{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "8d5fcb02",
   "metadata": {},
   "source": [
    "# 2D Gravity Inversion\n",
    "\n",
    "## Bayesian Inversion for Subsurface Density Estimation\n",
    "\n",
    "This notebook demonstrates solving a 2D gravity inverse problem using Bayesian estimation.\n",
    "\n",
    "### Problem Setup\n",
    "\n",
    "**State (x):** Density anomalies in subsurface prisms [g/cm³]  \n",
    "**Observations (z):** Vertical component of gravity field at surface [mGal]  \n",
    "**Forward model:** z = H @ x (Newtonian gravity from rectangular prisms)\n",
    "\n",
    "### Geometry\n",
    "- **Domain:** 100m horizontal × 40m depth\n",
    "- **Mesh:** 10 × 4 prisms (horizontal × vertical)\n",
    "- **Observations:** 41 surface gravity measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b724c1bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "\n",
    "from fips import Block, CovarianceMatrix, ForwardOperator, InverseProblem, Vector\n",
    "\n",
    "# Configure plotting\n",
    "plt.style.use(\"seaborn-v0_8-darkgrid\")\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a5fcbce",
   "metadata": {},
   "source": [
    "## Configuration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8077d031",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Physical constant\n",
    "GAMMA = 6.67e-4  # Gravitational constant in CGS units"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57a62cf4",
   "metadata": {},
   "source": [
    "## Define Geometry and Generate Synthetic Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "48f15093",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Data created:\n",
      "  Observations: 41\n",
      "  State dimension: 40 (10 × 4 prisms)\n",
      "  Gravity range: [0.0065, 0.1196] mGal\n",
      "  Domain: 0.0-1000.0 m (horizontal), 25.0-250.0 m (depth)\n"
     ]
    }
   ],
   "source": [
    "# Observed gravity anomalies\n",
    "z_obs = np.array(\n",
    "    [\n",
    "        6.5112333e-03,\n",
    "        7.1144759e-03,\n",
    "        7.8050213e-03,\n",
    "        8.6004187e-03,\n",
    "        9.5228049e-03,\n",
    "        1.0600394e-02,\n",
    "        1.1869543e-02,\n",
    "        1.3377636e-02,\n",
    "        1.5187140e-02,\n",
    "        1.7381291e-02,\n",
    "        2.0071869e-02,\n",
    "        2.3409173e-02,\n",
    "        2.7592423e-02,\n",
    "        3.2872699e-02,\n",
    "        3.9524661e-02,\n",
    "        4.7739666e-02,\n",
    "        5.7427097e-02,\n",
    "        6.8126652e-02,\n",
    "        7.9261565e-02,\n",
    "        9.0330964e-02,\n",
    "        1.0070638e-01,\n",
    "        1.0950167e-01,\n",
    "        1.1588202e-01,\n",
    "        1.1936106e-01,\n",
    "        1.1961197e-01,\n",
    "        1.1617789e-01,\n",
    "        1.0868957e-01,\n",
    "        9.7370419e-02,\n",
    "        8.3429883e-02,\n",
    "        6.9002570e-02,\n",
    "        5.6079733e-02,\n",
    "        4.5525921e-02,\n",
    "        3.7267881e-02,\n",
    "        3.0880404e-02,\n",
    "        2.5919366e-02,\n",
    "        2.2024198e-02,\n",
    "        1.8925481e-02,\n",
    "        1.6427182e-02,\n",
    "        1.4387142e-02,\n",
    "        1.2701558e-02,\n",
    "        1.1293783e-02,\n",
    "    ]\n",
    ")\n",
    "\n",
    "# Create observation locations (41 points from 0 to 1000 m)\n",
    "obs_locs = np.linspace(0, 1000, len(z_obs))\n",
    "\n",
    "# Create mesh boundaries (10 x 4 prisms)\n",
    "prism_x = np.linspace(0, 1000, 11)  # 11 boundaries for 10 prisms\n",
    "prism_z = np.linspace(25, 250, 5)  # 5 boundaries for 4 prisms\n",
    "\n",
    "n_obs = len(z_obs)\n",
    "n_x = len(prism_x) - 1\n",
    "n_z = len(prism_z) - 1\n",
    "n_state = n_x * n_z\n",
    "\n",
    "print(\"Data created:\")\n",
    "print(f\"  Observations: {n_obs}\")\n",
    "print(f\"  State dimension: {n_state} ({n_x} × {n_z} prisms)\")\n",
    "print(f\"  Gravity range: [{z_obs.min():.4f}, {z_obs.max():.4f}] mGal\")\n",
    "print(\n",
    "    f\"  Domain: {prism_x.min()}-{prism_x.max()} m (horizontal), {prism_z.min()}-{prism_z.max()} m (depth)\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf44a10c",
   "metadata": {},
   "source": [
    "## Build Forward Operator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "20f00d2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gravity_integral(x, z):\n",
    "    \"\"\"\n",
    "    Analytical integral for Newtonian gravity from a rectangular prism.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    x, z : array_like\n",
    "        Horizontal and vertical distances\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    array_like\n",
    "        Integrated gravity contribution\n",
    "    \"\"\"\n",
    "    return z * np.arctan(x / z) + x / 2 * np.log(z**2 + x**2)\n",
    "\n",
    "\n",
    "def build_forward_operator(obs_locs, prism_x, prism_z, gamma=GAMMA):\n",
    "    \"\"\"\n",
    "    Build forward operator H relating density to gravity.\n",
    "\n",
    "    Maps state (density in prisms) to observations (gravity at surface):\n",
    "        z = H @ x\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    obs_locs : array\n",
    "        Observation locations (horizontal positions) [m]\n",
    "    prism_x : array\n",
    "        Prism boundaries in x-direction [m]\n",
    "    prism_z : array\n",
    "        Prism boundaries in z-direction (depth) [m]\n",
    "    gamma : float\n",
    "        Gravitational constant\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    H : ndarray\n",
    "        Forward operator [n_obs × n_state]\n",
    "    \"\"\"\n",
    "    n_obs = len(obs_locs)\n",
    "    n_x = len(prism_x) - 1\n",
    "    n_z = len(prism_z) - 1\n",
    "    n_state = n_x * n_z\n",
    "\n",
    "    H = np.zeros((n_obs, n_state))\n",
    "\n",
    "    idx = 0\n",
    "    for ix in range(1, len(prism_x)):\n",
    "        x1 = prism_x[ix - 1] - obs_locs  # Lower x boundary\n",
    "        x2 = prism_x[ix] - obs_locs  # Upper x boundary\n",
    "\n",
    "        for iz in range(1, len(prism_z)):\n",
    "            z1 = prism_z[iz - 1]  # Upper z boundary (shallow)\n",
    "            z2 = prism_z[iz]  # Lower z boundary (deep)\n",
    "\n",
    "            # Compute gravity contribution using analytical formula\n",
    "            contrib = (\n",
    "                gravity_integral(x2, z2)\n",
    "                - gravity_integral(x2, z1)\n",
    "                - gravity_integral(x1, z2)\n",
    "                + gravity_integral(x1, z1)\n",
    "            )\n",
    "\n",
    "            H[:, idx] = 2 * gamma * contrib\n",
    "            idx += 1\n",
    "\n",
    "    return H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "aabb2f0e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Building forward operator...\n",
      "Forward operator shape: (41, 40)\n",
      "  Condition number: 5.38e+07\n"
     ]
    }
   ],
   "source": [
    "# Build forward operator\n",
    "print(\"Building forward operator...\")\n",
    "H = build_forward_operator(obs_locs, prism_x, prism_z)\n",
    "\n",
    "print(f\"Forward operator shape: {H.shape}\")\n",
    "print(f\"  Condition number: {np.linalg.cond(H):.2e}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb169318",
   "metadata": {},
   "source": [
    "## Setup Inverse Problem\n",
    "\n",
    "### Prior Information\n",
    "- **Mean:** x₀ = 0 (zero density anomaly)\n",
    "- **Covariance:** S_0 = 0.5² I (independent prisms)\n",
    "\n",
    "### Observation Error\n",
    "- S_z = (0.05 · max(z))² I (5% of maximum signal)\n",
    "\n",
    "### Bayesian Framework\n",
    "**Posterior estimate:**\n",
    "$$\\hat{x} = x_0 + K(z - Hx_0)$$\n",
    "\n",
    "**Posterior covariance:**\n",
    "$$\\hat{S} = S_0 - (HS_0)^T(HS_0H^T + S_z)^{-1}(HS_0)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1b84fab9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inverse problem configured.\n",
      "  Prior uncertainty: 0.5 g/cm³\n",
      "  Observation uncertainty: 0.0060 mGal\n"
     ]
    }
   ],
   "source": [
    "# Create indices\n",
    "obs_idx = pd.Index([f\"obs_{i:03d}\" for i in range(n_obs)], name=\"x\")\n",
    "state_idx = pd.Index([f\"prism_{i:03d}\" for i in range(n_state)], name=\"prism\")\n",
    "\n",
    "# Observation vector\n",
    "z = Vector(\n",
    "    name=\"observations\", data=[Block(pd.Series(z_obs, index=obs_idx, name=\"gravity\"))]\n",
    ")\n",
    "\n",
    "# Prior state (zero density anomaly)\n",
    "x_0 = Vector(\n",
    "    name=\"prior\",\n",
    "    data=[Block(pd.Series(np.zeros(n_state), index=state_idx, name=\"density\"))],\n",
    ")\n",
    "\n",
    "# Prior error covariance (independent prisms)\n",
    "sigma_x = 0.5  # Prior uncertainty [g/cm³]\n",
    "S_0 = CovarianceMatrix(\n",
    "    pd.DataFrame(\n",
    "        np.diag(sigma_x**2 * np.ones(n_state)), index=x_0.index, columns=x_0.index\n",
    "    )\n",
    ")\n",
    "\n",
    "# Observation error covariance\n",
    "sigma_z = 0.05 * np.max(z_obs)  # 5% of max signal\n",
    "S_z = CovarianceMatrix(\n",
    "    pd.DataFrame(np.diag(sigma_z**2 * np.ones(n_obs)), index=z.index, columns=z.index)\n",
    ")\n",
    "\n",
    "# Forward operator\n",
    "H_mat = ForwardOperator(pd.DataFrame(H, index=z.index, columns=x_0.index))\n",
    "\n",
    "# Create problem\n",
    "problem = InverseProblem(\n",
    "    prior=x_0, obs=z, forward_operator=H_mat, prior_error=S_0, modeldata_mismatch=S_z\n",
    ")\n",
    "\n",
    "print(\"Inverse problem configured.\")\n",
    "print(f\"  Prior uncertainty: {sigma_x} g/cm³\")\n",
    "print(f\"  Observation uncertainty: {sigma_z:.4f} mGal\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1d82f35",
   "metadata": {},
   "source": [
    "## Solve Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c6c1663a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solving...\n",
      "✓ Solution complete\n"
     ]
    }
   ],
   "source": [
    "# Solve using Bayesian estimator\n",
    "print(\"Solving...\")\n",
    "problem.solve(estimator=\"bayesian\")\n",
    "print(\"✓ Solution complete\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f78cfa4",
   "metadata": {},
   "source": [
    "## Diagnostics\n",
    "\n",
    "Analyze the solution quality and information content."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2750f6aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "POSTERIOR STATE (DENSITY)\n",
      "  Mean: 0.0609 g/cm³\n",
      "  Std:  0.0931 g/cm³\n",
      "  Range: [-0.0185, 0.3153] g/cm³\n",
      "\n",
      "OBSERVATION FIT\n",
      "  RMSE: 4.625043e-04 mGal\n",
      "  R²: 0.9999\n",
      "  Max residual: 1.205564e-03 mGal\n",
      "\n",
      "UNCERTAINTY REDUCTION\n",
      "  Mean: 18.9%\n",
      "  Range: [2.0%, 59.1%]\n",
      "\n",
      "INFORMATION CONTENT\n",
      "  DOFS: 12.0\n",
      "  Reduced χ²: 0.054\n"
     ]
    }
   ],
   "source": [
    "# Extract results\n",
    "x_post = problem.posterior.data.values\n",
    "z_obs_vals = problem.obs.data.values\n",
    "z_post = problem.posterior_obs.data.values\n",
    "z_prior = problem.prior_obs.data.values\n",
    "\n",
    "# Posterior state\n",
    "print(\"POSTERIOR STATE (DENSITY)\")\n",
    "print(f\"  Mean: {x_post.mean():.4f} g/cm³\")\n",
    "print(f\"  Std:  {x_post.std():.4f} g/cm³\")\n",
    "print(f\"  Range: [{x_post.min():.4f}, {x_post.max():.4f}] g/cm³\")\n",
    "\n",
    "# Observation fit\n",
    "print(\"\\nOBSERVATION FIT\")\n",
    "print(f\"  RMSE: {problem.estimator.RMSE:.6e} mGal\")\n",
    "print(f\"  R²: {problem.estimator.R2:.4f}\")\n",
    "residuals = z_obs_vals - z_post\n",
    "print(f\"  Max residual: {np.abs(residuals).max():.6e} mGal\")\n",
    "\n",
    "# Uncertainty reduction\n",
    "prior_std = np.sqrt(np.diag(problem.prior_error.values))\n",
    "post_std = np.sqrt(np.diag(problem.posterior_error.values))\n",
    "reduction = (1 - post_std / prior_std) * 100\n",
    "\n",
    "print(\"\\nUNCERTAINTY REDUCTION\")\n",
    "print(f\"  Mean: {reduction.mean():.1f}%\")\n",
    "print(f\"  Range: [{reduction.min():.1f}%, {reduction.max():.1f}%]\")\n",
    "\n",
    "# Information content\n",
    "print(\"\\nINFORMATION CONTENT\")\n",
    "print(f\"  DOFS: {problem.estimator.DOFS:.1f}\")\n",
    "print(f\"  Reduced χ²: {problem.estimator.reduced_chi2:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b5ee9b6",
   "metadata": {},
   "source": [
    "## Visualization\n",
    "\n",
    "### Data Fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9d5057a1",
   "metadata": {
    "tags": [
     "nbsphinx-thumbnail"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x1400 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Combined visualization: all plots with shared x-axis\n",
    "fig, axes = plt.subplots(\n",
    "    4, 1, figsize=(12, 14), sharex=True, gridspec_kw={\"hspace\": 0.4}\n",
    ")\n",
    "\n",
    "# Prepare data for pcolormesh plots\n",
    "x_post_2d = x_post.reshape(n_x, n_z).T\n",
    "x_post_std = np.sqrt(np.diag(problem.posterior_error.values))\n",
    "x_post_std_2d = x_post_std.reshape(n_x, n_z).T\n",
    "X, Z = np.meshgrid(prism_x, prism_z)\n",
    "\n",
    "# Plot 1: Data fit\n",
    "ax = axes[0]\n",
    "ax.plot(obs_locs, z_obs_vals, \"kx\", label=\"Observed\", markersize=8, markeredgewidth=2)\n",
    "ax.plot(obs_locs, z_post, \"b-\", label=\"Posterior\", linewidth=2.5)\n",
    "ax.plot(obs_locs, z_prior, \"g--\", label=\"Prior\", linewidth=2, alpha=0.7)\n",
    "ax.set(ylabel=\"Gravity (mGal)\")\n",
    "ax.set_title(\"Data Fit\", fontweight=\"bold\", fontsize=12)\n",
    "ax.legend(fontsize=10)\n",
    "ax.grid(True, alpha=0.3)\n",
    "\n",
    "# Plot 2: Posterior density\n",
    "ax = axes[1]\n",
    "im1 = ax.pcolormesh(X, Z, x_post_2d, cmap=\"Greys\", shading=\"flat\")\n",
    "ax.set(ylabel=\"Depth (m)\")\n",
    "ax.set_title(\"Posterior State\", fontweight=\"bold\", fontsize=12)\n",
    "ax.invert_yaxis()\n",
    "cax1 = make_axes_locatable(ax).append_axes(\"bottom\", size=\"8%\", pad=0.3)\n",
    "cbar1 = plt.colorbar(im1, cax=cax1, orientation=\"horizontal\")\n",
    "cbar1.set_label(\"Density (g/cm³)\", fontsize=10)\n",
    "\n",
    "# Plot 3: Posterior uncertainty\n",
    "ax = axes[2]\n",
    "im2 = ax.pcolormesh(X, Z, x_post_std_2d, cmap=\"viridis\", shading=\"flat\")\n",
    "ax.set(ylabel=\"Depth (m)\")\n",
    "ax.set_title(\"Posterior Uncertainty\", fontweight=\"bold\", fontsize=12)\n",
    "ax.invert_yaxis()\n",
    "cax2 = make_axes_locatable(ax).append_axes(\"bottom\", size=\"8%\", pad=0.3)\n",
    "cbar2 = plt.colorbar(im2, cax=cax2, orientation=\"horizontal\")\n",
    "cbar2.set_label(\"Std Dev (g/cm³)\", fontsize=10)\n",
    "\n",
    "# Plot 4: Residuals\n",
    "ax = axes[3]\n",
    "residuals = z_obs_vals - z_post\n",
    "ax.bar(obs_locs, residuals, width=8, alpha=0.7, edgecolor=\"black\")\n",
    "ax.axhline(0, color=\"r\", linestyle=\"--\", linewidth=2, label=\"Zero\")\n",
    "ax.set(xlabel=\"x (m)\", ylabel=\"Residual (mGal)\")\n",
    "ax.set_title(\"Observation Residuals\", fontweight=\"bold\", fontsize=12)\n",
    "ax.legend(fontsize=10)\n",
    "ax.grid(True, alpha=0.3, axis=\"y\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a2a6faa6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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