In this paper, a novel explicit time-marching procedure, which adapts to the properties of the spatially discretized model, is discussed for the time-domain solution of elastodynamic problems. The proposed technique is entirely automated and highly effective, providing a very attractive formulation to analyse complex wave propagation models. The novel approach is second-order accurate, truly explicit, truly self-starting, and it enables adaptive algorithmic dissipation and extended stability limits. In addition, automated subdomain/sub-cycling splitting procedures may also be carried out in the analyses, enhancing the performance of the proposed formulation. In this context, the technique automatically divides the domain of the model into multiple subdomains (according to the properties of the discretized problem), in which different time-step values are applied, still guaranteeing stability and enabling more accurate and efficient analyses. Adaptive values for the time-integration parameters of the method, which are established following the elements of the adopted spatial discretization, are also considered, providing a locally-defined self-adjustable formulation. This approach allows creating a link between the applied spatial and temporal solution procedures, enabling their errors to be better counterbalanced. Expressions for the adaptive time-integration parameters of the method and for the limiting time-step values of the elements of the discretized domain are presented and discussed. At the end of the paper, benchmark analyses are performed to demonstrate the effectiveness of the proposed technique, considering illustrative theoretical problems and applied intricate models, which are equivalent to those of real applications in the OIL & GAS industry.