inv_tdem_1d.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1D Inversion for a Single Sounding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{admonition} Intermediate notebook\n",
    ":class: caution\n",
    "This tutorial focusses on intermediate level functionality within SimPEG. Basic functionality within SimPEG is not discussed in detail, as we assume the user is already familiar. \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{admonition} Light-weight notebook\n",
    ":class: hint\n",
    "This tutorial requires minimal computational resources and can be executed quickly in the background while other computer processes are running.\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Author:** Devin C. Cowan\n",
    "\n",
    "</br>\n",
    "\n",
    "**Keywords:** total magnetic intensity, integral formulation, inversion, sparse norm, tensor mesh, tree mesh.\n",
    "\n",
    "</br>\n",
    "\n",
    "**Summary:** Here we invert total magnetic intensity data to recover a susceptibility model. We demonstrate two approaches for recovering a susceptibility model:\n",
    "\n",
    "1. Weighted least-squares inversion for a tensor mesh\n",
    "2. Iteratively re-weighted least-squares (IRLS) inversion for a tree mesh\n",
    "\n",
    "The *weighted least-squares* approach is a great introduction to geophysical inversion with SimPEG. One drawback however, is that it recovers smooth structures which may not be representative of the true model. To recover sparse and/or blocky structures, we demonstrate the *iteratively re-weighted least-squares* approach.\n",
    "\n",
    "**Learning Objectives:** Because this tutorial focusses primarily on inversion-related functionality, we urge the reader to become familiar with functionality explained in the [1D Forward Simulation of Time-Domain EM Data for a Single Sounding](fwd_tdem_1d.ipynb) tutorial before working through this one. For this tutorial, we focus on:\n",
    "\n",
    "- How to carry out 1D geophysical inversion with SimPEG.\n",
    "- How to assign appropriate uncertainties to TDEM data.\n",
    "- Choosing suitable parameters for the inversion.\n",
    "- Specifying directives that are applied throughout the inversion.\n",
    "- Weighted least-squares, sparse-norm and parametric inversion.\n",
    "- Analyzing inversion outputs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing Modules\n",
    "\n",
    "Here, we import all of the functionality required to run the notebook for the tutorial exercise.\n",
    "All of the functionality specific to the forward simulation of 1D time domain EM data are imported from the [simpeg.electromagnetics.time_domain](myst:simpeg#simpeg.electromagnetics.time_domain) module. Classes required to define the data misfit, regularization, optimization, etc... are imported from elsewhere within SimPEG. We also import some useful utility functions from [simpeg.utils](myst:simpeg#simpeg.utils). To generate the mesh used for the inversion, we use the [discretize](https://discretize.simpeg.xyz/en/main) package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# SimPEG functionality\n",
    "import simpeg.electromagnetics.time_domain as tdem\n",
    "from simpeg.utils import plot_1d_layer_model, download, mkvc\n",
    "from simpeg import (\n",
    "    maps,\n",
    "    data,\n",
    "    data_misfit,\n",
    "    regularization,\n",
    "    optimization,\n",
    "    inverse_problem,\n",
    "    inversion,\n",
    "    directives,\n",
    ")\n",
    "\n",
    "# discretize functionality\n",
    "from discretize import TensorMesh\n",
    "\n",
    "# Basic Python functionality\n",
    "import os\n",
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import tarfile\n",
    "\n",
    "mpl.rcParams.update({\"font.size\": 14})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Download and Extract the Tutorial Data\n",
    "\n",
    "For this tutorial, the frequencies and observed data for 1D sounding are stored within a tar-file. Here, we download and extract the data file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "overwriting /Users/sgkang09/Project/targeted-inversion/inv_tdem_1d_files.tar.gz\n",
      "Downloading https://github.com/simpeg/user-tutorials/raw/main/assets/08-tdem/inv_tdem_1d_files.tar.gz\n",
      "   saved to: /Users/sgkang09/Project/targeted-inversion/inv_tdem_1d_files.tar.gz\n",
      "Download completed!\n"
     ]
    }
   ],
   "source": [
    "# URL to assets folder\n",
    "data_source = \"https://github.com/simpeg/user-tutorials/raw/main/assets/08-tdem/inv_tdem_1d_files.tar.gz\"\n",
    "\n",
    "# download the data\n",
    "downloaded_data = download(data_source, overwrite=True)\n",
    "\n",
    "# unzip the tarfile\n",
    "tar = tarfile.open(downloaded_data, \"r\")\n",
    "tar.extractall()\n",
    "tar.close()\n",
    "\n",
    "# path to the directory containing our data\n",
    "dir_path = downloaded_data.split(\".\")[0] + os.path.sep\n",
    "\n",
    "# files to work with\n",
    "data_filename = dir_path + \"em1dtm_data.txt\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load and Plot the Data\n",
    "\n",
    "Here we load and plot the 1D sounding data. In this case, we have B-field data for a step-off excitation. The columns of the data file are: times (s) and Bz (T)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Load data\n",
    "dobs = np.loadtxt(str(data_filename), skiprows=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "times = dobs[:, 0]\n",
    "dobs = mkvc(dobs[:, -1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5, 5))\n",
    "ax = fig.add_axes([0.15, 0.15, 0.8, 0.75])\n",
    "ax.loglog(times, np.abs(dobs), \"k-o\", lw=3)\n",
    "ax.grid(which=\"both\")\n",
    "ax.set_xlabel(\"Times (s)\")\n",
    "ax.set_ylabel(\"|B| (T)\")\n",
    "ax.set_title(\"Observed Data\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining the Survey\n",
    "\n",
    "Here, we define the survey geometry. For a comprehensive description of constructing TDEM surveys in SimPEG, see the [1D Forward Simulation of Time-Domain EM Data for a Single Sounding](fwd_tdem_1d.ipynb) tutorial.\n",
    "\n",
    "Here, the survey consisted of a circular transmitter loop with a radius of 6 m located 20 m above the Earth's surface. The receiver measured the vertical component of the secondary magnetic field at a the loop's centre."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Source loop geometry\n",
    "source_location = np.array([0.0, 0.0, 1.0])  # (3, ) numpy.array_like\n",
    "source_orientation = \"z\"  # \"x\", \"y\" or \"z\"\n",
    "source_current = 1.0  # maximum on-time current (A)\n",
    "source_radius = 10.0  # source loop radius (m)\n",
    "\n",
    "# Receiver geometry\n",
    "receiver_location = np.array([0.0, 0.0, 1.0])  # or (N, 3) numpy.ndarray\n",
    "receiver_orientation = \"z\"  # \"x\", \"y\" or \"z\"\n",
    "\n",
    "# Receiver list\n",
    "receiver_list = []\n",
    "receiver_list.append(\n",
    "    tdem.receivers.PointMagneticFluxDensity(\n",
    "        receiver_location, times, orientation=receiver_orientation\n",
    "    )\n",
    ")\n",
    "\n",
    "# Define the source waveform.\n",
    "waveform = tdem.sources.StepOffWaveform()\n",
    "\n",
    "# Sources\n",
    "source_list = [\n",
    "    tdem.sources.CircularLoop(\n",
    "        receiver_list=receiver_list,\n",
    "        location=source_location,\n",
    "        waveform=waveform,\n",
    "        current=source_current,\n",
    "        radius=source_radius,\n",
    "    )\n",
    "]\n",
    "\n",
    "# Survey\n",
    "survey = tdem.Survey(source_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assign Uncertainties\n",
    "\n",
    "Inversion with SimPEG requires that we define the uncertainties on our data; that is, an estimate of the standard deviation of the noise on our data assuming it is uncorrelated Gaussian with zero mean. An online resource explaining uncertainties and their role in the inversion can be found [here](https://giftoolscookbook.readthedocs.io/en/latest/content/fundamentals/Uncertainties.html).\n",
    "\n",
    "For off-time TDEM data, a percent uncertainty plus a small floor value is generally applied to all data. Depending on many factors, we may apply a percent uncertainty between 5\\% and 20\\%. The floor uncertainty ensure we do not try to overfit late time channels when the signal to noise become sufficiently small. For systems where multiple field directions are measured for the same source, we may not want to apply a uniform percent uncertainty to all data. Doing so may cause the inversion to overfit weaker components. In this case, the uncertainty may be a percent of the amplitude of the secondary field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# 5% of the absolute value\n",
    "uncertainties = 0.05 * np.abs(dobs) * np.ones(np.shape(dobs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining the Data\n",
    "\n",
    "The SimPEG [Data](myst:simpeg#simpeg.data.Data) class is required for inversion and connects the observed data, uncertainties and survey geometry."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "data_object = data.Data(survey, dobs=dobs, standard_deviation=uncertainties)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Weighted Least-Squares Inversion\n",
    "\n",
    "Here, we use the weighted least-squares inversion approach to recover the log-conductivities on a 1D layered Earth. We impose no a-priori information about the number of layers (geological units) or their thicknesses. Instead, we define a large number of layers with exponentially increasing thicknesses. And the depth, thickness and electrical properties of the Earth are inferred from the recovered model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Defining a 1D Layered Earth\n",
    "\n",
    "Let us assume we have a reasonable estimate of the regional conductivity within our area of interest. For the earliest time channel and the estimated conductivity, we compute the minimum diffusion distance:\n",
    "\n",
    "$$\n",
    "d_{min} \\approx 1250 \\sqrt{\\dfrac{t_{min}}{\\sigma}}\n",
    "$$\n",
    "\n",
    "The minimum layer thickness is some fraction of the minimum diffusion distance. Next, we use the latest time channel and the estimated conductivity to compute the maximum diffusion distance:\n",
    "\n",
    "$$\n",
    "d_{max} \\approx 1250 \\sqrt{\\dfrac{t_{max}}{\\sigma}}\n",
    "$$\n",
    "\n",
    "Starting from our minimum layer thickness, we continue to add layers with exponentially increasing thicknesses. We do so until the layers extend to some multiple of the maximum diffusion distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MINIMUM DIFFUSION DISTANCE: 12.5 m\n",
      "MAXIMUM DIFFUSION DISTANCE: 395.28470752104744 m\n"
     ]
    }
   ],
   "source": [
    "# estimated host conductivity (S/m)\n",
    "estimated_conductivity = 0.1\n",
    "\n",
    "# minimum diffusion distance\n",
    "d_min = 1250 * np.sqrt(times.min() / estimated_conductivity)\n",
    "print(\"MINIMUM DIFFUSION DISTANCE: {} m\".format(d_min))\n",
    "\n",
    "# maximum diffusion distance\n",
    "d_max = 1250 * np.sqrt(times.max() / estimated_conductivity)\n",
    "print(\"MAXIMUM DIFFUSION DISTANCE: {} m\".format(d_max))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "depth_min = 3.  # top layer thickness\n",
    "depth_max = 300.0  # depth to lowest layer\n",
    "geometric_factor = 1.06  # rate of thickness increase"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Increase subsequent layer thicknesses by the geometric factors until\n",
    "# it reaches the maximum layer depth.\n",
    "layer_thicknesses = [depth_min]\n",
    "while np.sum(layer_thicknesses) < depth_max:\n",
    "    layer_thicknesses.append(geometric_factor * layer_thicknesses[-1])\n",
    "n_layers = len(layer_thicknesses) + 1  # Number of layers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model and Mapping to Layer Conductivities\n",
    "\n",
    "Recall from the [1D Forward Simulation of Time-Domain EM Data for a Single Sounding](fwd_tdem_1d.ipynb) tutorial that the 'model' is not necessarily synonymous with physical property values. And that we need to define a mapping from the model to the set of input parameters required by the forward simulation. When inverting to recover electrical conductivities (or resistivities), it is best to use the log-value, as electrical conductivities of rocks span many order of magnitude.\n",
    "\n",
    "Here, the model defines the log-conductivity values for a defined set of subsurface layers. And we use the [simpeg.maps.ExpMap](myst:simpeg#simpeg.maps.ExpMap) to map from the model parameters to the conductivity values required by the forward simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "log_conductivity_map = maps.ExpMap(nP=n_layers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Starting/Reference Models\n",
    "\n",
    "The **starting model** defines a reasonable starting point for the inversion. Because electromagnetic problems are non-linear, your choice in starting model does have an impact on the recovered model. For DC resistivity inversion, we generally choose our starting model based on apparent resistivities. For the tutorial example, the apparent resistivities were near 1000 $\\Omega m$. It should be noted that the starting model **cannot be vector of zeros,** otherwise the inversion will be unable to compute a gradient direction at the first iteration.\n",
    "\n",
    "The **reference model** is used to include a-priori information. The impact of the reference model on the inversion will be discussed in another tutorial. The reference model for basic inversion approaches is either zero or equal to the starting model.\n",
    "\n",
    "Notice that the length of the starting and reference models is equal to the number of model parameters!!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Starting model is log-conductivity values (S/m)\n",
    "starting_conductivity_model = np.log(1e-1 * np.ones(n_layers))\n",
    "\n",
    "# Reference model is also log-resistivity values (S/m)\n",
    "reference_conductivity_model = starting_conductivity_model.copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the Forward Simulation\n",
    "\n",
    "A simulation object defining the forward problem is required in order to predict data and calculate misfits for recovered models. A comprehensive description of the simulation object for 1D DC resistivity was discussed in the [1D Forward Simulation of Time-Domain EM Data for a Single Sounding](fwd_tdem_1d.ipynb) tutorial. Here, we use the [Simulation1DLayers](myst:simpeg#simpeg.electromagnetics.time_domain.Simulation1DLayers) which simulates the data according to a 1D Hankel transform solution.\n",
    "\n",
    "The layer thicknesses are a static property of the simulation, and we set them using the ``thicknessess`` keyword argument. Since our model consists of log-conductivities, we use ``sigmaMap`` to set the mapping from the model to the layer conductivities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "simulation_L2 = tdem.Simulation1DLayered(\n",
    "    survey=survey, thicknesses=layer_thicknesses, sigmaMap=log_conductivity_map\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Misfit\n",
    "\n",
    "To understand the role of the data misfit in the inversion, please visit [this online resource](https://giftoolscookbook.readthedocs.io/en/latest/content/fundamentals/Uncertainties.html).\n",
    "Here, we use the [L2DataMisfit](myst:simpeg#simpeg.data_misfit.L2DataMisfit) class to define the data misfit. In this case, the data misfit is the L2 norm of the weighted residual between the observed data and the data predicted for a given model. When instantiating the data misfit object within SimPEG, we must assign an appropriate *data object* and *simulation object* as properties."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "dmis_L2 = data_misfit.L2DataMisfit(simulation=simulation_L2, data=data_object)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regularization\n",
    "\n",
    "To understand the role of the regularization in the inversion, please visit [this online resource](https://giftoolscookbook.readthedocs.io/en/latest/content/fundamentals/ObjectiveFunction.html). \n",
    "\n",
    "To define the regularization within SimPEG, we must define a 1D [tensor mesh](myst:discretize#discretize.TensorMesh). Meshes are designed using the [discretize package](https://discretize.simpeg.xyz). Whereas layer *thicknesses* and our *model* are defined from our top-layer down, tensor meshes are defined from the bottom up. So to define a 1D tensor mesh for the regularization, we:\n",
    "\n",
    "- add an extra layer to the end of our thicknesses so that the number of cells in the 1D mesh equals the number of model parameters\n",
    "- reverse the order so that the model parameters in the regularization match up with the appropriate cell\n",
    "- define the tensor mesh from the cell widths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "34"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(layer_thicknesses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "  TensorMesh: 35 cells\n",
      "\n",
      "                      MESH EXTENT             CELL WIDTH      FACTOR\n",
      "  dir    nC        min           max         min       max      max\n",
      "  ---   ---  ---------------------------  ------------------  ------\n",
      "   x     35       -333.07         -0.00      3.00     20.52    1.06\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Define 1D cell widths\n",
    "h = np.r_[layer_thicknesses, layer_thicknesses[-1]]\n",
    "# h = np.flipud(h)\n",
    "# h = np.ones(36)\n",
    "# Create regularization mesh\n",
    "regularization_mesh = TensorMesh([h], \"N\")\n",
    "print(regularization_mesh)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By default, the regularization acts on the model parameters. In this case, the model parameters are the log-resistivities, not the electric resistivities!!! Here, we use the [WeightedLeastSquares](myst:simpeg#simpeg.regularization.WeightedLeastSquares) regularization class to constrain the inversion result. Here, length scale along x are used to balance the smallness and smoothness terms; yes, x is smoothness along the vertical direction. And the reference model is only applied to the smallness term. If we wanted to apply the regularization to a function of the model parameters, we would need to set an approprate mapping object using the ``mapping`` keyword argument."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "reg_L2 = regularization.WeightedLeastSquares(\n",
    "    regularization_mesh,\n",
    "    # length_scale_x=1.0,\n",
    "    alpha_x=1.,\n",
    "    alpha_s = 1e-10, \n",
    "    reference_model=reference_conductivity_model,\n",
    "    reference_model_in_smooth=False,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_L2.alpha_x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimization\n",
    "\n",
    "Here, we use the [InexactGaussNewton](myst:simpeg#simpeg.optimization.InexactGaussNewton) class to solve the optimization problem using the inexact Gauss Newton with conjugate gradient solver. Reasonable default values have generally been set for the properties of each optimization class. However, the user may choose to set custom values; e.g. the accuracy tolerance for the conjugate gradient solver or the number of line searches."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "opt_L2 = optimization.InexactGaussNewton(\n",
    "    maxIter=100, maxIterLS=20, maxIterCG=20, tolCG=1e-3\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inverse Problem\n",
    "\n",
    "We use the [BaseInvProblem](myst:simpeg#simpeg.inverse_problem.BaseInvProblem) class to fully define the inverse problem that is solved at each beta (trade-off parameter) iteration. The inverse problem requires appropriate *data misfit*, *regularization* and *optimization* objects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "inv_prob_L2 = inverse_problem.BaseInvProblem(dmis_L2, reg_L2, opt_L2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inversion Directives\n",
    "\n",
    "To understand the role of directives in the inversion, please visit this online resource. Here, we apply common directives for weighted least-squares inversion of gravity data and describe their roles. These are:\n",
    "\n",
    "- [UpdatePreconditioner](myst:simpeg#simpeg.directives.UpdatePreconditioner): Apply Jacobi preconditioner when solving optimization problem to reduce the number of conjugate gradient iterations. We set `update_every_iteration=True` because the ideal preconditioner is model-dependent.\n",
    "\n",
    "- [BetaEstimate_ByEig](myst:simpeg#simpeg.directives.BetaEstimate_ByEig): Compute and set starting trade-off parameter (beta) based on largest eigenvalues.\n",
    "\n",
    "- [BetaSchedule](myst:simpeg#simpeg.directives.BetaSchedule): Size reduction of the trade-off parameter at every beta iteration, and the number of Gauss-Newton iterations for each beta. In general, a `coolingFactor` between 1.5 and 2.5, and `coolingRate` of 3 works well for TDEM inversion. Cooling beta too quickly will result in portions of the model getting trapped in local minima. And we will not be finding the solution that minimizes the optimization problem if the cooling rate is too small.\n",
    "\n",
    "- [TargetMisfit](myst:simpeg#simpeg.directives.TargetMisfit): Terminates the inversion when the data misfit equals the target misfit. A `chifact=1` terminates the inversion when the data misfit equals the number of data.\n",
    "\n",
    "\n",
    "The directive objects are organized in a ``list``. Upon starting the inversion or updating the recovered model at each iteration, the inversion will call each directive within the list **in order**. The order of the directives matters, and SimPEG will throw an error if directives are organized into an improper order. Some directives, like the ``BetaEstimate_ByEig`` are only used when starting the inversion. Other directives, like ``UpdatePreconditionner``, are used whenever the model is updated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "update_jacobi = directives.UpdatePreconditioner(update_every_iteration=True)\n",
    "starting_beta = directives.BetaEstimate_ByEig(beta0_ratio=5)\n",
    "beta_schedule = directives.BetaSchedule(coolingFactor=2.0, coolingRate=3)\n",
    "target_misfit = directives.TargetMisfit(chifact=1.0)\n",
    "\n",
    "directives_list_L2 = [update_jacobi, starting_beta, beta_schedule, target_misfit]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define and Run the Inversion\n",
    "\n",
    "We define the inversion using the [BaseInversion](myst:simpeg#simpeg.inversion.BaseInversion) class. The inversion class must be instantiated with an appropriate *inverse problem* object and *directives list*. The ``run`` method, along with a starting model, is respondible for running the inversion. The output is a 1D numpy.ndarray containing the recovered model parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Running inversion with SimPEG v0.22.2.dev6+g67b3e9f1c\n",
      "\n",
      "                        simpeg.InvProblem is setting bfgsH0 to the inverse of the eval2Deriv.\n",
      "                        ***Done using same Solver, and solver_opts as the Simulation1DLayered problem***\n",
      "                        \n",
      "model has any nan: 0\n",
      "============================ Inexact Gauss Newton ============================\n",
      "  #     beta     phi_d     phi_m       f      |proj(x-g)-x|  LS    Comment   \n",
      "-----------------------------------------------------------------------------\n",
      "x0 has any nan: 0\n",
      "   0  7.83e+03  4.53e+03  0.00e+00  4.53e+03    8.73e+02      0              \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/sgkang09/Project/simpeg/simpeg/optimization.py:1072: UserWarning: tol is not a valid keyword for cg and will be ignored\n",
      "  Hinv = SolverICG(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   1  7.83e+03  1.42e+03  2.79e-02  1.64e+03    6.61e+02      1              \n",
      "   2  7.83e+03  4.90e+02  6.31e-02  9.84e+02    2.76e+02      0              \n",
      "   3  3.92e+03  3.84e+02  6.64e-02  6.44e+02    1.93e+02      0              \n",
      "   4  3.92e+03  2.38e+02  9.24e-02  6.00e+02    3.12e+01      0              \n",
      "   5  3.92e+03  2.36e+02  9.27e-02  5.99e+02    4.52e+00      0              \n",
      "   6  1.96e+03  2.34e+02  9.32e-02  4.16e+02    1.29e+02      0              \n",
      "   7  1.96e+03  1.35e+02  1.29e-01  3.89e+02    3.67e+01      0              \n",
      "   8  1.96e+03  1.38e+02  1.27e-01  3.87e+02    2.55e+00      0              \n",
      "   9  9.79e+02  1.36e+02  1.28e-01  2.62e+02    8.64e+01      0              \n",
      "  10  9.79e+02  7.46e+01  1.74e-01  2.45e+02    3.93e+01      0              \n",
      "  11  9.79e+02  7.78e+01  1.70e-01  2.44e+02    1.68e+00      0              \n",
      "  12  4.89e+02  7.59e+01  1.72e-01  1.60e+02    5.60e+01      0              \n",
      "  13  4.89e+02  4.26e+01  2.21e-01  1.51e+02    3.32e+01      0              \n",
      "  14  4.89e+02  4.43e+01  2.16e-01  1.50e+02    1.45e+00      0              \n",
      "  15  2.45e+02  4.32e+01  2.18e-01  9.66e+01    3.44e+01      0              \n",
      "------------------------- STOP! -------------------------\n",
      "1 : |fc-fOld| = 0.0000e+00 <= tolF*(1+|f0|) = 4.5289e+02\n",
      "1 : |xc-x_last| = 1.1134e+00 <= tolX*(1+|x0|) = 1.4622e+00\n",
      "0 : |proj(x-g)-x|    = 3.4379e+01 <= tolG          = 1.0000e-01\n",
      "0 : |proj(x-g)-x|    = 3.4379e+01 <= 1e3*eps       = 1.0000e-02\n",
      "0 : maxIter   =     100    <= iter          =     16\n",
      "------------------------- DONE! -------------------------\n"
     ]
    }
   ],
   "source": [
    "# Here we combine the inverse problem and the set of directives\n",
    "inv_L2 = inversion.BaseInversion(inv_prob_L2, directives_list_L2)\n",
    "\n",
    "# Run the inversion\n",
    "recovered_model_L2 = inv_L2.run(starting_conductivity_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inversion Outputs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Misfit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dpred_L2 = simulation_L2.dpred(recovered_model_L2)\n",
    "\n",
    "fig = plt.figure(figsize=(5, 5))\n",
    "ax1 = fig.add_axes([0.15, 0.15, 0.8, 0.75])\n",
    "ax1.loglog(times, np.abs(dobs), \"ko\")\n",
    "ax1.loglog(times, np.abs(dpred_L2), \"b-\")\n",
    "ax1.grid(which=\"both\")\n",
    "ax1.set_xlabel(\"times (s)\")\n",
    "ax1.set_ylabel(\"Bz (T)\")\n",
    "ax1.set_title(\"Predicted and Observed Data\")\n",
    "ax1.legend([\"Observed\", \"L2 Inversion\"], loc=\"upper right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Recovered Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Load the true model and layer thicknesses\n",
    "true_conductivities = np.array([0.1, 1.0, 0.1])\n",
    "true_layers = np.r_[40.0, 40.0, 160.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot true model and recovered model\n",
    "fig = plt.figure(figsize=(6, 6))\n",
    "\n",
    "ax1 = fig.add_axes([0.2, 0.15, 0.7, 0.7])\n",
    "plot_1d_layer_model(true_layers, 1./true_conductivities, ax=ax1, color=\"k\")\n",
    "plot_1d_layer_model(\n",
    "    layer_thicknesses, 1./(log_conductivity_map * recovered_model_L2), ax=ax1, color=\"b\"\n",
    ")\n",
    "ax1.grid()\n",
    "ax1.set_xlabel(r\"Resistivity ($\\Omega m$)\")\n",
    "x_min, x_max = true_conductivities.min(), true_conductivities.max()\n",
    "# ax1.set_xlim(0.8 * x_min, 1.5 * x_max)\n",
    "ax1.set_ylim([np.sum(true_layers), 0])\n",
    "ax1.legend([\"True Model\", \"L2-Model\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Iteratively Re-weighted Least-Squares Inversion\n",
    "\n",
    "Here, we use the iteratively reweighted least-squares (IRLS) inversion approach to recover sparse and/or blocky models on the set layers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the Forward Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "simulation_irls = tdem.simulation_1d.Simulation1DLayered(\n",
    "    survey=survey,\n",
    "    sigmaMap=log_conductivity_map,\n",
    "    thicknesses=layer_thicknesses,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define the Data Misfit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "dmis_irls = data_misfit.L2DataMisfit(simulation=simulation_irls, data=data_object)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regularization\n",
    "\n",
    "Here, we use the [Sparse](myst:simpeg#simpeg.regularization.Sparse) regularization class to constrain the inversion result using an IRLS approach. Here, the scaling constants that balance the smallness and smoothness terms are set directly. Equal emphasis on smallness and smoothness is generally applied by using the inverse square of the smallest cell dimension. The reference model is only applied to the smallness term; which is redundant for the tutorial example since we have set the reference model to an array of zeros. Here, we apply a 1-norm to the smallness term and a 1-norm to first-order smoothness along the x (vertical direction)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "reference_model = np.ones(len(h)) * np.log(1./20)\n",
    "\n",
    "reg_irls = regularization.Sparse(\n",
    "    regularization_mesh,\n",
    "    alpha_s=1e-12,    \n",
    "    alpha_x=1.,\n",
    "    reference_model_in_smooth=False,\n",
    "    norms=[0.0, 0.0],\n",
    "    reference_model = reference_model\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10., 10., 10., 10., 10., 10., 10., 10., 10., 10., 10., 10., 10.,\n",
       "       10., 10., 10., 10., 10., 10., 10., 10., 10., 10., 10., 10., 10.,\n",
       "       10., 10., 10., 10., 10., 10., 10., 10., 10.])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1./np.exp(starting_conductivity_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "opt_irls = optimization.InexactGaussNewton(\n",
    "    maxIter=100, maxIterLS=20, maxIterCG=30, tolCG=1e-3, tolG=1e-20, eps=1e-20\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inverse Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "inv_prob_irls = inverse_problem.BaseInvProblem(dmis_irls, reg_irls, opt_irls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Directives\n",
    "\n",
    "Here, we create common directives for IRLS inversion of total magnetic intensity data and describe their roles. In additon to the [UpdateSensitivityWeights](myst:simpeg#simpeg.directives.UpdateSensitivityWeights), [UpdatePreconditioner](myst:simpeg#simpeg.directives.UpdatePreconditioner) and [BetaEstimate_ByEig](myst:simpeg#simpeg.directives.BetaEstimate_ByEig)  (described before), inversion with sparse-norms requires the [Update_IRLS](myst:simpeg#simpeg.directives.Update_IRLS) directive.\n",
    "\n",
    "You will notice that we don't use the [BetaSchedule](myst:simpeg#simpeg.directives.BetaSchedule) and [TargetMisfit](myst:simpeg#simpeg.directives.TargetMisfit) directives. Here, the beta cooling schedule is set in the [Update_IRLS](myst:simpeg#simpeg.directives.Update_IRLS) directive using the `coolingFactor` and `coolingRate` properties. The target misfit for the L2 portion of the IRLS approach is set with the `chifact_start` property."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Running inversion with SimPEG v0.22.2.dev6+g67b3e9f1c\n",
      "simpeg.InvProblem will set Regularization.reference_model to m0.\n",
      "simpeg.InvProblem will set Regularization.reference_model to m0.\n",
      "\n",
      "                        simpeg.InvProblem is setting bfgsH0 to the inverse of the eval2Deriv.\n",
      "                        ***Done using same Solver, and solver_opts as the Simulation1DLayered problem***\n",
      "                        \n",
      "model has any nan: 0\n",
      "============================ Inexact Gauss Newton ============================\n",
      "  #     beta     phi_d     phi_m       f      |proj(x-g)-x|  LS    Comment   \n",
      "-----------------------------------------------------------------------------\n",
      "x0 has any nan: 0\n",
      "   0  1.35e+03  4.53e+03  0.00e+00  4.53e+03    8.73e+02      0              \n",
      "Reached starting chifact with l2-norm regularization: Start IRLS steps...\n",
      "irls_threshold 2.859508536388325\n",
      "   1  6.74e+02  1.85e+03  1.69e-02  1.86e+03    1.14e+03      1              \n",
      "   2  2.65e+02  8.43e+02  9.28e-02  8.67e+02    1.04e+03      1              \n",
      "   3  1.28e+02  1.43e+02  3.33e-01  1.86e+02    6.29e+02      0   Skip BFGS  \n",
      "   4  2.10e+02  2.42e+01  4.65e-01  1.22e+02    9.10e+01      0   Skip BFGS  \n",
      "   5  1.59e+02  4.09e+01  3.41e-01  9.49e+01    6.62e+01      0              \n",
      "   6  1.59e+02  3.15e+01  2.87e-01  7.70e+01    3.79e+01      0              \n",
      "   7  1.59e+02  2.97e+01  1.62e-01  5.54e+01    3.72e+01      0              \n",
      "   8  2.68e+02  2.24e+01  7.29e-02  4.20e+01    7.07e+01      0              \n",
      "   9  4.89e+02  1.89e+01  2.85e-02  3.28e+01    6.45e+01      0   Skip BFGS  \n",
      "  10  9.18e+02  1.76e+01  1.30e-02  2.96e+01    4.68e+01      0   Skip BFGS  \n",
      "  11  1.72e+03  1.77e+01  6.31e-03  2.85e+01    4.81e+01      0   Skip BFGS  \n",
      "  12  3.24e+03  1.77e+01  3.15e-03  2.78e+01    4.15e+01      0   Skip BFGS  \n",
      "  13  6.08e+03  1.76e+01  1.57e-03  2.72e+01    3.93e+01      0              \n",
      "  14  1.14e+04  1.76e+01  7.82e-04  2.66e+01    4.29e+01      0              \n",
      "  15  2.15e+04  1.76e+01  3.91e-04  2.60e+01    5.39e+01      0   Skip BFGS  \n",
      "------------------------- STOP! -------------------------\n",
      "1 : |fc-fOld| = 5.4781e-01 <= tolF*(1+|f0|) = 4.5289e+02\n",
      "1 : |xc-x_last| = 7.9108e-03 <= tolX*(1+|x0|) = 1.4622e+00\n",
      "0 : |proj(x-g)-x|    = 5.3918e+01 <= tolG          = 1.0000e-20\n",
      "0 : |proj(x-g)-x|    = 5.3918e+01 <= 1e3*eps       = 1.0000e-17\n",
      "1 : maxIter   =      15    <= iter          =     15\n",
      "------------------------- DONE! -------------------------\n"
     ]
    }
   ],
   "source": [
    "simulation_irls = tdem.simulation_1d.Simulation1DLayered(\n",
    "    survey=survey,\n",
    "    sigmaMap=log_conductivity_map,\n",
    "    thicknesses=layer_thicknesses,\n",
    ")\n",
    "dmis_irls = data_misfit.L2DataMisfit(simulation=simulation_irls, data=data_object)\n",
    "reference_model = np.ones(36) * np.log(1./20)\n",
    "\n",
    "reg_irls = regularization.Sparse(\n",
    "    regularization_mesh,\n",
    "    alpha_s=1e-10,\n",
    "    alpha_x=1.,\n",
    "    reference_model_in_smooth=False,\n",
    "    norms=[2.0, 0.0],\n",
    ")\n",
    "# reg_irls.regularization_mesh._base_length = 1.\n",
    "opt_irls = optimization.InexactGaussNewton(\n",
    "    maxIter=15, maxIterLS=20, maxIterCG=100, tolCG=1e-10, tolG=1e-20, eps=1e-20\n",
    ")\n",
    "\n",
    "inv_prob_irls = inverse_problem.BaseInvProblem(dmis_irls, reg_irls, opt_irls)\n",
    "\n",
    "starting_beta_irls = directives.BetaEstimate_ByEig(beta0_ratio=1)\n",
    "update_jacobi_irls = directives.UpdatePreconditioner(update_every_iteration=True)\n",
    "update_irls = directives.Update_IRLS(\n",
    "    coolingFactor=2,\n",
    "    coolingRate=1,\n",
    "    f_min_change=1e-10,\n",
    "    max_irls_iterations=20,\n",
    "    chifact_start=np.inf,\n",
    "    beta_search=False,\n",
    "    chifact_target=1.\n",
    ")\n",
    "update_irls.coolEpsFact = 2.\n",
    "directives_list_irls = [\n",
    "    update_irls,        \n",
    "    # sensitivity_weights_irls,\n",
    "    # update_jacobi_irls,\n",
    "    starting_beta_irls,\n",
    "    \n",
    "]\n",
    "# Here we combine the inverse problem and the set of directives\n",
    "inv_irls = inversion.BaseInversion(inv_prob_irls, directives_list_irls)\n",
    "\n",
    "# Run the inversion\n",
    "recovered_model_irls = inv_irls.run(starting_conductivity_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31.0"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "update_irls.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "31"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "survey.nD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Misfit and Recovered Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot true model and recovered model\n",
    "fig = plt.figure(figsize=(6, 6))\n",
    "\n",
    "ax1 = fig.add_axes([0.2, 0.15, 0.7, 0.7])\n",
    "plot_1d_layer_model(true_layers, 1./true_conductivities, ax=ax1, color=\"k\")\n",
    "plot_1d_layer_model(\n",
    "    layer_thicknesses, 1./(log_conductivity_map * inv_prob_irls.l2model), ax=ax1, color=\"b\"\n",
    ")\n",
    "plot_1d_layer_model(\n",
    "    layer_thicknesses, 1./(log_conductivity_map * recovered_model_irls), ax=ax1, color=\"r\"\n",
    ")\n",
    "ax1.grid()\n",
    "ax1.set_xlabel(r\"Resistivity ($\\Omega m$)\")\n",
    "x_min, x_max = 0.1, 100\n",
    "ax1.set_xlim(0.8 * x_min, 1.5 * x_max)\n",
    "ax1.set_ylim([np.sum(true_layers), 0])\n",
    "ax1.legend([\"True Model\", \"L2 Model\", \"IRLS Model\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "reference_model = np.ones(len(h)) * np.log(1./10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Running inversion with SimPEG v0.22.2.dev6+g67b3e9f1c\n",
      "\n",
      "                        simpeg.InvProblem is setting bfgsH0 to the inverse of the eval2Deriv.\n",
      "                        ***Done using same Solver, and solver_opts as the Simulation1DLayered problem***\n",
      "                        \n",
      "model has any nan: 0\n",
      "============================ Inexact Gauss Newton ============================\n",
      "  #     beta     phi_d     phi_m       f      |proj(x-g)-x|  LS    Comment   \n",
      "-----------------------------------------------------------------------------\n",
      "x0 has any nan: 0\n",
      "   0  7.68e+01  4.53e+03  0.00e+00  4.53e+03    8.73e+02      0              \n",
      "   1  3.84e+01  4.07e+03  2.15e+00  4.15e+03    3.97e+02      0              \n",
      "   2  1.92e+01  3.66e+03  8.43e+00  3.82e+03    4.03e+02      0   Skip BFGS  \n",
      "   3  9.60e+00  2.95e+03  2.84e+01  3.22e+03    4.93e+02      0              \n",
      "   4  4.80e+00  1.52e+03  9.05e+01  1.95e+03    6.51e+02      0              \n",
      "   5  2.40e+00  2.03e+02  1.89e+02  6.57e+02    4.19e+02      0              \n",
      "   6  1.20e+00  1.73e+02  1.90e+02  4.01e+02    1.04e+03      0              \n",
      "   7  6.00e-01  1.28e+02  1.78e+02  2.35e+02    1.06e+03      0   Skip BFGS  \n",
      "   8  3.00e-01  1.06e+02  1.65e+02  1.56e+02    1.12e+03      0   Skip BFGS  \n",
      "   9  1.50e-01  3.30e+01  1.63e+02  5.74e+01    3.62e+02      0   Skip BFGS  \n",
      "Reached starting chifact with l2-norm regularization: Start IRLS steps...\n",
      "irls_threshold 3.527008042191828\n",
      "  10  7.50e-02  2.10e+01  3.17e+02  4.48e+01    1.78e+02      0   Skip BFGS  \n",
      "  11  1.27e-01  2.25e+01  2.88e+02  5.90e+01    2.05e+02      0   Skip BFGS  \n",
      "  12  2.01e-01  2.63e+01  2.09e+02  6.84e+01    2.66e+02      1   Skip BFGS  \n",
      "  13  3.15e-01  2.75e+01  1.27e+02  6.74e+01    2.60e+02      1   Skip BFGS  \n",
      "  14  4.98e-01  2.67e+01  3.92e+01  4.62e+01    1.59e+02      0              \n",
      "  15  8.10e-01  2.48e+01  1.80e+01  3.94e+01    2.09e+01      0   Skip BFGS  \n",
      "  16  1.33e+00  2.43e+01  9.28e+00  3.66e+01    2.99e+01      0              \n",
      "  17  2.19e+00  2.37e+01  4.97e+00  3.46e+01    8.11e+01      0              \n",
      "  18  3.66e+00  2.31e+01  2.64e+00  3.28e+01    9.35e+01      0              \n",
      "  19  6.15e+00  2.29e+01  1.43e+00  3.17e+01    1.21e+02      0              \n",
      "  20  1.03e+01  2.28e+01  6.90e-01  2.99e+01    2.03e+02      0              \n",
      "  21  1.74e+01  2.28e+01  3.16e-01  2.82e+01    1.45e+02      0              \n",
      "  22  2.92e+01  2.27e+01  1.58e-01  2.73e+01    1.33e+02      0   Skip BFGS  \n",
      "  23  4.91e+01  2.27e+01  7.88e-02  2.66e+01    1.34e+02      0   Skip BFGS  \n",
      "  24  8.27e+01  2.27e+01  3.94e-02  2.60e+01    1.36e+02      0   Skip BFGS  \n",
      "  25  1.39e+02  2.27e+01  1.97e-02  2.54e+01    1.37e+02      0   Skip BFGS  \n",
      "  26  2.34e+02  2.27e+01  9.84e-03  2.50e+01    1.38e+02      0   Skip BFGS  \n",
      "  27  3.94e+02  2.27e+01  4.92e-03  2.46e+01    1.39e+02      0   Skip BFGS  \n",
      "  28  6.63e+02  2.27e+01  2.46e-03  2.43e+01    1.40e+02      0   Skip BFGS  \n",
      "  29  1.12e+03  2.27e+01  1.23e-03  2.41e+01    1.41e+02      0   Skip BFGS  \n",
      "  30  1.88e+03  2.27e+01  6.15e-04  2.38e+01    1.42e+02      0   Skip BFGS  \n",
      "  31  3.16e+03  2.27e+01  3.08e-04  2.37e+01    1.42e+02      0   Skip BFGS  \n",
      "  32  5.32e+03  2.27e+01  1.54e-04  2.35e+01    1.43e+02      0   Skip BFGS  \n",
      "  33  8.96e+03  2.27e+01  7.69e-05  2.34e+01    1.43e+02      0   Skip BFGS  \n",
      "  34  1.51e+04  2.27e+01  3.85e-05  2.33e+01    1.43e+02      0   Skip BFGS  \n",
      "  35  2.54e+04  2.27e+01  1.92e-05  2.32e+01    1.44e+02      0   Skip BFGS  \n",
      "  36  4.27e+04  2.27e+01  9.62e-06  2.31e+01    1.43e+02      0   Skip BFGS  \n",
      "  37  7.19e+04  2.27e+01  4.81e-06  2.30e+01    1.44e+02      0   Skip BFGS  \n",
      "  38  1.21e+05  2.27e+01  2.40e-06  2.30e+01    1.58e+03      0   Skip BFGS  \n",
      "  39  2.04e+05  2.27e+01  1.20e-06  2.29e+01    1.43e+05      0   Skip BFGS  \n",
      "  40  3.43e+05  2.27e+01  6.01e-07  2.29e+01    1.46e+02      0              \n",
      "  41  5.78e+05  2.27e+01  3.01e-07  2.29e+01    5.86e+05      0              \n",
      "  42  9.72e+05  2.27e+01  1.50e-07  2.28e+01    1.97e+06      0              \n",
      "  43  1.64e+06  2.27e+01  7.51e-08  2.28e+01    6.65e+06      0              \n",
      "  44  2.76e+06  2.27e+01  3.76e-08  2.28e+01    2.24e+07      0              \n",
      "  45  4.64e+06  2.27e+01  1.88e-08  2.28e+01    7.51e+07      0              \n",
      "  46  7.81e+06  2.27e+01  9.49e-09  2.28e+01    2.52e+08      0              \n",
      "  47  1.31e+07  2.27e+01  4.88e-09  2.27e+01    8.35e+08      1              \n",
      "  48  2.21e+07  2.27e+01  2.70e-09  2.27e+01    2.66e+09      0              \n",
      "  49  3.72e+07  2.27e+01  1.76e-09  2.27e+01    7.47e+09      0              \n",
      "  50  6.27e+07  2.27e+01  1.30e-09  2.28e+01    1.64e+10      0              \n",
      "  51  1.06e+08  2.27e+01  9.96e-10  2.28e+01    3.18e+10      0              \n",
      "  52  1.78e+08  2.27e+01  7.74e-10  2.28e+01    5.97e+10      0              \n",
      "  53  2.99e+08  2.27e+01  6.54e-10  2.29e+01    1.20e+11      0              \n",
      "  54  5.03e+08  2.27e+01  4.38e-10  2.29e+01    1.85e+11      0              \n",
      "  55  8.47e+08  2.27e+01  2.04e-10  2.29e+01    2.55e+11      0              \n",
      "  56  1.43e+09  2.27e+01  7.80e-11  2.28e+01    3.47e+11      0              \n",
      "  57  2.40e+09  2.27e+01  3.82e-11  2.28e+01    7.88e+11      0              \n",
      "  58  4.04e+09  2.27e+01  1.26e-11  2.27e+01    1.08e+12      0              \n",
      "  59  6.80e+09  2.27e+01  7.34e-12  2.27e+01    2.26e+12      0              \n",
      "Reach maximum number of IRLS cycles: 50\n",
      "------------------------- STOP! -------------------------\n",
      "1 : |fc-fOld| = 0.0000e+00 <= tolF*(1+|f0|) = 4.5289e+02\n",
      "1 : |xc-x_last| = 6.0892e-03 <= tolX*(1+|x0|) = 1.4622e+00\n",
      "0 : |proj(x-g)-x|    = 2.2607e+12 <= tolG          = 1.0000e-20\n",
      "0 : |proj(x-g)-x|    = 2.2607e+12 <= 1e3*eps       = 1.0000e-17\n",
      "0 : maxIter   =     100    <= iter          =     60\n",
      "------------------------- DONE! -------------------------\n"
     ]
    }
   ],
   "source": [
    "simulation_irls = tdem.simulation_1d.Simulation1DLayered(\n",
    "    survey=survey,\n",
    "    sigmaMap=log_conductivity_map,\n",
    "    thicknesses=layer_thicknesses,\n",
    ")\n",
    "dmis_irls = data_misfit.L2DataMisfit(simulation=simulation_irls, data=data_object)\n",
    "\n",
    "\n",
    "reg_irls = regularization.Sparse(\n",
    "    regularization_mesh,\n",
    "    # alpha_s=1.,\n",
    "    reference_model_in_smooth=False,\n",
    "    reference_model = reference_model,\n",
    "    norms=[0.0, 0.0],\n",
    ")\n",
    "\n",
    "opt_irls = optimization.InexactGaussNewton(\n",
    "    maxIter=100, maxIterLS=20, maxIterCG=100, tolCG=1e-10, tolG=1e-20, eps=1e-20\n",
    ")\n",
    "\n",
    "inv_prob_irls = inverse_problem.BaseInvProblem(dmis_irls, reg_irls, opt_irls)\n",
    "\n",
    "# starting_beta_irls = directives.BetaEstimate_ByEig(beta0_ratio=1e-2)\n",
    "starting_beta_irls = directives.BetaEstimate_ByEig(beta0_ratio=1.)\n",
    "\n",
    "update_jacobi_irls = directives.UpdatePreconditioner(update_every_iteration=True)\n",
    "update_irls = directives.Update_IRLS(\n",
    "    coolingFactor=2,\n",
    "    coolingRate=1,\n",
    "    f_min_change=1e-10,\n",
    "    max_irls_iterations=50,\n",
    "    chifact_start=1.,\n",
    "    beta_search=False,\n",
    "    chifact_target=1.\n",
    ")\n",
    "update_irls.coolEpsFact = 2.\n",
    "save_dict_irls = directives.SaveOutputDictEveryIteration()\n",
    "\n",
    "directives_list_irls = [\n",
    "    update_irls,        \n",
    "    # sensitivity_weights_irls,\n",
    "    # update_jacobi_irls,\n",
    "    starting_beta_irls,\n",
    "    save_dict_irls,\n",
    "    \n",
    "]\n",
    "\n",
    "# Here we combine the inverse problem and the set of directives\n",
    "inv_irls = inversion.BaseInversion(inv_prob_irls, directives_list_irls)\n",
    "\n",
    "# Run the inversion\n",
    "# recovered_model_irls_l0l0 = inv_irls.run(recovered_model_L2)\n",
    "recovered_model_irls_l0l0 = inv_irls.run(starting_conductivity_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "8414b806953044c8904067db46fcf05d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='iteration', max=60, min=1), Output()), _dom_classes=('wi…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.foo(iteration)>"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plot true model and recovered model\n",
    "iterations = list(save_dict_irls.outDict.keys())\n",
    "def foo(iteration):\n",
    "    fig = plt.figure(figsize=(6, 6))\n",
    "    ax1 = fig.add_axes([0.2, 0.15, 0.7, 0.7])\n",
    "    plot_1d_layer_model(true_layers, 1./true_conductivities, ax=ax1, color=\"k\")\n",
    "    plot_1d_layer_model(\n",
    "        layer_thicknesses, 1./(log_conductivity_map * save_dict_irls.outDict[iteration]['m']), ax=ax1, color=\"b\"\n",
    "    )\n",
    "    plot_1d_layer_model(\n",
    "        layer_thicknesses, 1./(log_conductivity_map * recovered_model_irls_l0l0), ax=ax1, color=\"r\"\n",
    "    )\n",
    "    ax1.grid()\n",
    "    ax1.set_xlabel(r\"Resistivity ($\\Omega m$)\")\n",
    "    x_min, x_max = 0.1, 100\n",
    "    ax1.set_xlim(0.8 * x_min, 1.5 * x_max)\n",
    "    ax1.set_ylim([np.sum(true_layers), 0])\n",
    "    ax1.legend([\"True Model\", \"L2 Model\", \"IRLS Model\"])\n",
    "    plt.show()\n",
    "from ipywidgets import widgets, interact\n",
    "interact(foo, iteration=widgets.IntSlider(min=1, max=len(iterations), value=1, step=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Plot true model and recovered model\n",
    "iterations = list(save_dict_irls.outDict.keys())\n",
    "def foo(iteration):\n",
    "    fig = plt.figure(figsize=(6, 6))\n",
    "    ax1 = fig.add_axes([0.2, 0.15, 0.7, 0.7])\n",
    "    plot_1d_layer_model(true_layers, 1./true_conductivities, ax=ax1, color=\"k\")\n",
    "    plot_1d_layer_model(\n",
    "        layer_thicknesses, 1./(log_conductivity_map * save_dict_irls.outDict[iteration]['m']), ax=ax1, color=\"b\"\n",
    "    )\n",
    "    plot_1d_layer_model(\n",
    "        layer_thicknesses, 1./(log_conductivity_map * recovered_model_irls_l0l0), ax=ax1, color=\"r\"\n",
    "    )\n",
    "    ax1.grid()\n",
    "    ax1.set_xlabel(r\"Resistivity ($\\Omega m$)\")\n",
    "    x_min, x_max = 0.1, 100\n",
    "    ax1.set_xlim(0.8 * x_min, 1.5 * x_max)\n",
    "    ax1.set_ylim([np.sum(true_layers), 0])\n",
    "    ax1.legend([\"True Model\", \"L2 Model\", \"IRLS Model\"])\n",
    "    plt.show()\n",
    "from ipywidgets import widgets, interact\n",
    "interact(foo, iteration=widgets.IntSlider(min=1, max=len(iterations), value=1, step=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parametric Inversion\n",
    "\n",
    "Here, we assume the subsurface is defined by a 3-layered Earth. However, the electrical properties and thicknesses of the layers are unknown. Here, we define our model to include log-conductivities and log-thicknesses. When including quantities that span different scales, it is frequently best to define the model in terms of log values so that each quantity influences the predicted data evenly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model and Mapping\n",
    "\n",
    "For a 3-layered Earth model, the model consists of 2 log-thicknesses and 3 log-conductivities. Similar to the [1D Forward Simulation of Time Domain EM Data for a Single Sounding](fwd_tdem_1d.ipynb) tutorial, need a mapping that extract log-thicknesses and log-resistivities from the model, and mappings that convert log-values to property values. For this, we require the [simpeg.maps.Wires](myst:simpeg#simpeg.maps.Wires) mapping and [simpeg.maps.ExpMap](myst:simpeg#simpeg.maps.ExpMap) mapping classes. Note that successive mappings can be chained together using the $*$ operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Wire maps to extract log-thicknesses and log-conductivities\n",
    "wire_map = maps.Wires((\"log_thicknesses\", 2), (\"log_resistivity\", 3))\n",
    "\n",
    "# Maping for layer thicknesses\n",
    "log_thicknesses_map = maps.ExpMap() * wire_map.log_thicknesses\n",
    "\n",
    "# Mapping for conductivities\n",
    "log_resistivity_map = maps.ExpMap() * wire_map.log_resistivity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Starting and Reference Model\n",
    "\n",
    "This problem is highly non-linear so it is important to have a reasonable estimate of the true model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "starting_parametric_model = np.log(np.r_[30.0, 20.0, 20, 0.5, 5])\n",
    "\n",
    "reference_parametric_model = starting_parametric_model.copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forward Simulation\n",
    "\n",
    "Because the layer thicknesses are part of the model, we define the ``thicknessesMap``. Because we are working in terms of electrical resistivity, we must define the ``rhoMap``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "simulation_parametric = tdem.simulation_1d.Simulation1DLayered(\n",
    "    survey=survey,\n",
    "    rhoMap=log_resistivity_map,\n",
    "    thicknessesMap=log_thicknesses_map,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Misfit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "dmis_parametric = data_misfit.L2DataMisfit(\n",
    "    simulation=simulation_parametric, data=data_object\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (Combo) Regularization\n",
    "\n",
    "We need to define a regularization for each model parameter type. In this case, we have log-thicknesses and log-conductivities. For each model parameter type, we create a 1D [tensor mesh](myst:discretize#discretize.TensorMesh) with length equal to the number of parameters. In the ``mapping`` keyword argument, we used the wire map that extracts the specific model parameters from the model.\n",
    "\n",
    "Using the $*$ operator, separate regularizations can be summed to form a regularization that is also a [ComboObjectiveFunction](myst:simpeg#simpeg.objective_function.ComboObjectiveFunction). By setting the ``multipliers`` property, we can emphasize the relative contributions of the log-thicknesses and log-conductivities regularizations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "reg_1 = regularization.Smallness(\n",
    "    TensorMesh([(np.ones(2))], \"0\"),\n",
    "    mapping=wire_map.log_thicknesses,\n",
    "    reference_model=reference_parametric_model,\n",
    ")\n",
    "\n",
    "reg_2 = regularization.Smallness(\n",
    "    TensorMesh([(np.ones(3))], \"0\"),\n",
    "    mapping=wire_map.log_resistivity,\n",
    "    reference_model=reference_parametric_model,\n",
    ")\n",
    "\n",
    "reg_parametric = reg_1 + reg_2\n",
    "reg_parametric.multipliers = [1.0, 0.1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "opt_parametric = optimization.InexactGaussNewton(\n",
    "    maxIter=100, maxIterLS=20, maxIterCG=20, tolCG=1e-3\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inverse Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "inv_prob_parametric = inverse_problem.BaseInvProblem(\n",
    "    dmis_parametric, reg_parametric, opt_parametric\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Directives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "update_jacobi = directives.UpdatePreconditioner(update_every_iteration=True)\n",
    "starting_beta = directives.BetaEstimate_ByEig(beta0_ratio=10)\n",
    "beta_schedule = directives.BetaSchedule(coolingFactor=2.0, coolingRate=3)\n",
    "target_misfit = directives.TargetMisfit(chifact=1.0)\n",
    "\n",
    "directives_list_parametric = [\n",
    "    update_jacobi,\n",
    "    starting_beta,\n",
    "    beta_schedule,\n",
    "    target_misfit,\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define and Run Inversion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "inv_parametric = inversion.BaseInversion(\n",
    "    inv_prob_parametric, directives_list_parametric\n",
    ")\n",
    "recovered_model_parametric = inv_parametric.run(starting_parametric_model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Misfit and Recovered Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "dpred_parametric = simulation_parametric.dpred(recovered_model_parametric)\n",
    "\n",
    "fig = plt.figure(figsize=(5, 5))\n",
    "ax1 = fig.add_axes([0.15, 0.15, 0.8, 0.75])\n",
    "ax1.loglog(times, np.abs(dobs), \"k-o\")\n",
    "ax1.loglog(times, np.abs(dpred_L2), \"b-o\")\n",
    "ax1.loglog(times, np.abs(dpred_irls), \"r-o\")\n",
    "ax1.loglog(times, np.abs(dpred_parametric), \"g-o\")\n",
    "ax1.grid(which=\"both\")\n",
    "ax1.set_xlabel(\"times (s)\")\n",
    "ax1.set_ylabel(\"Bz (T)\")\n",
    "ax1.set_title(\"Predicted and Observed Data\")\n",
    "ax1.legend(\n",
    "    [\"Observed\", \"L2 Inversion\", \"IRLS Inversion\", \"Parametric Inversion\"],\n",
    "    loc=\"upper right\",\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(6, 6))\n",
    "\n",
    "ax1 = fig.add_axes([0.2, 0.15, 0.7, 0.7])\n",
    "plot_1d_layer_model(true_layers, true_conductivities, ax=ax1, color=\"k\")\n",
    "plot_1d_layer_model(\n",
    "    layer_thicknesses, log_conductivity_map * recovered_model_L2, ax=ax1, color=\"b\"\n",
    ")\n",
    "plot_1d_layer_model(\n",
    "    layer_thicknesses, log_conductivity_map * recovered_model_irls, ax=ax1, color=\"r\"\n",
    ")\n",
    "plot_1d_layer_model(\n",
    "    log_thicknesses_map * recovered_model_parametric,\n",
    "    1 / (log_resistivity_map * recovered_model_parametric),\n",
    "    ax=ax1,\n",
    "    color=\"g\",\n",
    ")\n",
    "ax1.grid()\n",
    "ax1.set_xlabel(r\"Resistivity ($\\Omega m$)\")\n",
    "ax1.set_xlim(0.8 * x_min, 2 * x_max)\n",
    "ax1.set_ylim([np.sum(true_layers), 0])\n",
    "ax1.legend([\"True Model\", \"L2 Model\", \"IRLS Model\", \"Parametric Model\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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