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We present a new method for gravity data inversion for the linear problem (reconstruction of density distribution by given gravity field). This is an iteration algorithm based on the ideas of local minimization (also known as local corrections method). Unlike the gradient methods, it does not require a nonlinear minimization, is easier to implement and has better stability. The algorithm is based on the finite element method. The finite element approach in our study means that the medium (part of a lithosphere) is represented as a set of equal rectangular prisms, each with constant density. We also suggest a time-efficient optimization, which speeds up the inversion process. This optimization is applied on the gravity field calculation stage, which is a part of every inversion iteration. Its idea is to replace multiple calculations of the gravity field for all finite elements in all observation points with a pre-calculated set of uniform fields for all distances between finite element and observation point, which is possible for the current data set. Method is demonstrated on synthetic data and real-world cases. The case study area is located on the Timan-Pechora plate. This region is one of the promising oil- and gas-producing areas in Russia. Note that in this case we create a 3D density model using joint interpretation of seismic and gravity data.

A new method to solve thermal conjugacy problems is presented for layered models with a thermal conductivity jump at their boundaries. The purpose of this method is to approximate the inverse thermal conductivity coefficient, which has breaks, by using a combination of step functions. A generalized continuous operator is constructed in a continuous space of piecewise–homogeneous media. We obtained an analytical solution for the stationary problem of heat conjugacy in the layered model with finite thickness and with Dirichlet–Neumann conditions at the external boundaries. An algorithm was constructed for downward continuation of the heat flux to depths that correspond to the top of the mantle layer. The advantages of this method are illustrated by testing the crustal seismic, gravity and geothermal data of a study area in the Urals and neighboring regions of Russia. We examined statistical relations between density and thermal parameters and determined heat flux components for the crust and the mantle. The method enables a downward continuation of the heat flux to the base of the upper mantle and allows us to determine the thermal effects of the lateral and vertical features of deep tectonic structures.

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