## 1 Introduction  
In situ observations showed that slow deformation waves with propagation velocities much lower than those of transverse and longitudinal waves generated by earthquakes exist in Earth's crust. Slow deformation waves have different names with less essential differences, for example, seismoactive waves [1], creeping stress waves [2], tectonic waves [2, 3], plastic flow waves [4, 5, 6] etc. According to the concept of epicenter migration-related waves [7], their propagation velocities in the seismic belt may reach only several dozens of kilometers per year [8]. The presence of creeping waves can be related to the instability caused by frictional sliding [9]. As to the occurrence mechanism of these waves, it is believed that they are jointly triggered by external factors and the changes in the properties of the media in the focal area [10]. Inside the Earth's crust, there is an interlayer composed of volatile media. Under certain conditions, the propagation of slow deformation waves may be triggered in such volatile media, and they play a crucial role in seismic development and occurrence [11]. Studies on the plastic flow network and plastic flow waves of the continental lithosphere [5, 6] have shown that the driving force at the margin of the continental plate is transmitted over a long distance, primarily through the network-like flow and slow deformation waves in the lower lithosphere, including the lower crust and lithospheric mantle. This driving force also controls the intapseismic activities. Under the Indian plate's pushing effect, the deformation flow waves with different quasi-periodicity are present in the central and eastern Asian continent, such as ten-year and one-hundred-year period waves. Deformation and failure of solids under the action of external factors are among the top research concerns in materials science and engineering [12; 13]. In recent years, both the spatial and temporal scales of deformation and failure of solids studied by the researchers have constantly been expanding [14]. [PERSON] et al. [15] applied the continuous phase transition theory and the Lagrangian mechanics theory to construct a theoretical model of slow deformation waves in rock surrounding deep level tunnel. The scales related to slow deformation waves may range from global to atomic scales, and the types of loading causing the deformation and failure vary from short-term (rapid) loading to long-term loading (at creep rates) [16; 17]. The theoretical study by [PERSON] and [PERSON] [18] applied the multi-microcrack model to study the macroscopic brittle creep failure caused by microcrack growth under step loading and unloading in rocks. During large-scale field observations, significant variations of the geophysical field's spatial-temporal characteristics were measured to determine slow waves' features. It was found that the directional migration of the epicenter was a prevalent phenomenon, which could be observed, for example, in the Hindu Kush region [19; 20], in the Baikal Lake region of Siberia [21; 22], and in China [23]. As to the deformation waves at the laboratory level, compression and tensile tests have been performed for the sylvite, marble, and alkali halide samples. The slow deformation waves traveling in the samples were studied [24; 25]. It was found that the slow deformation waves traveling in the rock samples and the alkali halide samples were similar to those observed previously in the metallic materials [26]. All of these findings are of high significance to the study of slow deformation waves in geomaterials. Most of the existing experimental studies on the slow deformation waves have been conducted on such homogeneous materials as metals or metal halides, but less commonly on rocks. The propagation and evolution characteristics of the deformation waves in rocks have not yet been adequately studied. The microscopic and mesoscopic mechanism of the slow deformation wave has not been clearly explained.