The article shows the possibility of solving an underdetermined system of petrophysical equations for carbonate reservoirs of polymineral composition containing calcite, dolomite, anhydrite, quartz and clay minerals characterized by a complex structure of the void space (a combination of intergranular pores, fractures and caverns), imposing restrictions on the proportions of mineral components and the coefficient of porosity. The solution of the system of petrophysical equations is calculated numerically by minimizing the value of the discrepancy function between the synthetic curves and well logging, measured in the borehole. The reliability of the solution of the system is studied with the exception of one or several methods and the corresponding petrophysical equations. It is shown that excluding from the system of petrophysical equations the parameters of a single geophysical method - density gamma gamma logging - leads to a slight loss of accuracy. When calculating porosity, the minimum complex of geophysical methods should consist of acoustic, neutron and natural gamma-activity method. The calculated values of the porosity coefficient are correlated with core determinations. The discrepancy between the computed values of the porosity coefficient from the geophysical survey data and the values of the porosity coefficient for the core is ±3%. An adaptation of the system of petrophysical equations for the complex structure of the pore space of carbonates is proposed. In the intervals of the section with secondary porosity, the system of petrophysical equations varies in accordance with the behavior of the acoustic wave. Using the results of logging on longitudinal waves, calculations were made of the cavernous and fractured constituents of the void space of carbonate rocks. It is obtained that the coefficient of fractured porosity of carbonate rocks varies from 0.01 to 1%. Coefficient of caverns porosity reaches 10%. The values calculated for the geophysical data of the coefficient of caverns porosity fit into the range of values determined on large core samples.
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