Cartesian Meshing Spherical Earth (CMSE): A Code Package to Incorporate the Spherical Earth in SPECFEM3D Cartesian Simulations

The SPECFEM3D_Cartesian code package is widely used in simulating seismic wave propagation on local and regional scales due to its computational efficiency compared with the one-chunk version of the SPECFEM3D_Globe code. In SPECFEM3D_Cartesian, the built-in meshing tool maps a spherically curved cube to a rectangular cube using the Universal Transverse Mercator projection (UTM). Meanwhile, the geodetic east, north, and up directions are assigned as the local x–y–z directions. This causes coordinate orientation issues in simulating waveform propagation in regions larger than 6° × 6° or near the Earth’s polar regions. In this study, we introduce a new code package, named Cartesian Meshing Spherical Earth (CMSE), that can accurately mesh the 3D geometry of the Earth’s surface under the Cartesian coordinate frame, while retaining the geodetic directions. To benchmark our new package, we calculate the residual amplitude of the CMSE synthetics with respect to the reference synthetics calculated by SPECFEM3D_Globe. In the regional scale simulations with an area of 1300 km × 1300 km, we find a maximum of 5% amplitude residual for the SPECFEM3D_Cartesian synthetics using the mesh generated by the CMSE, much smaller than the maximum amplitude residual of 100% for the synthetics based on its built-in meshing tool. Therefore, our new meshing tool CMSE overcomes the limitations of the internal mesher used by SPECFEM3D_Cartesian and can be used for more accurate waveform simulations in larger regions beyond one UTM zone. Furthermore, CMSE can deal with regions at the south and north poles that cannot be handled by the UTM projection. Although other external code packages can be used to mesh the curvature of the Earth, the advantage of the CMSE code is that it is open-source, easy to use, and fully integrated with SPECFEM3D_Cartesian.

A study on the Delta-Bullington irregular terrain radiofrequency propagation model : assessing model suitability for use in decision support tools

Modeling the propagation of radiofrequency signals over irregular terrain is both challenging and critically important in numerous Army applications. One application of particular importance is the performance and radio connectivity of sensors deployed in scenarios where the terrain and the environment significantly impact signal propagation. This report investigates both the performance of and the algorithms and assumptions underlying the Delta-Bullington irregular terrain radiofrequency propagation model discussed in International Telecommunications Union Recommendation P.526-15. The aim is to determine its suitability for use within sensor-planning decision support tools. After reviewing free-space, spherical earth diffraction, and terrain obstacle diffraction losses, the report dis-cusses several important tests of the model, including reciprocity and geographic continuity of propagation loss over large areas of rugged terrain. Overall, the Delta-Bullington model performed well, providing reasonably rapid and geographically continuous propagation loss estimates with computational demands appropriate for operational use.

FDTD analysis of ELF radio wave propagation in the spherical Earth-ionosphere waveguide and its validation based on analytical solutions

The FDTD model of electromagnetic wave propagation in the Earth-ionosphere cavity was developed under assumption of axisymmetric system, solving the reduced Maxwell’s equations in a 2D spherical coordinate system. The model was validated on different conductivity profiles for the electric and magnetic field components for various locations on Earth along the meridian. The characteristic electric and magnetic altitudes, the phase velocity and attenuation rate were calculated. We compared the results of numerical and analytical calculations and found good agreement between them. The undertaken FDTD modeling enables us to analyze the Schumann resonances and the propagation of individual lightning discharges occurring at various distances from the receiver. The developed model is particularly useful when analyzing ELF measurements.

Children’s Astronomy. Development of the Shape of the Earth Concept in Polish Children between 5 and 10 Years of Age

The Earth’s shape concept develops as consecutive cognitive problems (e.g., the location of people and trees on the spherical Earth) are gradually resolved. Establishing the order of problem solving may be important for the organisation of teaching situations. This study attempted to determine the sequence of problems to be resolved based on tasks included in the EARTH2 test. The study covered a group of 444 children between 5 and 10 years of age. It captured the order in which children solve cognitive problems on the way to constructing a science-like concept. The test results were compared with previous studies. The importance of cultural influences connected to significant differences (24%) in test results was emphasised. Attention was drawn to the problem of the consistency of the mental model approach highlighted in the literature. The analysis of the individual sets of answers provided a high level of consistency of indications referring to the same model (36%), emphasising the importance of the concept of mental models.

Internal co-seismic displacement and strain changes inside a homogeneous spherical Earth

Summary In this study, we devised a new set of analytical foundation solutions to compute the internal co-seismic displacement and strain changes caused by four independent point sources (strike-slip, dip-slip, horizontal tensile, and vertical tensile) inside a homogeneous spherical Earth model. Our model provides constraints on the deformation properties at depth, and reveals that the internal co-seismic deformation is larger than that on the surface. The deformation near the source is convergent with our formulae. For the internal deformation at radial section plane, the patterns of horizontal displacements ${u_\theta },{u_\phi }$ and strain changes ${e_{rr}},{e_{\theta \theta }},{e_{\phi \phi }},{e_{\theta \phi }}$ caused by strike-slip and tensile sources appear symmetric at the equidistance above and below the source. Their amplitudes are not identical but with a small discrepancy actually. Unlike these, the patterns of radial displacements ${u_r}$ for strike-slip and tensile sources exhibit point symmetry with the equidistance from the source. Also, the corresponding amplitudes are slightly different. The displacements ${u_\theta },{u_\phi }$ and strain changes ${e_{rr}},{e_{\theta \theta }},{e_{\phi \phi }},{e_{\theta \phi }}$ caused by dip-slip also appear the same properties as ${u_r}$ of strike-slip source. The magnitudes of the displacements and strain changes depend on the source types. The curvature effect on the near-field surface deformations is small, and it increases with the studied depth. But for the far-field deformation caused by the strike-slip source (ds = 20 km), the curvature effect can be as large as 77 per cent when the epicentral distance approximates to 1778 km.