Bull. Volcanol. Soc. Japan
Vol. 58 (2013) No. 1, pp. 291-306

ArticleEllipse-approximated Isopach Maps for Estimating
Ashfall Volume at Sakurajima Volcano
Yasuhisa TAJIMA＊, Keiji TAMURA＊＊,†, Takao YAMAKOSHI＊＊,Akira TSUNE＊＊＊ and Shinjiro TSURUMOTO＊＊＊＊,††(Received May 6, 2011 ; Accepted January 7, 2013)
In studies of volcanic tephra, it is usual that the overall volume of tephra is estimated ashfall volumes based on
representative locations within the ashfall area. The precision of the volume estimation largely depends on the numberof the locations. However, in the case of ongoing eruptions on island volcanoes, such as Sakurajima volcano, theobservation locations are usually limited. We therefore have developed a practical method for estimating ashfallvolume and distribution in such case. The method approximates the distribution of ashfall as ellipses, with the-1distribution area (A) and thickness or weight of deposit (T) determined by A =αT . The ellipse-approximatedisopachs can be determined by using the direction of the ellipse axis and ashfall data at two points. In determing theellipse axis exactly, we usually need additional ashfall amounts from the other locations. We set 37 samplers around
Sakurajima volcano, and retrieved the samplers 15 times, from April to December, 2008. Using the propose method,
we are able to determine the volume of ash produced by small, continuous eruptions.
Key words : ashfall distribution; isopach; ellipse approximation; volume estimation; Sakurajima volcano

1．Introduction
The difficulty of ashfall volume estimation for small
islands or short intermittent eruptions in Japan is a majorissue, when forecasting the progress of volcanic eruptions.
Hence, we propose a tool for estimating ashfall volumeusing limited ashfall observation locations as inputs. Suchtool is useful in the case of ongoing eruptions when observation locations are usually limited.
Many authors have proposed methods to calculate thedistribution or volume of pyroclastic falls. The most advanced method is to produce an isopach map (lines ofequal thickness) of tephra deposits, based on many points
determined by geological surveys. Other approaches tovolumetric calculations include simulation models basedon the dynamics of the eruption column and existingmodels or codes (Ishimine, 2007). An isopach is a contour
line that shows the same thickness of tephra for a given
area. Whole ashfall volume can be estimated using
isopach map by applying integral calculus. Many studies
have shown that tephra thickness decreases exponentiallywith distance from the vent. Thorarinsson (1954) showed＊

Nippon Koei Co., Ltd., 2, Kojimachi, 4-chome, Chiyodaku, Tokyo 102-0083, Japan.
＊＊
Public Works Research Institute, 1-6 Minamihara,Tsukuba-shi, Ibaraki 305-8516, Japan.
＊＊＊
Deep Ocean Resources Development Company, Ltd.,
1-3-15, Nihonbashi Horidome-cho, Chuo-ku, Tokyo
103-0012, Japan.
＊＊＊＊
Ministry of Land, Infrastructure, Transport and Tourism,
Osumi Office of River and National Highway, 1013-1

important results related to the exponential decrease intephra thickness with increasing distance from the source.
Porter (1973) considered that the correlation of thickness
and distance followed a power relationship for Hawaiian
tephra. Suzuki (1981) presented a logarithm approximation method that explained these correlations.
If the area and tephra thickness are correlated, then thevolume of tephra can be deduced. Rose et al. (1973)
estimated ashfall volume by integrating the plot of log (T)against log(A) with distribution area (A) and thickness orweight of deposit (T). Recently, ashfall deposits wereshown to follow exponential decreases of log(T) againstlog ( A ) for plinian tephra (Pyle, 1989). Fierstein andNathenson (1992) used two proximal and distal exponential rates (κ) of the plot of log(T) against log ( A ),which changed at the break in slope, in order to calculate
the volume. Bonadonna and Houghton (2005) used apower method to estimate the volume of Plinian tephra
deposits. When using the exponential method or thepower formula, many isopachs are required to estimate theashfall volume over large areas accurately.
Shintomi, Kimotsuki-cho, Kimotsuki-gun, Kagoshima893-1207, Japan.
†Sabo and Landslide Technical Center††
Ministry of Land, Infrastructure, Transport and Tourism,
Miyazaki Office of River and National Highway
Corresponding author: Yasuhisa Tajima
e-mail: tajima-ys@n-koei.jp