**Appendix A**

#### *Error estimation for o*ff*set measurements during the precursory plug extrusion*

To differentiate significant from erroneous pixel offsets during the precursory plug extrusion stage, we applied an analytical approach that is usually used to remove DEM errors for change analysis of river beds and slope failures. This approach uses stable areas for calculation of errors [65] that follow a normal distribution around 0 (i.e., no changes), and are assumed to be independent [66,67]. Following the approach of Lane et al. [68], we assume that the error of the point-to-point distance between DEMs is equal to the offset uncertainty, which may be expressed as:

$$
\sigma\_{offset} = \sqrt{\sigma^2 + \sigma^2},
\tag{A1}
$$

where σ is the standard deviation of offsets in a stable area with a size of 100 × 100 pixels. The statistic t-score is then calculated by the following equation of Bennet et al. [69]:

$$t\_{\text{score}} = \frac{\Delta\_{\text{px}}}{\sigma\_{offset}} \,\text{\,\,\,\,}\tag{A2}$$

where Δpx is the absolute pixel offset within the stable area. To determine whether the offsets of individual pixels in the stable areas are significant, a simple one-sided t-Test with a confidence interval of 80% (tc > 0.845) was applied to the area of real surface motion. Thus, only pixel offsets in the deforming area larger than the median of Δpx > tc were considered as real displacements. Moreover, since motion in the stage prior the first recognised eruption was directed towards the satellite, pixel offsets away from the satellite were omitted in the deformation area. Finally, pixel offsets for the same stage were compared with the Signal-to-Noise Ratio (SNR) to estimate the degree of error estimation:

$$\text{SNR} = \frac{ccp}{std} \tag{A3}$$

where ccp depicts the cross-correlation peak and std the corresponding standard deviation.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
