This article presents a tool to quantify uncertainties in magnitude–depth (⁠M‐H⁠) estimates for earthquakes associated with macroseismic intensity data. The tool is an open‐source code written in Python and is named quantifying uncertainties in earthquakes’ magnitude and depth (QUake‐MD). In QUake‐MD, uncertainties are propagated from the individual intensity data point (IDP) to the final magnitude (M), depth (H), epicentral intensity (⁠I0⁠) solution. It also accounts for epistemic uncertainties associated with the use of different intensity prediction equations (IPEs). For each IPE, QUake‐MD performs a sequential least‐square inversion process to estimate the central M, H value. QUake‐MD then explores the uncertainties around this central M, H solution by constructing a probability density function (PDF) constrained to be consistent with the range of plausible epicentral intensity I0⁠, a plausible depth range, and IDP uncertainties. The resulting PDFs of all IPEs provided to QUake‐MD are then stacked to obtain a final PDF of possible M, H, I0 solutions representative of both data quality and IPE epistemic uncertainties. This tool is geared toward end users who would like to grasp a more complete understanding of the uncertainties associated with historical earthquake parameters beyond the classical standard deviation values proposed today in parametric earthquake catalogs. We apply QUake‐MD to two events of the SisFrance macroseismic database to illustrate the challenges involved in building realistic spaces of M, H, I0 solutions reflecting the quality of the data and the epistemic uncertainties in IPEs.

中文翻译：

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QUake-MD：开源代码，用于量化宏观地震烈度的震级-深度估计中的不确定性

本文提供了一种工具，可量化与大地震烈度数据相关的地震的震级-深度（M-H⁠）估计值的不确定性。该工具是用Python编写的开放源代码，被称为量化地震震级和深度的不确定性（QUake‐MD）。在QUake-MD中，不确定性从单个强度数据点（IDP）传播到最终强度（M），深度（H），震中强度（⁠IO）解决方案。它还说明了与使用不同强度预测方程（IPE）相关的认知不确定性。对于每个IPE，QUAKE-MD都会执行顺序最小二乘反演过程，以估计中心的M，H值。然后，Quake‐MD探索围绕该中心M的不确定性，通过构造概率密度函数（PDF）的H解，将其约束为与合理的震中强度I0？的范围，合理的深度范围和IDP不确定性一致。然后将提供给QUake-MD的所有IPE的结果PDF进行堆叠，以获得代表数据质量和IPE认知不确定性的可能的M，H，I0解决方案的最终PDF。该工具面向最终用户，他们希望对参数化地震目录中今天提出的经典标准偏差值以外的历史地震参数的不确定性有更全面的了解。我们将Quake‐MD应用于SisFrance宏观地震数据库的两个事件，以说明构建M，H，