In this paper, two fully-adaptive explicit time-marching procedures are discussed for the time-domain solution of wave propagation in elastic media. In these procedures, the time integration parameters of the methods are adaptively locally evaluated, following the properties of the discretized model and the values of the calculated responses, engendering more accurate solution procedures. In addition, automated domain decomposition and sub-cycling procedures are also performed, providing more efficient analyses. In this case, a domain decomposition procedure divides the domain of the model into different time-marching subdomains according to the properties of the discretized problem and the stability limit of the adopted time-marching technique, so that a different time-step value is applied to each subdomain, leading to more efficient (and yet stable) explicit time-domain computations. As it is indicated in this work, the adoption of multi-time-steps/sub-cycling splitting procedures further improves the accuracy of the discussed adaptive time-marching formulations. At the end of the paper, benchmark analyses are performed to illustrate the effectiveness of the proposed techniques, followed by synthetic case analyses, with degrees of complexity equivalent to that of real geophysical applications in the OIL & GAS industry, demonstrating the robustness of the proposed explicit approaches.

在本文中，讨论了弹性介质中波传播的时域解的两种完全自适应显式时间推进程序。在这些程序中，根据离散模型的特性和计算响应的值，方法的时间积分参数被自适应地局部评估，从而产生更准确的求解程序。此外，还执行自动域分解和子循环程序，提供更有效的分析。在这种情况下，域分解过程根据离散化问题的性质和采用的时间推进技术的稳定性极限将模型的域划分为不同的时间推进子域，从而应用不同的时间步长值到每个子域，导致更有效（且稳定）的显式时域计算。正如这项工作所表明的，采用多时间步/子循环分裂程序进一步提高了所讨论的自适应时间推进公式的准确性。在论文的最后，进行了基准分析以说明所提出技术的有效性，然后进行综合案例分析，其复杂程度与石油和天然气行业中实际地球物理应用的复杂程度相当，证明了所提出技术的稳健性明确的方法。