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Global warming firstly influences the permafrost regions where numerous and rich world hydrocarbon deposits are located. Permafrost thawing has caused severe problems in exploring known hydrocarbon deposits and searching for new targets. This process is also dangerous for any industrial and living regions in cold regions. Knowledge of permafrost’s ice and unfrozen water content is critical for predicting permafrost behavior during the water–ice transition. This is especially relevant when ice and permafrost are melting in many regions under the influence of global warming. It is well known that only part of the formation’s pore water turns into ice at 0 °C. After further lowering the temperature, the water phase transition continues, but at gradually decreasing rates. Thus, the porous space is filled with ice and unfrozen water. Laboratory data show that frozen formations’ mechanical, thermal, and rheological properties strongly depend on the moisture content. Hence, porosity and temperature are essential parameters of permafrost. In this paper, it is shown that by combining research in three fields, (1) geophysical exploration, (2) numerical modeling, and (3) temperature logging, it is possible to estimate the porosity of permafrost in situ. Five examples of numerical modeling (where all input parameters are specified) are given to demonstrate the procedure. This investigation is the first attempt to quantitatively analyze permafrost’s porosity in situ.

The concept of infinitesimal elastic deformation and the theory of elastic seismic waves was formed in the first part of the 19th century and was based mainly on the Fermat, Huygens and Snell developments in the theory of optics. At the same time, seismic wave propagation (utilized in geophysical prospecting) and optic wave propagation through defined media are based on the same physical-mathematical principles, making it possible to transfer nonconventional procedures developed in the first domain to the second one and back. In this investigation, we propose transferring advanced methodologies established in seismic prospecting to practical optics. We selected two advanced approaches with the following aims: (a) homeomorphic imaging; (b) novel description of boundary conditions. The first approach is established with the utilization of the revealed local theoretical relationship between the geometrical features of two fundamental beams and the geometrical properties of hidden geological targets of the media under study. The employed geometrical characteristics of the fundamental beams are spreading functions and curvatures of the singular wavefronts. The second approach is based on a novel description of the boundary conditions. It enables the determination of a faultless seismic (optical) system with the preassigned focusing and imaging assets when any aberrations are absent. An optimal optical system is usually determined as some arrangement agreeing to some perfect system with acceptable correctness. Employment of the developed procedures in the optical design will permit the application of a description of the optical surface using: (1) parametric functions, (2) differential equations, and (3) mixed (parametric-differential). On this basis, optical systems with a minimal number of optical features with complicated shapes can be promptly computed. Another important application field of the suggested methods is the design of optical systems with diffractive elements.

The Easternmost Mediterranean is a transition region from the ocean to the continent where the spreading and collision zones of the lithospheric plates join. The methodology of paleomagnetic mapping of the transition zones is based on combining geological and geophysical techniques for continental and oceanic platforms: magnetic data interpretation, paleomagnetic reconstructions, results of magnetized rock radiometric dating, satellite data analysis, tectonic–structural reconstructions, biogeographical studies, and utilization of different geophysical survey results. The satellite-derived gravity map reflects practically all significant tectonic units in the region, which assists us in the supposed paleomagnetic mapping. The satellite-derived and aeromagnetic maps with the tectonic features and the map of Curie discontinuity of Israel indicate the complexity of this region. Advanced magnetic data analysis supported by paleomagnetic data attraction and other geological–geophysical methods allowed the revealing of the block of oceanic crust with the Kiama paleomagnetic zone relating to the Early Permian age. A narrow reversely magnetized Earth crust block was revealed in the Lower Galilee. Some examples of advanced magnetic anomaly analysis are presented for several areas where the magnetization vector inclination is other than the modern direction: the Sea of Galilee, Carmel, Rosh-Ha-Ayin, Malqishon, and Hebron. In Israeli land, for the combined paleomagnetic mapping, the well-studied using paleomagnetic and radiometric methods (as well as tectonic–structural) areas were selected: (1) Makhtesh Ramon, (2) the Sea of Galilee with the adjoining zones, (3) Carmel, (4) Hula, and (5) Hermon. It is shown that the regional analysis of paleomagnetic data distribution played an essential role in detecting the influence of the recently recognized counterclockwise rotating mantle structure on the near-surface layers.

The problem of creating methods for calculating tsunami parameters and predicting these dangerous events is currently being solved by integrating the equations of the theory of water waves. Both numerical methods and powerful computers are used, as well as analytical solutions. The essential stage is the stage of the tsunami reaching the shelf and shallow coastal waters. The tsunami amplitude increases here, and nonlinear effects become important. Nonlinearity excludes the solution’s unicity and the superposition principle’s fulfillment. The nonlinear theory can have many solutions, depending on various external conditions; there could be nontrivial ones. In this article, we explore the properties of several nonlinear solutions. With their help, we can find the maximum possible amplitude of tsunami waves when approaching the coast and estimate the seismological parameters of an earthquake-generating tsunami.

In the cold regions, warm mud is usually used to drill deep wells. This mud causes formation thawing around wells, and as a rule is an uncertain parameter. For frozen soils, ice serves as a cementing material, so the strength of frozen soils is significantly reduced at the ice–water transition. If the thawing soil cannot withstand the load of overlying layers, consolidation will take place, and the corresponding settlement can cause significant surface shifts. Therefore, for long-term drilling or oil/gas production, the radius of thawing should be estimated to predict platform stability and the integrity of the well. It is known that physical properties of formations are drastically changed at the thawing–freezing transition. When interpreting geophysical logs, it is therefore important to know the radius of thawing and its dynamics during drilling and shut-in periods. We have shown earlier that for a cylindrical system the position of the phase interface in the Stefan problem can be approximated through two functions: one function determines the position of the melting-temperature isotherm in the problem without phase transitions, and the second function does not depend on time. For the drilling period, we will use this approach to estimate the radius of thawing. For the shut-in period, we will utilize an empirical equation based on the results of numerical modelling.

The easternmost Mediterranean is a distinct transition zone from the ocean to the continent located at the junction between the largest Earth’s lithospheric segments: Eurasian and African. The methodology of paleomagnetic mapping of such transition zones is based on integrating the mapping techniques for both continental and oceanic platforms: paleomagnetic reconstructions, results of radiometric dating of magnetized rocks, tectonic-structural reconstructions, biogeography, and utilization of the results of various geophysical surveys. The geodynamic-paleomagnetic mapping makes it possible to reveal the multilevel structural heterogeneity and display complex elements of the geodynamics of different ages inherent in this transition zone. The region of northern Israel is the most complex area in the easternmost Mediterranean. For the combined paleomagnetic mapping, well-studied paleomagnetically and radiometrically areas were selected: (1) the Carmel area, (2) the Atlit area (internal part of the Carmel area), (3) the Sea of Galilee with the adjoining zones (primarily, the Kinnarot Valley), and (4) the area of the Hula Basin with adjacent areas of the Golan Plateau, Hermon Mt., and Galilea uplift. The constructed paleomagnetic profiles for the Carmel area (on the top of the accumulative surface of the Lower Cretaceous traps) and the Kinnarot Valley—Sea of Galilee—Hula Basin, evidently indicate the complex history of the paleogeodynamic evolution of the region. These studies demonstrate the effectiveness of paleomagnetic mapping integrated with paleomagnetic profiles crossing these geologically complex areas.

The origin of the man on Earth is directly associated with the determination of directions of the flow distribution of the ancient man dispersal to adjacent territories. In such studies, mainly landscape and climatological changes are traditionally considered. We suggest that along with the above factors, regional tectonic-geodynamic factors played a dominant role in the character of dispersal. The considered African-Levantine-Caucasian region is one of the most geologically complex regions of the world, where collisional and spreading processes of geodynamics converge. For the first time, we determined an essential influence of the Akchagylian hydrospheric maximum (about 200 m above the mean sea level) limiting the early dispersal of hominins from Africa to Eurasia. We propose that the Levantine Corridor emerged after the end of the Akchagylian transgression and landscape forming in the Eastern Mediterranean. This corridor location was formed by the movements between the Dead Sea Transform and the boundary of the carbonate platform of the Mesozoic Terrane Belt. Further landscape evolution was largely determined by the geodynamic behavior of the deep mantle rotating structure occurring below the central part of the region under study. All the mentioned events around and in the Levantine Corridor have been studied in detail on the basis of the combined geodynamic, paleogeographic, and paleomagnetic analyses performed in northern Israel (Carmel Uplift and Galilee Plateau). Careful studies of the Evron Quarry geological section indicate that it is unique for the dating of marine and continental archaeological sequences and sheds light on the early dispersal of hominins along the Levantine Corridor.

The self-potential (SP) method is one of the most inexpensive and unsophisticated geophysical methods. However, its application is limited due to the absence of a reliable interpreting methodology for the complex geological-environmental conditions. To exclude disturbances appearing in the SP method, a few ways for their removal (elimination) before quantitative analysis are presented. A brief review of the available interpretation methods is included. For the magnetic method of geophysical prospecting, special quantitative procedures applicable under complex physical-geological environments (oblique polarization, uneven terrain relief and unknown level of the normal field), have been developed. The detected common peculiarities between the magnetic and SP fields make it possible to apply the advanced procedures developed in magnetic prospecting to the SP method. Besides the reliable determination of the depth of anomalous targets, these methodologies enable the calculation of the corrections for non-horizontal SP observations and to determine the orientation of the polarization vector. For the classification of SP anomalies, is proposed to use a new parameter: the ‘self-potential moment’. The quantitative procedures (improved modifications of characteristic point, tangent techniques and the areal method) including the determination of the SP vector and SP moment, have been successfully tested on models and employed in real situations in mining, archaeological, environmental and technogenic geophysics. The obtained results indicate the effectiveness of the presented methodologies.

The main problems of remote sensing of the Earth’s surface within the frequency range 1.2–1.6 GHz are discussed. They are related to the resonant quantum properties of the radio wave propagation medium in the lower ionosphere. It is shown that, for the passive remote sensing, the main source is incoherent microwave radiation of the D and E ionospheric layers in the decimeter range. For the first time, a theoretically grounded principally new scheme of measurements is suggested. The scheme assumes that the radiation source exists below the satellite orbit and accounts for the fact that two types of radiation (direct and reflected) reach the satellite sensor. The separation of the respective fluxes is a serious problem that should be solved for the correct interpretation of the measurements. The question is raised regarding the correct calibration of measuring equipment, depending on the current state of the ionosphere.

The modern gravimetric equipment allows to register very small effects of gravity field changes and can be applied solving different geological, geophysical and environmental problems. However, sometimes insufficient calculation of various kinds of geological noise complicates effective application of detailed gravity field analysis. One of such factors is the temperature regime over and outside different buried objects of investigation. In this paper temperature changes in a subvertical zone over a hydrocarbon deposit and outside its contour are analyzed. The integrated density change and corresponding gravity effects are calculated for the Muradkhanly oil deposit situated within the south-east part of the Middle Kura Depression (central Azerbaijan). Calculation of these effects on the basis of density- temperature data correlation analysis could significantly improve the microgravity field examination over the hydrocarbon deposits. The similar correction procedure may be applied also over underground water horizons and some environmental targets.

Microgravity investigations are widely applied at present for solving various environmental and geological problems. Unfortunately, microgravity survey is comparatively rarely used for searching for hidden ancient targets. It is caused mainly by small geometric size of the desired archaeological objects and various types of noise complicating the observed useful signal. At the same time, development of modern generation of field gravimetric equipment allows to register promptly and digitally microGal (10-8 m/s2) anomalies that offer a new challenge in this direction. An advanced methodology of gravity anomalies analysis and modern 3D modeling, intended for ancient targets delineation, is briefly presented. It is supposed to apply in archaeological microgravity the developed original methods for the surrounding terrain relief computing. Calculating second and third derivatives of gravity potential are useful for revealing some closed peculiarities of the different Physical-Archaeological Models (PAMs). It is underlined that physical measurement of vertical gravity derivatives in archaeological studying has a significant importance and cannot be replaced by any transformation methods. Archaeological targets in Israel have been ranged by their density/geometrical characteristics in several groups. The performed model computations indicate that microgravity investigations might be successfully applied at least in 20–25% of archaeological sites in Israel.