The authors describe a modified scenario simulation to assessing the risks of financial instruments. It is based on the technique proposed by F. Jamshidian and Y. Zhu, which allows considerable acceleration of calculating risk indicators for large portfolios, relative to the Monte Carlo approach. The modification proposed in this work consists of changing the way of selecting scenarios (points of the approximating distribution) and allows the quality of the approximation and the accuracy of the estimates to be improved. It does not impose restrictions on the distribution of factors influencing the portfolio price, expanding the scope of its application. The VaR indicator estimates obtained in the two ways are compared in a financial portfolio consisting of an interest rate swap for cases where the values of the factors influencing its price have normal, gamma, and Student’s t distributions.

The concept has been substantiated and a statistical analysis procedure has been developed to identify regularities of spatiotemporal distribution of parameters of deterministic and random processes occurring in the geomechanical space of geotechnical objects at the industrial development stage. The approach consists in long time series creation describing: (1) the evolution of stress fields S (obtained by calculation using a verified 3D geomechanical model); (2) the number N and total energy W of seismic events caused by mining operations in various spatial blocks of the object under study. Next, the correlation coefficients between these series were calculated and statistically significant relationships N-S and W-S were revealed, which can be used for predictive estimates of the integral parameters of the seismic process. When implementing the approach, based on the induced seismicity database of the Tashtagol ore mine (Kemerovo region, Russia) and the original 3D geomechanical model (implemented by FEM), it was established that: with increasing mining depth, the centers of seismic energy release in blocks migrate towards the goaf and located, as a rule, in the ore body; at almost all mining levels, there are pairs of spatial blocks in which the total energy W and the number N of seismic events have a strong correlation with the average value of the maximum shear stress.

The continuum dual-porosity medium model is used to substantiate and to evaluate under laboratory conditions the method for determination of parameters (permeability of fractures $$k_{1}$$ and matrix $$k_{2}$$ and mass-transfer coefficient $$\beta$$ ), describing mass transfer processes in the fractured-porous rock masses on the basis of solution to inverse problems by the stationary percolation test data. The researchers proposed and employed the test scheme involving three sequential measurements of the stationary flow rate ( $$F_{0}$$ , $$F_{1}$$ and $$F_{2}$$ ) in a specimen at different input pressure values: according to the standard scheme $$F_{0}$$ , the fractures are sealed at one $$F_{1}$$ and other $$F_{2}$$ ends of the test specimen. The model of the experiment is developed, the analytical solution is obtained for the direct problem on unidimensional steady flow of fluid in a dual-porosity medium, viz. distribution of pressure in fractures and a matrix. The algorithm for solution to an inverse problem is derived with determination of $$k_{1}$$ , $$k_{2}$$ and $$\beta$$ by the recorded flow rates. The approach allowing establishment of the empirical dependence of $$k_{1}$$ and $$k_{2}$$ versus effective stress is theoretically justified and verified on the basis of simulated data. The numerical analysis revealed low stability of inversion procedure by input data, so higher precision of the process can be gained due to a series of measurements at increasing input pressure with subsequent smoothening of obtained results.

Разработан и в лабораторных условиях на слоистых образцах из искусственного геоматериала апробирован экспериментальный метод, позволяющий в рамках модели среды с двойной проницаемостью определить параметры, контролирующие процессы миграции флюидов и пороупругое деформирование трещиновато-пористых породных массивов - трещинную проницаемость k1 и коэффициент массообмена β, а также их зависимость от напряжений σ. Предложена и реализована процедура испытаний: при ступенчато возрастающем нормальном напряжении σ измеряются стационарные расходы Q1(σ) и Q2(σ) в трещиновато-пористом образце квазирегулярной структуры при заданном перепаде давления: по стандартной схеме (Q1) и закрытых трещинах на торце (Q2). Создана математическая модель эксперимента, получено аналитическое решение задачи о стационарной фильтрации: распределение давления в трещинах и матрице, зависимость расходов от σ. Представлен алгоритм для интерпретации данных эксперимента - расчета k1 и β по зарегистрированным расходам Q1 и Q2. Показано, что проницаемость k1 пропорциональна σ -2, а β практически не меняется. The experimental procedure is developed and tested on a laboratory scale and using layered samples of manmade geomaterials. Within the dual-permeability model, the procedure enables determining parameters that govern fluid flow and poroelastic deformation in fractured porous rock masses, namely, fracture permeability k1 and mass transfer coefficient β, as well as their dependence on stresses σ. The testing procedure is proposed and implemented. In the procedure, under the stepwise increasing normal stress σ, the stationary flow rates Q1(σ) and Q2(σ) are measured in a quasiregular fractured porous sample at the preset pressure difference: using a standard setup (Q1) and in closed end-face fractures (Q2). The mathematical model of the experiment is constructed, and the analytical solution of the problem on stationary flow is obtained: pressure patterns in fractures, and stress-dependence of flow rates. The experimental data interpretation algorithm enables calculating k1 and β by the recorded flow rates Q1 and Q2. It is shown that the permeability k1 is proportional to σ -2, and β remains almost unchanged.

Within the framework of a geomechanical model that describes deformation of rock mass during extraction of subhorizontal coal beds, the outburst hazard mechanism is substantiated: the approach of a working face to a weak zone at the coal-bed-host rock interface initiates tensile stress areas, which creates the prerequisites for the face spalling and loss of coal with methane. The inverse problem of determining conditions at the horizontal boundaries of a coal bed is formulated and solved using tomography data (patterns of P-wave velocity V) and the empirical dependence of V on the mean normal stress sigma. Lab-scale test results on stepwise compression of parallelepipeds made of artificial geomaterials are presented. Tomography of the specimens was performed by acoustic sounding data, and the pattern of velocities V* was obtained. Using the pre-found empirical dependence V(sigma) for geomaterial, the distribution sigma*=V-1(V*) in the specimen was calculated, which served as the input data for the inverse problem on the shear stresses sigma xy at the specimen- press plate interface. The inversion of the lab data confirmed the possibility of identifying weak zones at the boundaries where sigma xy approximate to 0. These zones are associated with probable sources of failure and outbursts.

The experimental procedure is developed and tested on a laboratory scale and using layered samples of manmade geomaterials. Within the dual-permeability model, the procedure enables determining parameters that govern fluid flow and poroelastic deformation in fractured porous rock masses, namely, fracture permeability k_1 and mass transfer coefficient β , as well as their dependence on stresses σ . The testing procedure is proposed and implemented. In the procedure, under the stepwise increasing normal stress σ , the stationary flow rates Q_1(σ) and Q_2(σ) are measured in a quasiregular fractured porous sample at the preset pressure difference: using a standard setup ( Q_1 ) and in closed end-face fractures ( Q_2 ). The mathematical model of the experiment is constructed, and the analytical solution of the problem on stationary flow is obtained: pressure patterns in fractures, and stress-dependence of flow rates. The experimental data interpretation algorithm enables calculating k_1 and β by the recorded flow rates Q_1 and Q_2 . It is shown that the permeability k_1 is proportional to σ^-2 , and β remains almost unchanged.

Theoretical substantiation and lab tests of the method for synthesis of a relationship describing angular anisotropy of the effective permeability in borehole environment based on the inverse coefficient problem solution in terms of the data on percolation tests of regularly non-uniform cylindrical specimens with a central hole are set forth in the paper. With a view to provide the algorithmic support of GIS data inversion in the course of determination of poroperm properties of production intervals the researchers developed and implemented by the hybrid numerical method to realize the multiphysical model of the evolution of geomechanical and electrohydrodynamic fields under filtration of multiphase fluid in the borehole environment with consideration for anisotropy of permeability induced by difference in components of the external stress fields. The numerical experiments enabled to establish that in the overbalanced drilling the configuration of invaded zone depends on the proportion between horizontal stress components outside of the well influence zone.

Within the framework of a geomechanical model that describes the deformation of a rock mass during the subhorizontal coal-bed extraction, the mechanism for the formation and implementation of a sudden outburst is substantiated: as working face gets close to the weak zone of coal-bed – host rock joint, areas of tensile stresses arise, which creates the prerequisites for face space spalling and coal loss with methane. The inverse problem of determining the conditions at the horizontal boundaries of a coal-bed is formulated and solved using tomography data (longitudinal wave velocity V distribution) and the empirical dependence of V on the mean normal stress σ. Lab tests results on stepwise compression of parallelepipeds made of artificial geomaterials are presented. Tomography of the specimens was performed by acoustic sounding data, and the distribution of velocities V* was found. Using the pre-established empirical dependence V(σ) for geomaterial, the distribution σ*=V-1(V*) in the specimen was calculated, which served as input data for inverse problem of determining the shear stresses σxy at the “specimen faces – press platens” joints. Lab data inversion confirmed the possibility of identifying weak zones of the boundaries where σxy=0. These zones are associated with probable nucleus of failure and sudden outbursts.

A dual-porosity continuum model describing mass transfer in fractured porous reservoirs is used to develop and algorithmically implement a method for the quantitative estimation of the matrix and fracture permeabilities by solving the inverse coefficient problem whose input data are well output measurements in the stop–start operation mode. The algorithm is based on the obtained analytical solution of the direct problem of the evolution of hydrodynamic fields in the near-wellbore zone. The results of numerical experiments show that the inverse problem has a unique solution with a moderate level of noise in the input data.

The authors have developed and implemented a 3D geomechanical model using the finite element method for a typical configuration of an underground space during room-and-pillar mining. The authors formulate and solve an inverse problem on determination of values and orientation of external horizontal stresses and deformation characteristics of structural elements of the geotechnology by the measurement data of sidewall convergence in rooms in the course of mining. The level curves of different objective functions are analyzed, the mixed inverse problem resolvability is demonstrated, and the equivalence domain size is correlated with the relative error of input data.

The method for correlation of poroperm properties and effective stresses in weakly coherent rocks has been developed and tested on a lab scale. An appropriate lab testing installation is designed and manufactured; it includes a hydraulic press, a system of force plungers, a polyurethane measurement cell to be filled with sized sand, a compressor and a high-precision autonomous measurement system for fluid flow rate and pressure. The method consists in sequential steady-state and unsteady-state flow tests of a granular geomaterial sample placed in the measurement cell where nonuniform stress state generated by application of the external load to the cell. In the unsteady-state flow tests, the change in pressure was measured during gas release from the cell. In the steady-state flow tests, the flow rates were measured at the varied input pressure. The measured flow rates and pressures were used as the given data in the inverse coefficient problems on determinations of the empirical parameters in the exponential dependence of porosity, permeability on effective stress. Resolvability of the formulated inverse problems within the nonlinear models of mass transfer in a granular media is demonstrated.

The nonlinear model has been developed and implemented to describe gas emission from coal slack placed in a sealed container ('canister test'). The model accounts for initial gas content S, coefficients of diffusion D, mass transfer beta and desorption kinetics gamma, as well as for fractional composition of the sample. Using the developed analytical method of the initial boundary value problem solution, it is found that the pressure P(t) of gas in the container tends to a constant value with time. The inverse problem of determining the kinetic parameters S, D, beta and gamma of gas by the pressure P(t) readouts in the experiments has been formulated and subjected to solvability tests. The introduced objective function (discrepancy between P(t) and the calculated pressure) is almost independent of beta. Based on the modification of the conjugate gradient method, the inverse problem algorithm is proposed. Using the data of in situ measurements of pressure in three containers, the authors perform quantification of gas content, as well as diffusion and desorption kinetics coefficients in terms of a coal bed in Berezovskaya Mine (Kuznetsk Coal Basin). The range of the mass transfer coefficient is estimated by the results of the grain-size analysis of the test samples.

The process, justified by theory and physical modeling, enables to establish dependence of poroperm properties of loose geomaterials versus fluid pressure and stresses. The laboratory unit designed and manufactured by researchers, comprises a measurement cell filled with a loose material, a hydraulic press, and a recorder of pressure, flow rate, and stress $$ \sigma_{m} $$ , stepwise applied to the cell. At each loading stage the permeability test was carried out at different input gas pressures $$ p_{n} $$ . The stationary measured flowrate data $$ Q_{mn} $$ and the back analysis were employed to establish the empirical permeability–effective stress dependence, followed with approximation by two-parameter exponential function. The measurement cell was vacuumized at fixed $$ \sigma_{m} $$ the cell was connected to a vessel, filled with air of a preset mass. Porosity $$ \varphi_{m} $$ was calculated based on the equilibrium pressure gained in “cell–vessel” system. The experiments performed with the medium-grained sand revealed that the exponent factor characterizing the relationship between permeability and effective stress is something like 0.02 bar−1; the permeability–porosity relation can be described by a power function; thereto, Kozeny–Carman equation is fulfilled with good precision as well.

The reservoir properties (reservoir properties) of reservoir rocks depend not only on the petrophysical characteristics of the formation, but also on the stresses acting in the rock mass. The redistribution of the latter during drilling causes the occurrence of permeability anisotropy in the near-wellbore zone, which affects not only the flow characteristics of the wells, but also the process of penetration of the drilling mud filtrate into the formation. This should be taken into account when building a geomechanical-electrohydrodynamic model of the near-wellbore space. The results of filtration tests of regularly inhomogeneous cylindrical samples made of artificial geomaterial are presented and a method for synthesizing the dependence of the effective permeability on the polar angle based on the solution of the coefficient inverse problem is proposed. The obtained dependencies added to the database of reservoir properties of rocks used for inversion of GIS data for quantitative assessment of reservoir properties, an example of which is presented in this article.

The research methodology for anisotropic permeability of geomaterials due to nonuniform stress state is theoretically justified and tested on a laboratory scale. The poroperm properties of fine grain sand and cryogel are investigated in diametral compression tests of cylindrical specimens with a center hole. The time-independent flow rate is measured in various areas of side surfaces of the specimens. The inverse coefficient problem on empirical permeability–effective stress relationship is formulated, and its solvability is demonstrated.

This paper is focused on research into options pricing models. The most popular ones are variancegamma and Heston models. They are powerful and flexible to some extent, but they also have drawbacks. Among their shortcomings are instability and long-time calibration. The model proposed in the paper combines neural network (autoencoder) and relatively simple option pricing (mixture normal) model. The autoencoder gives flexibility to the model and reduces the number of parameters. The mixture normal model gives a certain logic to neural network and minimizes calibration time of the new model. So the resulting model eliminates drawbacks of variance-gamma and Heston models and also keeps their advantages. It has fast calibration and shows good enough precision on S&P futures options market.

Thermobaric tests are performed on Bazhenov oil-bearing shale containing above 10% of kerogen in view to determine its rheological properties. The test specimen under a statistical axial load is heated stepwise at temperatures \( T_{n} = 60 \), 100 and 150 ℃ with measurements of height \( H\left( t \right) \). The temperature is risen if relative velocity of \( H \) gets less than 0.05. Deformation of the specimen is described by Kelvin–Voigt model, within which the inverse problem is stated and solved to determine Young module \( E_{n} \) and effective viscosity \( \eta_{n} \) of rocks by \( H\left( t \right) \). The results of solution are approximated by two-parameter exponential functions, \( E = E\left( T \right) \) and \( \eta = \eta \left( T \right) \) relationships are established.

Method of estimation of rheological properties of constructive elements of room-and-pillar mining of solid mineral deposits is considered. The method is based on solution of inverse problems of mixed type in the context of two dimensional viscoelastic model of structure. Feasibility of in situ determination of parameters for constitutive equations describing rheological deformation of rocks is shown. The numerical experiments implemented with synthetic input data (relative displacements recorded at the points of mined-out void boundary using in-mine geodetics techniques) for the preset absolute precision of equipment provide the measurement data amount required to ensure resolvability of inverse problem.

Under consideration is the approach allowing quantitative estimation of natural stress field components in the vicinity of underground objects based on solution of an inverse boundary-value problem using the data on acoustic sounding in an extended mine working. To ensure solvability of an inverse problem, the optimal sonic transmitter-receivers positioning and the limiting nominal error of measurements are determined. The objective function is set as a root-mean-square difference between the theoretical and actual head P-wave arrival times at the receivers; unimodelity of the objective function is illustrated using synthetic input data.

The method for determination of mass transfer and filtration characteristics of fractured porous reservoir rocks, considered as dual porosity and dual permeability media is developed and implemented under laboratory conditions. The procedure for filtration tests consists in series of three measurements of the fluid flowrate in the same specimen: standard scheme (\( Q_{0} \)), fractures are tamped at one face (\( Q_{1} \)) and at another face (\( Q_{2} \)). The mathematical model of the experiment is developed; analytical solution is worked out to the problem on the stationary filtration in a dual permeability medium; the inversion relationships are derived based on the new solutions in view to calculate fracture \( k_{1} \) and matrix \( k_{2} \) permeability as well as mass transfer coefficient by using the measured flowrate values \( Q_{0} \), \( Q_{1} \) and \( Q_{2} \). Numerical analysis revealed low stability of the inverse problem solution against input data, as this implies more rigorous requirements regarding measurement precision. The laboratory tests of the oil-bearing rock specimens of Bazhenov formation with well pronounced fracturing justifies that ratio \( k_{2} /k_{1} \) lies within the range 0.04–0.055.