tokens: environment theoretically depends on the Mach number or wave amplitude (e.g., Priest 2014 ; Vršnak et al. 2016 ). As the shock wave propagates, its amplitude decreases due to the geometric expansion of its front and the fact that its leading edge is propagating faster than its trailing edge. The amplitude decrease results in the deceleration of the shock wave. Additionally, a power-law fit is a better representation of the distance–time curves of freely propagating shock waves (Warmuth Mann 2011 ) according the the Sedov solution (Sedov 1959 ). On the other hand, we found that the speed of the reflected wave (243.1 ± 30.8 km s −1 ) is much smaller than the speed of the incident wave (which approximately equals that of the unaffected wave at around 05:13 UT: 591.0 ± 25.9 km s −1 ). In other words, the reflected wave was slower than the primary wave. There may be several possibilities for this feature. The primary wave is a nonlinear wave or shock, which is propagating with a Mach number larger than unity, while the reflected wave had changed to be a linear one traveling at the characteristic speed (Liu Ofman 2014 ; Warmuth 2015 ). The reflected wave has to propagate in the rest frame of the flow field associated with the primary wave, which may result in an apparently lower speed (Kienreich et al. 2013 ). Additionally, it may be related to the properties of the medium (magnetic separatrix) causing the shock wave to reflect. The compressible magnetic separatrix may cause the decrease in the reflected wave speed, when the shock wave reacted with the magnetic separatrix. Moreover, it is interesting to find that the refracted and diffracted waves decelerated with a bigger nonconstant deceleration rate. We find that their deceleration rate was decreasing with time, as in a damping motion. These phenomena would help us to further understand the nature of the interaction between magnetohydrodynamic shock waves and the local magnetic field. Appendix Error Estimations In this study, we determine the dynamic characteristics of EUV waves by using the method in Liu et al. ( 2010 ). The track technique ignores the heights of EUV waves by assuming that all emission originates from the spherical solar surface, and this distance measurement was corrected by the sphericity of the solar photosphere. This method would cause an overestimation in the measurement of some parameters (e.g., distance, velocity). We will supply some error estimations in subsequent sections. As Figure A1 (a) shows, a coronal structure B at a height of Δ h above the solar surface is projected onto the solar surface A observed by an observer on Earth (E). We set a new “north pole” at the disk center ( D ) and make AC = d , AC ⊥ OE, OA = OD = R ⊙ , OB = OF = R ⊙ + Δ h , and DE = 1 au. Defining θ = ∠AEO, we can get We make OG ⊥ EG and get Then, we getAccording to the law of sines, in △BOE, we can get Based on the above equations, we can get whereFirst, if the EUV wave originally
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