019 for magnitudes Mw 5. 5+ and 6.5+ in the first case, and in the Italian instrumental catalog from 1960 to 2021 for magnitudes Mw 4.0+ and 5.5+ in the second case. A subset of the global catalog is also used to study the Japanese region. We will focus our attention on short-term time windows of 1, 7, and 30 days, which have been poorly explored in previous studies. We model the earthquake numbers using two discrete probability distributions, i.e., Poisson and Negative Binomial. Using the classical chi-squared statistical test, we found that the Poisson distribution, widely used in seismological studies, is always rejected when tested against observations, while the Negative Binomial distribution cannot be disproved for magnitudes Mw 6.5+ in all time windows of the global catalog. However, if we consider the Japanese or the Italian regions, it cannot be proven that the Negative Binomial distribution performs better than the Poisson distribution using the chi-squared test. When instead we compared the performances of the two distributions using the Akaike Information Criterion, we found that the Negative Binomial distribution always performs better than the Poisson one. The results of this study suggest that the Negative Binomial distribution, largely ignored in seismological studies, should replace the Poisson distribution in modeling the number of earthquakes.

We present a new tomographic procedure for the analysis of natural source electromagnetic (EM) induction field data collected over any complex 2D buried structure beneath a flat air-earth boundary. The tomography is developed in a pure physical context and the primary goal is the depiction of the space distribution of two occurrence probability functions for the induced electrical charge accumulations on resistivity discontinuities and current channelling inside conductive bodies, respectively. The procedure to obtain tomographic image consists of a scanning operation governed analytically by a set of multiple interference cross-correlations between the observed EM components and the corresponding synthetic components of a pair of elementary charge and dipole. To show the potentiality of the proposed physical tomography, we discuss the results from three 2D synthetic examples.

The deformation and stress fields accompanying dyke injection in rift zones are described in terms of a vertical crack opening in response to internal overpressure, in plane-strain configuration. Previous numerical computations of the displacement field induced by shallow dykes are found to be affected, in some cases, by significant dis- tortion, mainly due to the limited extension of the computational domain, difficultiesin handling the singularities in the proximity of the free surface and an incorrect choice of the reference frame; in particular, it is found that no subsidence can be ascribed to the mere opening of a tensile crack in a homogeneous, elastic half-space. If analytical constant-dislocation models are employed, surface displacements compare reasonably well with crack-model solutions if the upper tip is not too shallow; however, constant dislocation solutions present unphysical singularities along the tips, which distort significantly the near-field stress pattern with respect to crack solutions. If the principal stress axes are computed from crack models, a broad region is found on both sides of the dyke where the induced stress has a nearly vertical intermediate axis while the com- pressive axis is normal to the dyke plane. Strike-slip earthquakes are expected to prevail in this region. Above the upper crack tip, a small region is present where the tensile stress is dominant and the intermediate stress is still vertical. In the proximity of the free surface, typically within a few tens of metres of it, induced tensile stresses are greater than the lithostatic pressure: open fissures might then develop in cohesionless soil or pre-faulted rock. The induced pressure in the host rock is found to be negative (suction) in the proximity of the ground surface and positive at greater depth: fluid flow within the aquifers can be significantly altered by this induced overpressure and by the anisotropic modification of the pre-existing permeability. According to the modified Coulomb failure criterion, in the short term the shallower region, characterized by suction, is strengthened, while the deeper, pressurized region is weakened. These results can explain in a straightforward way the abundance of strike-slip focal mechanisms in vol- canic areas, the switch between tensional and compressional axes inferred from focal mechanisms of earthquakes in connection with a dyke injection episode on Mount Etna, en echelon fracture systems observed at Piton de la Fournaise above the feeding dyke and precursory geochemical anomalies.

The monitoring of the underground medium requires estimation of accuracy of the methods used. Numerical simulation of the solution of 2D inverse problem on the reconstruction of seismic and electrical parameters of local (comparable in size with the wavelength) inhomogeneities by the diffraction tomography method based upon the first order Born approximation is considered. The direct problems for the Lame and Maxwell equations are solved by the finite difference method that allows us to take correctly into account the diffraction phenomenon produced by the target inhomogeneities with simple and complex geometry. For reconstruction of the local inhomogeneities the algebraic methods and the optimizing procedures are used. The investigation includes a parametric representation of inhomogeneities by the simple and complex functions. The results of estimation of the accuracy of the reconstruction of elastic inhomogeneities and inhomogeneities of electrical conductivity by the diffraction tomography method are represented.

We present a coupled fluid-dynamic and electromagnetic model for volcanic ash plumes. In a forward approach, the model is able to simulate the plume dynamics from prescribed input flow conditions and generate the corresponding synthetic thermal infrared (TIR) image, allowing a comparison with field-based observations. An inversion procedure is then developed to retrieve vent conditions from TIR images, and to independently estimate the mass eruption rate. The adopted fluid-dynamic model is based on a one-dimensional, stationary description of a self-similar turbulent plume, for which an asymptotic analytical solution is obtained. The electromagnetic emission/absorption model is based on Schwarzschild's equation and on Mie's theory for disperse particles, and we assume that particles are coarser than the radiation wavelength (about 10 μm) and that scattering is negligible. In the inversion procedure, model parameter space is sampled to find the optimal set of input conditions which minimizes the difference between the experimental and the synthetic image. Application of the inversion procedure to an ash plume at Santiaguito (Santa Maria volcano, Guatemala) has allowed us to retrieve the main plume input parameters, namely mass flow rate, initial radius, velocity, temperature, gas mass ratio, entrainment coefficient and their related uncertainty. Moreover, by coupling with the electromagnetic model we have been able to obtain a reliable estimate of the equivalent Sauter diameter of the total particle size distribution. The presented method is general and, in principle, can be applied to the spatial distribution of particle concentration and temperature obtained by any fluid-dynamic model, either integral or multidimensional, stationary or time-dependent, single or multiphase. The method discussed here is fast and robust, thus indicating potential for applications to real-time estimation of ash mass flux and particle size distribution, which is crucial for model-based forecasts of the volcanic ash dispersal process.

Radon migration along vertical profiles in the soils of Irno River alluvial Valley (Southern Italy) was studied using radioactive disequilibrium between 226 Ra and 210 Pb. Fractional Radon loss, migration length, diffusion and emanation coefficient and Radon flux density were determined. Our results are in agreement with a migra- tion model by simple diffusion. The migration parameters are within typical values, except the Radon flux density, which is about one order of magnitude higher than the values reported in literature. The values of fractional Radon loss are sensitive to changes in the physical properties of the soil.

Secular variation of the geomagnetic field observed at the Earth's surface has been found to undergo impulsive accelerations Gerks) lasting less than a few years. In this paper the relations between jerks and the occurrence of strong earthquakes (Ms ≥ 7.0) is analysed for this century , disclosing a positive correlation between the maximum number of recorded strong earthquakes and jerk occurrence. Analysing only very strong earth- quakes (Ms ≥ ; 8.0) the jerks seem to take pIace with a time delay of about 2-5 years with respect to earthquake occurrence. Reliable processes that could justify this intriguing correspondence are suggested.

We propose a novel nite-di erence approach for the numerical solution of linear elasticity problems in arbitrary unbounded domains. The method is an extension of a recently proposed ghost-point method for the Poisson equation on bounded domains with arbitrary boundary conditions (Coco, Russo, JCP, 2013) to the case of the Cauchy-Navier equations on unbounded domains. The technique is based on a smooth coordinate transformation, which maps an unbounded domain into a unit square. Arbitrary geometries are de ned by suitable level-set functions. The equations are discretized by classical ninepoint stencil on interior points, while boundary conditions and high order reconstructions are used to de ne the eld variable at ghost-point, which are grid nodes external to the domain with a neighbor inside the domain. The approach is then adopted to solve elasticity problems applied to volcanology for computing the displacement caused by an underground pressure source. The method is suitable to treat problems in which the geometry of the source often changes (explore the e ects of di erent scenarios, or solve inverse problems in which the geometry itself is part of the unknown), since it does not require complex re-meshing when the geometry is modi ed. Several numerical tests are performed, which asses the e ectiveness of the present approach. Keywords: Linear Elasticity, Cauchy-Navier equations, ground deformation, unbounded domain, coordinate transformation method, Cartesian grid, Ghost points, Level-set methods

A theoretical melting curve for iron is determined in the pressure range of the Earth's core by a relation derived from the Ross-Lindemann melting criterium. On this basis the melting point of pure iron is estimated to be about 4800°C at the mantle-core boundary, and 6600°C at the inner core-outer core boundary with a melting point gradient of about 0-8 deglkm.