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Update paleopiezometry_module.ipynb
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marcoalopez committed Jan 30, 2024
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"source": [
"# The paleopiezometry module\n",
"\n",
"📣 The GrainSizeTools script includes a **Jupyter notebook template** to promote the reproducibility of palaeopizometry studies. Use it as a template by deleting and adding as necessary and use it as supplementary material to your study so that anyone can reproduce your results."
"**What is paleopizometry?** \n",
"Paleopiezometers refer to microstructural features of deformed rocks that vary with the magnitude of the applied differential stress under which they formed (Twiss and Moores, 2006). They serve to infer differential stresses in the geological past, hence the name paleopiezometry, and they are an essential tool for validating rheological models of the lithosphere. The most prevalent microstructure used for this purpose is the average recrystallized (apparent) grain size. This choice is due to its ease of measurement in recrystallized rocks.\n",
"\n",
"> 📣 The GrainSizeTools script includes a **Jupyter notebook template** to promote the reproducibility of palaeopizometry studies. Use it as a template by deleting and adding as necessary and use it as supplementary material to your study so that anyone can reproduce your results."
]
},
{
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},
"outputs": [],
"source": [
"# modules import\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt"
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"\n",
"### Before you begin\n",
"\n",
"The paleopiezometry module includes a function named ``calc_diffstress()`` for estimating differential stress based on \"average\" recrystallized grain sizes. The function requires careful consideration of the following factors for correct differential stress estimation:\n",
"The paleopiezometry module includes a function named ``calc_diffstress()`` for estimating differential stress based on average recrystallized grain sizes. The function requires careful consideration of the following factors for correct differential stress estimation:\n",
"\n",
"1. definition of the mineral phase and the piezometer relationship to be used\n",
"2. enter the (apparent) grain size as **equivalent circular diameters** in microns\n",
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"\n",
"Regarding the first factor, GrainSizeTools includes a database of paleopiezometric relations, including the most common mineral phases quartz, calcite, olivine and albite feldspar. In addition, the script facilitates the writing of ad hoc piezometric relations. As we will see later, it is also very easy to add new piezometric relationships.\n",
"\n",
"For the second factor, the function assumes by default that the average grain size you specify has been estimated using equivalent circular diameters (ECDs). As some piezometric relationships, especially those established longer ago, were established using linear intercepts (LI) rather than ECDs, the function will automatically convert ECDs to linear intercepts if necessary using the Hoff and Rhines (1968) correction. This means that **you do not need to worry about whether the piezometer was originally calibrated using linear intercepts**, always use averages based on equivalent circular diameters in microns. The function will explicitly warn you when using this ECD ti LI of conversion.\n",
"For the second factor, the function assumes by default that the average grain size you specify has been estimated using equivalent circular diameters (ECDs). As some piezometric relationships, especially those established longer ago, were established using linear intercepts (LI) rather than ECDs, the function will automatically convert ECDs to linear intercepts if necessary using the Hoff and Rhines (1968) correction. This means that **you do not need to worry about whether the piezometer was originally calibrated using linear intercepts or not**, always use averages based on equivalent circular diameters in microns. The function will explicitly warn you when using this ECD ti LI of conversion.\n",
"\n",
"The third factor is key for the correct estimation of differential stress, as each paleopiezometry relationship has been calibrated to a specific average grain size (e.g. the arithmetic mean, median or RMS mean) and thus **only gives valid results if the same type of average is used**. In addition, **you must not apply any type of stereological correction to the calculated grain average**, if the author(s) of the piezometer used any type of stereological correction during calibration, your input will be automatically corrected by the function.\n",
"\n",
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"tags": []
},
"source": [
"## How to synthesise a palaeopizometric dataset\n",
"## How to synthesise a set of piezometric values\n",
"\n",
"TODO\n",
"\n",
"> ⚠️ **Never combine means -or any other statistic- as if they were data points**. A common mistake is to take different piezometric estimates and averaged them. However, the stress estimates are already an average and calculating a mean of the averages is mathematically incorrect. Similarly, to look at the raw grain size data from all the grain maps and make the estimate from there is also mathematically incorrect. The first approach ignores the uncertainty in any estimate of the average and the second ignores the uncertainty within and between experimental conditions (or measured areas). The correct procedure is to take the weighted mean of the averages, where each mean is weighted by its variance."
"> ⚠️ **Never combine averages -or any other statistic- as if they were data points**. In the context of meta-analysis, which is a statistical procedure for combining data from multiple studies or experiments, a common mistake is to take different estimates and averaged them. However, the stress estimates are already an average and calculating a mean of the averages is mathematically incorrect because this approach ignores the uncertainty of the average. Similarly, to look at the raw grain size data from all the grain maps and make the estimate from there is also incorrect because this ignores the uncertainty within and between experimental conditions. The correct procedure here is to take the weighted mean of the averages, where each mean is weighted by its variance or the squared standard error of the mean (SEM). The GrainSize Tools script has a function to do this named ```weighted_mean_and_se()```"
]
},
{
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