## 1 Introduction  
The radon-222 isotope is constantly formed in almost all natural environments during the radioactive decay of its parent radium-226 isotope. The half-life of radon is 3.82 days [1; 2; 3; 4; 5]. Radon is an inert gas, the physical and chemical properties of which allow it to be used as an optimal indicator for studying the processes occurring in the environment [6; 7; 8; 9; 10; 4]. First of all, radon is used as a tracer in its \"free\" state, which allows it to migrate freely in various media both in gaseous form and as a water-soluble compound [3; 11; 12; 13]. This process leads to the appearance of an emanation field in the near-surface horizons of rocks, grounds, and soils [3; 14; 15]. The analysis of emanation fields is widely used in geochemical, geophysical, and geodynamic research [4], including the search for mineral deposits [16; 17; 18; 19].  
Emanation studies carried out on the territory of the kimberlite fields of the Arkhangelsk diamondiferous province showed that anomalous values of radon radiation are observed above the kimberlite pipes [20; 21]. The authors showed that the nature of the distribution of radon over kimberlite pipes has a sub-annular shape, which is associated with the development of faults and fractures of the host lithologies [19; 22]. To explain the formation mechanisms of such radon fields, we carried out experimental work [23] to identify the radiation and physical parameters of the rocks of the kimberlite pipe. We showed that diatreme kimberlites are characterised by low values of emanation coefficient, the level of porosity, the activity of radium-226, and radon production rate. In turn, the country rocks, represented by the host Ediacaran sedimentary rocks V\({}_{2}\), produce the highest amounts of radon in \"free\" state and are characterised by high values of radiation and physical parameters (porosity, permeability).  
The radon radiation largely depends on the geological, geochemical, physical and radiation characteristics of the object [4; 24; 25]. Some authors [3; 4; 26; 27; 28; 29; 30] have paid attention to the porosity, density, and permeability of the rocks, which in turn depend on the temperature processes (as well as tectonic) that occur after magmatic crystallisation. Radon can enter the surrounding space both due to radioactive recoil and due to diffusion. To understand these processes, scientists have developed mathematical models of radon transport in solid geological media. There are three groups of radon transport models: diffusion (based on the diffusion equation) [31; 32; 33; 34; 35; 36], convection [37; 38], diffusion-convection and diffusion-advection [39]. However, the latest calculation results obtained from convection and diffusion-convection models show a low level of comparability with experimental data. This is due to the fact that the calculated versions of the models, as a rule, are very simplified, and most of them require very specific input parameters, which in some cases cannot even be determined for a real system [40]. The group of diffusion models show good results in convergence with experimental data, and at the moment, the diffusion mechanism is considered to be the main one for radon transfer process [36]. The results of modelling the processes of radon transfer are of great importance in radioecology, geological exploration and geophysics, for example, in the study of lithospheric-atmospheric relations, or the search for earthquake precursors or fossil deposits [41].  
The main purpose of this work is to study the distribution of radon radiation and the gas permeability of soils in the territory of a kimberlite pipe, as well as to calculate a model of diffusive radon transport along three profiles (pipe, near-pipe space, sandstones with siltstone interlayers of Ediacaran sedimentary rocks) using the results of the work [23]. In this work, we calculated the radiation and physical characteristics of the host rocks and kimberlite.