Degradation mechanisms and efficiency of heavily cratered regions on Ceres: Supplementary Materials

Summary This repository contains Python code and supporting data for analyzing crater size-frequency distributions (CSFDs) on Ceres. The package combines crater count data derived from mapped imagery with analytical production and equilibrium models to estimate surface ages and characterize equilibrium states. The main analysis script is `csfd-ceres.py`, which processes multiple counting regions defined in an Excel parameter table. Code Code Overview The main analysis script (`csfd-ceres.py`) performs the following steps for each counting region listed in `parameters.xlsx`: 1. Reads crater diameter data or an existing CSFD file for the region 2. Computes the observed CSFD normalized by map area 3. Calculates the cumulative crater density at 1 km diameter, N(>1km) 4. Computes Lunar-Derived (LDM) and Asteroid-Derived (ADM) production curves 5. Visually aligns the production curves with the observed CSFD over the production-dominated diameter range 6. Estimates best-fit surface ages from the LDM and ADM chronology functions 7. Computes an analytical equilibrium CSFD curve parameterized by β and ρ 8. Generates and saves a log-log CSFD plot and prints a summary of the parameters The code is written in a modular format, with each function performing a single step in the CSFD analysis pipeline. Parameter estimation In addition to the main analysis pipeline, this repository includes a parameter estimation script (`parameters.py`) used to derive CSFD parameters prior to running the full CSFD analysis. This script reads region data from `parameters.xlsx`, constructs cumulative CSFDs from crater CSV files, and applies piecewise log–log fits across a specified break diameter. The production normalization (ξ) and equilibrium slope parameter (β) are estimated for each region, while the production slope is fixed at η = 3.2. The resulting parameters are provided as fixed inputs to the main CSFD analysis script. This calibration code is intended for parameter derivation and validation only and is not executed as part of the final production workflow. Definitions and notation for the CSFD parameters (η, ξ, β, ρ) follow El Ghazal et al. (in review) and Hirabayashi et al. (2024). Code Input The primary inputs to the code are: - `parameters.xlsx` - Crater CSV files containing diameters for each region Details on these inputs are described in the Data section below. Code output For each counting region, the code produces: - A log–log CSFD plot showing: - The observed cumulative CSFD derived from crater counting - The best-fit LDM production curve - The best-fit ADM production curve - The analytical equilibrium CSFD curve All figures are saved as PNG files in the same directory as the corresponding input files. After all regions are processed, a summary of fitted parameters is printed to the terminal. Example outputs can be found in the repository. Data The crater data used by this package consists of crater diameters measured from mapped imagery of Ceres using QGIS. Craters are manually identified and measured within defined counting regions. Target locations Crater counts were performed in five countng regions located in the Ac-2, Ac-6, Ac-8, and Ac-12 qudrangles on Ceres. These regions were selected to represent heavily crater terrains with minimal evidence of recent resurfacing. A map showing the locations of the counting regions can be found in this repository (El Ghazal et al., in review). What this data compiles Each dataset compiles individual crater identifications into region-based crater populations suitable for crater size–frequency distribution (CSFD) analysis. These crater populations are used to derive cumulative CSFDs normalized by map area, which serve as inputs for production and equilibrium modeling. Data format: Crater CSV files - One file per counting region - One row per crater - Required column: `Diam_km` (crater diameter in kilometers) These files are produced from manual crater counting in QGIS and represent the raw crater measurements used by the analysis. Parameter table (`parameters.xlsx`) - One row per counting region - Required columns: - 'quadrangle' - 'ref' - 'file name' - 'area (km2)' - 'break diameter' - 'eta' - 'beta' - 'rho' Additional columns may be present but are ignored by the code. How the data is used For each row in `parameters.xlsx`, the code locates the corresponding crater CSV file using the `file name` field. The script automatically converts each CSV file into a `.txt` file if one does not already exist. These files contain two columns: Crater diameter (km) and CSFD (km\^-2\) The resulting CSFDs are used to fit production curves, estimate surface ages, and compute the analytical equilibrium CSFD for each counting region. How to Use 1. Place `csfd-ceres.py` and `parameters.xlsx` in the same directory 2. Place crater CSV files (`*.csv`) in the same directory or update the data path in the script 3. Run the script using Python References: Hirabayashi, M. et al. (2024), "Crater Equilibrium State Characterization given Crater Production from a Single Power Law," PSJ, 5, 250, doi:10.3847/PSJ/ad8883 El Ghazal, R. et al. (in review), "Degradation mechanisms and efficiency of heavily cratered regions on Ceres" (in code) Hiesinger, H. et al. (2016), "Cratering on Ceres: Implications for its crust and evolution," Science, 353(6303) doi.org/10.1126/science.aaf4759 Neukum, G. et al. (2001), "Cratering Records in the Inner Solar System in Relation to the Lunar Reference System," doi.org/10.1007/978-94-017-1035-0_3摘要 本仓库包含用于分析谷神星（Ceres）表面撞击坑尺寸-频率分布（crater size-frequency distributions, CSFDs）的Python代码与配套数据。本研究包整合了由测绘影像提取的撞击坑计数数据，结合解析生产模型与平衡模型，用于估算谷神星表面年龄并表征其平衡状态。 核心分析脚本为`csfd-ceres.py`，可处理Excel参数表中定义的多个计数区域。 代码 代码概览 核心分析脚本（`csfd-ceres.py`）会针对`parameters.xlsx`中列出的每个计数区域执行以下步骤： 1. 读取该区域的撞击坑直径数据或已有的CSFD文件 2. 计算经测绘区域面积归一化的观测CSFD 3. 计算直径大于1 km处的累积撞击坑密度N(>1km) 4. 生成月球衍生模型（Lunar-Derived Model, LDM）与小行星衍生模型（Asteroid-Derived Model, ADM）的生产曲线 5. 在生产主导的直径范围内，将生产曲线与观测CSFD进行视觉对齐 6. 基于LDM与ADM的年代学函数估算最优拟合的表面年龄 7. 计算以β和ρ为参数的解析平衡CSFD曲线 8. 生成并保存双对数CSFD绘图，同时输出参数汇总结果 本代码采用模块化架构设计，每个函数仅执行CSFD分析流程中的单一环节。 参数估算 除核心分析流程外，本仓库还包含参数估算脚本`parameters.py`，用于在完整CSFD分析前推导CSFD相关参数。 该脚本从`parameters.xlsx`中读取区域数据，从撞击坑CSV文件构建累积CSFD，并针对指定的分界直径执行分段双对数拟合。每个区域的生产归一化参数（ξ）与平衡斜率参数（β）均会被估算，而生产斜率固定为η=3.2。 估算得到的参数将作为固定输入提供给核心CSFD分析脚本。本校准代码仅用于参数推导与验证，不会在最终生产流程中执行。 CSFD参数（η、ξ、β、ρ）的定义与符号规范遵循El Ghazal等人（待刊）与Hirabayashi等人（2024）的研究。 代码输入 本代码的主要输入包括： - `parameters.xlsx` - 包含各区域撞击坑直径数据的CSV文件 关于这些输入的详细说明详见下文的数据章节。 代码输出 针对每个计数区域，代码将生成以下内容： - 一张双对数CSFD绘图，包含以下内容： - 由撞击坑计数得到的观测累积CSFD - 最优拟合的LDM生产曲线 - 最优拟合的ADM生产曲线 - 解析平衡CSFD曲线 所有绘图将以PNG格式保存至对应输入文件所在的目录中。待所有区域处理完成后，程序会在终端输出拟合参数的汇总结果。 本仓库中可获取示例输出结果。 数据 本研究包使用的撞击坑数据，源自利用QGIS对谷神星测绘影像进行人工识别与测量得到的撞击坑直径数据，测量工作在预先定义的计数区域内完成。 目标区域 撞击坑计数工作在谷神星Ac-2、Ac-6、Ac-8与Ac-12四个象限（quadrangles）内的五个计数区域中开展。这些区域被选为代表撞击坑密布且几乎无近期表面改造痕迹的地形。本仓库中可查看展示计数区域位置的地图（El Ghazal等人，待刊）。 数据整合内容 每个数据集将单颗撞击坑的识别结果整合为基于区域的撞击坑种群，以适配CSFD分析需求。这些撞击坑种群可用于构建经测绘区域面积归一化的累积CSFD，作为生产与平衡模型的输入数据。 数据格式 撞击坑CSV文件 - 每个计数区域对应一个文件 - 每个撞击坑占一行 - 必需列：`Diam_km`（撞击坑直径，单位：千米） 此类文件由QGIS中的人工撞击坑计数流程生成，为分析所用的原始撞击坑测量数据。 参数表（`parameters.xlsx`） - 每个计数区域占一行 - 必需列包括： - 象限（quadrangle） - 参考文献标识（ref） - 文件名（file name） - 面积（km²） - 分界直径（break diameter） - η（eta） - β（beta） - ρ（rho） 可包含额外列，但代码会忽略这些列。 数据使用方式 针对`parameters.xlsx`中的每一行，代码会通过`file name`字段定位对应的撞击坑CSV文件。若不存在对应文本文件，脚本会自动将每个CSV文件转换为`.txt`格式文件。此类文件包含两列：撞击坑直径（km）与CSFD（km⁻²）。 得到的CSFD将用于拟合生产曲线、估算表面年龄，并计算每个计数区域的解析平衡CSFD。 使用方法 1. 将`csfd-ceres.py`与`parameters.xlsx`放置于同一目录下 2. 将撞击坑CSV文件（`*.csv`）放置于同一目录下，或更新脚本中的数据路径 3. 通过Python运行该脚本 参考文献 Hirabayashi, M. 等人（2024），《基于单一幂律撞击坑生产函数的撞击坑平衡状态表征》，PSJ，5，250，doi:10.3847/PSJ/ad8883 El Ghazal, R. 等人（待刊），《谷神星撞击坑密布区域的退化机制与效率》 （代码内参考文献） Hiesinger, H. 等人（2016），《谷神星的撞击作用：对其壳层与演化的启示》，《科学》，353(6303)，doi.org/10.1126/science.aaf4759 Neukum, G. 等人（2001），《内太阳系撞击记录与月球参考系统的关联》，doi.org/10.1007/978-94-017-1035-0_3