Assessment of correctness conditionsin kinematic seismic tomography: uncertainty calculation and grid size approximation

Purpose. To justify and quantitatively evaluate the characteristic dimensions of regions L within which the linearization of the eikonal equation has a correct solution in the context of kinematic ray tomography based on the principles of geometrical optics. Methodology. The authors use the theoretical foundations for determining the correctness of solving the seismic problem of the kinematic ray tomography method based on Taylor approximation combined with regularization (the Geyko’s method). To assess the characteristic dimensions of the regions, model seismic profiles, including PANCAKE, as well as global mantle tomography data, are applied. The analysis was carried out using models of the velocity structure of the Earth’s crust and mantle in the Carpathian region, taking into account the main tectonic units. Findings. The characteristic dimensions of the linearization region, which determine the resolution of the method, vary significantly ‒ from  0.2 km in the crust to ≈100 km in the mantle. It was determined that these sizes mainly depend on the geometry of seismic rays and the velocity structure of the medium. The main factor influencing the size of region L was found to be the size of the time spline window selected when forming one-dimensional travel-time curves in the common midpoint format. It was established that the errors of the kinematic tomography method are errors in estimating the depth of penetration of refracted rays. The paper shows how to calculate these errors and use them to assess the accuracy of the kinematic tomography method in the format of seismic velocities. Originality. Quantitative criteria are proposed for the applicability of the linearized approach to solving the eikonal equation in heterogeneous media within the framework of the kinematic method using Taylor approximation. For the first time, a survey design network for regional tomography by the kinematic method with the possibility of setting the resolution was calculated. The effect of errors on the method’s results is demonstrated. Practical value. The study results have important applied significance for optimizing the configurations of seismic observation networks. They allow for a more substantiated parameterization when constructing kinematic models, ensuring a balance between resolution and stability of solutions. The methodology makes it possible to design kinematic tomography surveys using natural sources of seismic waves with predictability of results at a level comparable to deep seismic sounding methods, despite the uneven distribution of sources and receivers.