地球-空间力（地面作用）后果引起的波动数学探索
Mathematical Exploration of Wave Motion due to Earth-Space Force (Ground Action) Consequences
- Nigeria Institute of Soil Science（尼日利亚土壤科学研究所）
- Institute of Biopaleogeography named under Charles R. Darwin（以查尔斯·达尔文命名的生物古地理学研究所）
- Federal University of Lafia（拉菲亚联邦大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究通过建立和求解微分方程，并利用COMSOL模拟，数学探索了地面作用引起的波动传播，揭示了初始能量、介质属性及振幅频率对波动行为的影响，为地震预测和工程减灾提供指导。
AI中文摘要：
本研究从数学上探索了由地球-空间力（特别是地面作用）引起的波动。通过建立并求解控制微分方程，深入了解了这些力引起的复杂传播动力学。数值模拟对波动行为进行了建模，并对结果进行了分析以理解地面作用的影响。使用COMSOL Multiphysics模拟了初始波的产生和后续传播，该软件可模拟物理介质中的波动动力学。应用描述波动的偏微分方程以及傅里叶变换技术来分析频率分量。数学推导得出了波动方程，而COMSOL内置的统计分析工具对结果进行了分析。数据可视化采用了软件内的绘图工具来创建详细图表。波幅相对于距离（单位：km）在0 km处为0.001，在10 km处为0.001，距离跨度为10 km。振幅在0.05、0.1、0.15、0.2、0.25、1.05、1.1、1.15、1.2和1.25秒的时间间隔处记录。振幅和频率变化对行为的影响范围从案例1（0.2，200）中0.1振幅下的1秒到案例3（0.2，300）中0.2振幅下的1秒。结果表明：（1）初始能量输入显著影响传播特性，有助于地震预测和减灾设计；（2）传播细节强调了介质属性在塑造行为中的重要性，这对地震工程和准确的地面运动预测至关重要；（3）对振幅和频率的敏感性表明，调整参数可以优化基于波的地球物理调查和环境监测。本研究可作为理解波动动力学的政策指南，为建筑规范和防灾减灾策略提供信息，以减轻地震影响。
英文摘要：
This study mathematically explores wave motion induced by earth-space forces specifically ground actions. Developing and solving governing differential equations provides insights into intricate propagation dynamics caused by these forces. Numerical simulation modeled wave behavior and results were analyzed to understand ground action impacts. Initial wave generation and subsequent propagation were simulated using COMSOL Multiphysics which models wave dynamics in physical media. Partial differential equations describing wave motion alongside Fourier transform techniques were applied to analyze the frequency components. Mathematical derivations yielded wave equations while COMSOL's built-in statistical analysis tool analyzed results. Data visualization employed plotting tools within the software to create detailed graphs. The wave amplitude relative to distance km varied at 0.001 at 0 km and 0.001 at 10 km over 10 km. Amplitudes were recorded at intervals 0.05 0.1 0.15 0.2 0.25 1.05 1.1 1.15 1.2 and 1.25 s. The impact of varying amplitude and frequency on the behavior ranges from 1 s at 0.1 amplitude in Case 1 (0.2, 200) to 1 s at 0.2 amplitude in Case 3 (0.2, 300). Outputs indicate: (1) initial energy input significantly influences the propagation characteristics aiding seismic prediction and mitigation design; (2) propagation details underscore the medium properties' importance in shaping behavior vital for earthquake engineering and accurate ground-motion prediction; (3) sensitivity to amplitude and frequency suggests tailoring parameters can optimize wave-based geophysical surveys and environmental monitoring. This study serves as a policy guide for understanding wave dynamics to inform building codes and disaster preparedness strategies for mitigating seismic impacts.
