The rheology of the Earth’s mantle is studied on the basis of data on the Love numbers for ten tidal components (M2, Mqm, Msqm, Mtm, Mstm, SN, Mf, Msf, Mm, and Msm). An adaptation of the Preliminary Reference Earth Model (PREM) is used to model the internal structure of the Earth, while the inelasticity is modeled using the Andrade rheology. The Andrade model depends on two empirical parameters (α and ζ) that are unknown for mantle minerals at high pressures and temperatures and very slow deformations. As a result, in various problems of planetary geophysics where inelasticity in the interior of planets or satellites must be taken into account, authors are often faced with the difficulty of which values of the Andrade rheology parameters to use. To address this issue, an Earth-based calibration of the rheology was performed. The Love numbers of the Earth were calculated at ten tidal frequencies for two viscosity distributions and for 1530 different combinations of the parameters α and ζ. The comparison of the model values with the observed ones allowed us to determine a set of values for α and ζ that are suitable for describing the inelasticity of the Earth’s mantle.

In this work, we explore the challenges associated with the formation of satellite measurement datasets for constructing models of Mars’ magnetic field. Several approaches to dataset construction have been proposed and implemented. Using the regional method of S-approximations, analytical approximations of the magnetic field have been developed, and analytical continuations of the field to a uniform selected altitude have been presented. Calculations were performed for an area of Mars that includes the landing sites of the InSight spacecraft and the Chinese rover Zhurong. The modeling was based on datasets derived from calibrated insitu.calibrated level 2 data of the MAVEN mission.

The load Love numbers for different rheological models of Venus are calculated, based on a static approach for the surface load (the planetary relief) and buried anomalous density waves. The planet was modeled as an elastic self-gravitating body with radius-dependent density, compression modulus, and shear modulus. The calculations have been performed for each harmonic up to the degree and order n = 70, based on the accuracy of determining the gravity field at the moment. This article considers three rheological models of Venus. A purely elastic model (model A) was analyzed first. In the second case (model B) we assume the presence of an elastic lithosphere, under which a weakened layer extending to the core was introduced, which partially lost its elastic properties. The weakening in this layer was modeled by a ten times lower shear modulus. The thickness of the elastic lithospheric layer varied from 100 to 500 km. In the third model (model C), a gradient change in the shear modulus was set in the weakened layer under the crust, that is, a ten times decrease in the shear modulus directly under the crust gradually increased to its value in the elastic model at the core boundary. On the basis of the described models, the interpretation of the anomalous external gravitational field has been carried out. It is shown that the load numbers are sensitive to the rheological structure of the planet and this can be used when choosing between the rheological models of Venus. A relief map of the crust–mantle boundary was constructed, as calculated under the assumption of isostatic compensation. The obtained values of the crust thickness may be slightly less than the real ones, since the component of dynamic compensation was not taken into account in the work.

It is shown that most of the epicenters of marsquakes are located in the zones of extension and fairly large shear stresses associated with the deviation of Mars from hydrostatic equilibrium. Non-hydrostatic stresses in the interior of Venus are calculated for two types of models: an elastic model and a model with a lithosphere of varying thickness (150–500 km) overlying a weakened layer that has partially lost its elastic properties. Numerical modeling of the system of elastic equilibrium equations for a gravitating planet is carried out with a step of 1°×1° in latitude and longitude up to a depth of 480 km – the first phase transition zone in the mantle. The topography and the gravitational field of the planet are the boundary conditions of the problem. Overall, the level of nonhydrostatic stress on Venus is not very high. On the surface and in the crust, the highest shear stresses are observed in the region of the Maxwell Monte on Ishtar Terra. Beneath the Maxwell Monte, shear stresses in the crust reach 80 MPa and compressive stresses, 125–150 MPa, depending on the model. Tensile stresses around this region are about 20 MPa. The highest tensile stresses occur in the regions beneath structures such as Lavinia Planitia, Sedna Planitia, and Aino Planitia.

Tidal Love numbers are often used for studying the interior structure of planets and satellites of the Solar System. Measuring the deformation in response to tidal loading belongs to the methods for probing the interiors. The algorithm for computing tidal deformation depends on a series of assumptions and approximations and, therefore, can differ according to different authors. In this paper we compare the existing methods and, based on them, we propose a new and more precise algorithm for computing the tidal Love numbers of the Earth and other bodies with a similar interior structure.

The results of numerical modeling of the values of the Chandler wobble period of Mars have been presented for a set of internal structure models that satisfy all currently available observable data: geodetic (average radius, mass, moment of inertia, tidal Love number k2) and crustal thickness and core radius values obtained from seismic data processing. Andrade rheology was used to take into account inelasticity when calculating model values of the tidal Love number k2 and the Chandler wobble period. It has been shown how the model values of the Love number k2 and the Chandler period depend on the Andrade rheological parameter and the adopted viscosity distribution.

The Chandler wobble of Venus has been analyzed on the basis of the Earth-like models of the planet. The method for calculating the Chandler wobble period of Venus was tested on the example of the Earth. To take into account the inelasticity of the interior of a planet, the Andrade rheology was used; and the values of the rheologic model parameters, which can explain the observed period of the Chandler wobble of the Earth, were determined. Projections on the Chandler wobble period of Venus were obtained. For the most plausible models of the internal structure of Venus, in which the core radius is assumed to be within an interval of 3288 ± 167 km, the Chandler wobble period is 30–48 thousand years. A large error in the results is mainly caused by a wide range of probable values for the constant of precession of Venus.

The Chandler period of Mars is a new parameter determined from observational data that characterizes the properties of the planetary interior. Numerical modeling of the period of the Chandler wobble of Mars was performed for a number of internal structure models that satisfy not only geodetic data (moment of inertia, tidal Love number k2), but also data obtained during a seismic experiment in the years 2019–2022. To reconcile the theoretical and observed values of the Chandler wobble, it is necessary to take into account the inelasticity of the mantle. To take into account the viscoelastic behavior of the interior, the Andrade rheological model was used. It is demonstrated how the value of the Chandler period depends on the rheological model parameters.

Based on the PREM Earth model, more than a thousand models of the internal structure of Venus have been built, differing in the radius and density of the core, the density of the mantle, the viscosity distribution and rheology. The core radius varies from 2800 to 3600 km, and the density in the mantle and core varies within a few percent of the PREM model values. When calculating tidal Love numbers, Andrade rheology is used to take into account the inelasticity of the mantle. Specifically the values of the Andrade rheological model parameters that best describe the tidal deformation of the Earth are used. This significantly reduces the error when calculating Love numbers. It has been shown that Venus can have an internal solid core only if the composition of the planet is very different from that of Earth. Comparison of the observed values of the moment of inertia and tidal Love number k2 with model values allowed us to conclude that the radius of the core of Venus is with a high probability in the range of 3288 ± 167 km.

— Models of the internal structure of Venus have been constructed with a wide range of crustal thickness (30–70 km) and core radius (2800–3500 km). An analysis of the pressure values in the center of the planet allows us to conclude that the presence of a solid inner core is unlikely if the composition and temperature profile of Venus correspond to that of the Earth. Andrade’s rheology was used to take into account the inelasticity of the interior of Venus when calculating the tidal Love numbers and the angle of delay of the tidal hump. Comparison of experimental values of the Love number k 2 with the model gives the radius of the core of Venus in the range of 3100–3500 km. It is shown that to determine the characteristic viscosity of the Venusian mantle, the key factor is the determination of the angle of retardation of the tidal bulge: values of 0.9° correspond to low viscosity and high temperature, and 0.4° to high viscosity and low temperature, so the planned measurements of tidal parameters and the moment of inertia of the planet in the VERITAS and EnVision missions will be able to impose restrictions on the distribution of viscosity and temperature in the interior of Venus.

A new combined method for solution of nonlinear reverse gravimetry tasks is tested in this work using three data types: gravity field, topography, and crustal thickness in the area of Elysium Planitia on Mars.

Based on topography and gravitational field data, model variations in the crust thickness of Mars and Venus were calculated using the Love numbers method. The method takes into account the adjustment of the planetary interior to loads on the surface and in the interior. Numerical modeling was carried out using the expansion in spherical harmonics of the topography and gravitational field data up to the 90th degree and order for Mars and up to the 70th degree and order for Venus. The topography of the crust–mantle boundary suggests partial Airy isostatic compensation. The model of the Martian crust is consistent with the interval of crustal thickness values under the site of the InSight station in the southwestern part of Elysium Planitia obtained from the results of a seismic experiment. The comparison with the available global models of the crust of Mars and Venus was carried out.

It has been demonstrated for the first time in this paper that the frequently used approximation of the Andrade rheology with only one parameter is oversimplified and might lead to incorrect conclusions when studying the internal structure of the planets of the Solar System. Instead, we have used the Andrade rheology with two empirical parameters: α and ζ. The Earth’s viscoelastic Love numbers for the principal lunar semidiurnal tide M2 were computed for two viscosity profiles and for 16 100 different combinations of α and ζ. The comparison of the computed Love numbers with the measured values makes it possible to constrain the range of values of both parameters that successfully describes the rheological properties of the Earth’s mantle.

We compare several recent Martian interior models and evaluate how these are impacted by the tidal constraints provided by the Love number k2 and the secular acceleration in longitude s of its main moon, Phobos. The expression of the latter is developed up to harmonic degree 5 to match the accuracy of the current observations. We match a number of current interior structure models to the recent measurements of the tidal parameters and derive estimations of the possible core radius, temperature profile, and attenuation in the Martian interior. Our estimation of the core radius is 1,820 ± 80 km, consistent with recent seismic measurements. The attenuation profiles in the Martian interior at the main tidal period of Phobos are similar between the considered models, giving a range for the degree‐2 bulk tidal attenuation Q2 = 93.0 ± 8.40 but diverge at seismic frequencies. At seismic frequencies, model shear attenuation Qμ ranges between 100 and 4,000 in the lower mantle, so that a measurement of seismic shear attenuation could be used as an effective means for distinguishing between the models considered. Other constraints such as elastic lithosphere thickness and Chandler Wobble period favor a thicker elastic lithosphere and models with a frequency dependence α of the shear attenuation between 0.15 and 0.4. Improved constraints on the Martian interior should be possible with additional seismic and radio observations from the InSight mission.

The NASA InSight mission to Mars successfully landed on 26 November 2018 in Elysium Planitia. It aims to characterize the seismic activity and aid in the understanding of the internal structure of Mars. We focus on the Cerberus Fossae region, a giant fracture network ∼1,200 km long situated east of the InSight landing site where M ∼3 marsquakes were detected during the past 2 years. It is formed of five main fossae located on the southeast of the Elysium Mons volcanic rise. We perform a detailed mapping of the entire system based on high‐resolution satellite images and Digital Elevation Models. The refined cartography reveals a range of morphologies associated with dike activity at depth. Width and throw measurements of the fossae are linearly correlated, suggesting a possible tectonic control on the shapes of the fossae. Widths and throws decrease toward the east, indicating the long‐term direction of propagation of the dike‐induced graben system. They also give insights into the geometry at depth and how the possible faults and fractures are rooted in the crust. The exceptional preservation of the fossae allows us to detect up to four scales of segmentation, each formed by a similar number of 3–4 segments/subsegments. This generic distribution is comparable to continental faults and fractures on Earth. We anticipate higher stress and potential marsquakes within intersegment zones and at graben tips.

A new three-staged technique based on various versions of the linear integral representation method (S-, F- and R-approximations) is applied to solve the problem of analytical modelling of the magnetic field on the surface of Mars. At the first step, we build an analytical approximation from the given data set (in local or regional cases). In the second step, we analyze the previous stage results and solve an ordinary differential equation system to find the integral curve of the gravity or magnetic field. The points of this curve are included in an extended data set, and we repeat the procedure described above for the first stage. The final approximation of the anomalous field elements or the topographic data allows us to find various linear transformations of the field under investigation, e.g. higher derivatives of the potential or Fourier-spectra of the field elements.Analytical downward continuations of the magnetic field of Mars at various distances, including the planet's surface is presented.