## Is it possible to estimate surface displacement vector via distance measurement in two directions? : A case of distance measurement at a lava dome of Mt. Unzen‐Fugen‐Dake

Yasuyuki HIRAKAWA, Takuya KANNO, Takeshi TAMURA, Masahiko MIYAWAKI and Kazuo YOSHIKAWA

#### Abstract

Distance measurement by Total Station (TS) is often used in long‐range monitoring for slope displacement. Assuming the vertical displacement can be ignored, distance measurements in two directions allow to calculate surface displacement vectors. However, it is unclear if the assumption is appropriate. In this study, the authors derived mathematical model representing the relation between 3‐dimentional vector of surface displacement and distance changes of two‐direction, and then examined the impact of the assumption of vertical component for calculating horizontal component by a case study of TS measurement in Mt. Unzen‐Fugen‐Dake. The results showed that calculated horizontal displacement could change up to 78 degrees in direction and 0.34 times in magnitude following the change of assumed vertical displacement in possible range. It was identified that the vertical displacement cannot be ignored easily. Furthermore, the authors proposed a method to estimate each component of 3‐dimention, using supplemental data from LiDAR. Three‐dimensional vector is likely to be estimated within a certain level of accuracy under the following conditions:(1) when the angle between two observation directions is larger than 25 degrees, and (2) when the angle between each observation direction of two TSs and estimated moving direction is smaller than 75 degrees.

#### Key words

surface displacement, vector, total station, distance measurement, long‐range monitoring