We investigate both analytically and numerically the dynamics of modulated waves in a modified Burridge and Knopoff mechanical model of earthquake. We take into account the velocity-dependent and hydrodynamics friction forces between the rock blocks of the system. The theoretical framework for the analysis is presented using the multiple scale expansion method. We show that the system can be governed by the complex Ginzburg–Landau equation, which admits soliton solutions. The modulational instability of the system is performed, showing that the bandwidth of instability increases with the friction forces parameter. The planar wave solution used as the initial condition leads to more unstable waves in the system with chaotic-like behaviour, allowing energy localization. It is also found that the wave parameters, namely, the frequency, magnitude and velocity (as well as the energy of the system) strongly depend on $\eta$. In the non-friction limit, the obtained waves propagate with a coherent behaviour for a very short time, before disappearing. Our results suggest that the damages caused by an earthquake can be important as the friction forces increase and may excite the possibility of relative predictions for the dynamics of waves propagating in the earth in the field of nonlinear science.

我们在地震的修正 Burridge 和 Knopoff 力学模型中对调制波的动力学进行了分析和数值研究。我们考虑了系统岩石块之间的速度相关摩擦力和流体动力学摩擦力。使用多尺度扩展方法提出了分析的理论框架。我们表明该系统可以由复杂的 Ginzburg-Landau 方程控制，该方程允许孤子解。执行系统的调制不稳定性，表明不稳定性的带宽随着摩擦力参数的增加而增加。用作初始条件的平面波解导致系统中更不稳定的波具有类似混沌的行为，从而允许能量局部化。还发现波参数，即频率，$\eta$. 在非摩擦极限下，获得的波以相干行为传播很短的时间，然后消失。我们的结果表明，随着摩擦力的增加，地震造成的损害可能很重要，并且可能激发非线性科学领域对地球中波传播动力学的相对预测的可能性。