Characterization of explosive volcanic eruptive processes from interpretation of deposits is a key for assessing volcanic hazard and risk, particularly for infrequent large explosive eruptions and those whose deposits are transient in the geological record. While eruption size—determined by measurement and interpretation of tephra fall deposits—is of particular importance, uncertainties for such measurements and volume estimates are rarely presented. Here, tephra volume estimates are derived from isopach maps produced by modeling raw thickness data as cubic B-spline curves under tension. Isopachs are objectively determined in relation to original data and enable limitations in volume estimates from published maps to be investigated. The eruption volumes derived using spline isopachs differ from selected published estimates by 15–40 %, reflecting uncertainties in the volume estimation process. The formalized analysis enables identification of sources of uncertainty; eruptive volume uncertainties (>30 %) are much greater than thickness measurement uncertainties (~10 %). The number of measurements is a key factor in volume estimate uncertainty, regardless of method utilized for isopach production. Deposits processed using the cubic B-spline method are well described by 60 measurements distributed across each deposit; however, this figure is deposit and distribution dependent, increasing for geometrically complex deposits, such as those exhibiting bilobate dispersion.

中文翻译：

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制作等厚线图的客观方法及其对估计火山灰沉积量及其不确定性的影响

通过对沉积物的解释来表征爆炸性火山喷发过程是评估火山危害和风险的关键，特别是对于不常见的大型爆炸性喷发和那些在地质记录中沉积物是短暂的。虽然由火山灰沉积物的测量和解释确定的喷发规模特别重要，但很少提出此类测量和体积估计的不确定性。在这里，火山灰体积估计值来自通过将原始厚度数据建模为张力下的三次 B 样条曲线而生成的等厚图。等厚线是根据原始数据客观确定的，并且可以调查已发布地图中体积估计的局限性。使用样条等厚线推导出的喷发量与选定的已发表估计值相差 15-40%，反映了体积估计过程中的不确定性。形式化分析能够识别不确定性的来源；喷发体积的不确定性 (>30%) 远大于厚度测量的不确定性 (~10%)。测量次数是体积估计不确定性的关键因素，无论用于等厚线生产的方法如何。使用三次 B 样条方法处理的矿床通过分布在每个矿床的 60 次测量得到了很好的描述；然而，这个数字取决于沉积物和分布，几何复杂的沉积物会增加，例如那些表现出双叶形分散的沉积物。30 %) 远大于厚度测量不确定度 (~10 %)。测量次数是体积估计不确定性的关键因素，无论用于等厚线生产的方法如何。使用三次 B 样条方法处理的矿床通过分布在每个矿床的 60 次测量得到了很好的描述；然而，这个数字取决于沉积物和分布，几何复杂的沉积物会增加，例如那些表现出双叶形分散的沉积物。30 %) 远大于厚度测量不确定度 (~10 %)。测量次数是体积估计不确定性的关键因素，无论用于等厚线生产的方法如何。使用三次 B 样条方法处理的矿床通过分布在每个矿床的 60 次测量得到了很好的描述；然而，这个数字取决于沉积物和分布，几何复杂的沉积物会增加，例如那些表现出双叶形分散的沉积物。