## 1 Introduction  
The paper presents the problem of construction and validation of seismic wave Velocity Interval Depth (VID) models with the application of geophysical and geological data. One of the validation methods of VID models is the evaluation of spatial positioning errors of selected seismic horizons after the application of the PreSDM procedure in relation to the interpretation of well log datasets. This is the standard Quality Control (QC) procedure executed during the processing of reflection seismic data. It is correct in the areas where the wells have already been completed and the relevant well logs have been recorded. Additional applicability criteria of this validation method are depth interval and quality of recorded geophysical data. Unfortunately, the available geophysical datasets commonly do not cover the full depth interval. The lack of suitable well logs contributes to attempts to validate the VID models with the independent geophysical data [1, 2]. Taking into account the professional experience of the authors and the available publications [1, 2, 3], it is assumed that in the areas where the well-log markers are unavailable, it is necessary to use the processing results of data acquired with the geophysical methods other than reflection seismic, i.e., gravity and magnetotelluric. The geophysical method commonly used as complementary for seismic surveys is gravity. Its application is justified by close mathematical relationships of seismic wave velocity, bulk density of rock formations and their elastic parameters [4; 5]. In addition to gravity, the processing and interpretation of seismic data can be supported by the results of magnetotelluric surveys, which ensure the relatively great depth of geoelectric recognition of rock formations [6; 7] as well as a depth range independent of the distribution of seismic waves velocities. Unfortunately, the close physical relationship between the seismic wave velocity and the electric resistivity does not exist [4; 5; 8]. Thus, if the methods based on the resistivity distribution within the rock formations must be applied, the empirical statistical relationships are in use [4; 5; 9]. In practice, the determination of correlations between resistivity and seismic wave velocity is possible for genetically defined, relatively homogenous rock formations but, unfortunately, it often is rather ambiguous. Modern statistical methods are quite helpful [4] together with machine learning methodologies [10; 11; 12; 13]. In the project reported below, the authors applied the modern method of integrated inversion of independent geophysical data, which is still under development. The definition of this method is quite broad and is often equated with the SJI, i.e., one of the options of the Cooperative Joint Inversion (CJI) methodology [9; 14]. Another variant of this method is the CJI with the application of structural (or parametric) bonds, which replace the not-always correlations between various physical parameters (velocity, density and resistivity) [3; 9]. In the Polish literature, this CJI variant is known as the integrated inversion (interpretation) with constraints (Integrated Inversion Interpretation) [6; 7; 15]. In this variant, more emphasis is placed on the structural image than on ensuring the correlation of physical parameters at a satisfactory determination level \(\mathbb{R}^{2}\). Due to the progress in the development of these methodologies and access to relevant software tools, this CJI variant has become the additional validation method of velocity field determinations. The SJI method provides automatic and simultaneous computation of inversion for two or more sets of geophysical data, which are completely independent of each other [1; 2; 3; 9]. It must be emphasized that the procedure described in this paper has already been the subject of interest by leading working groups in the world involved in the development of this methodology [1; 2; 3; 9; 14]. Also, the research teams from Poland focused on the following subjects [15; 16; 17; 18; 19; 20].