Begin adding content

Author: domfournier

docs/fundamentals/regularization/images/fold_model.png

@@ -98,6 +98,80 @@
     "\n",
     "\n"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fe021d63-9952-4a7e-8ebb-e5ff94b04a3b",
+   "metadata": {},
+   "source": [
+    "## Example\n",
+    "\n",
+    "This section demonstrates the use of rotated gradients on a semi-realistic synthetic example. \n",
+    "\n",
+    "### Setup \n",
+    "\n",
+    "The model has been generated with the help of [Gempy](https://app.readthedocs.com/projects/mirageoscience-gempy-drivers/builds/?version__slug=stable). The model comprises a folded and faulted magnetic layer (0.5 SI) dipping 20 degrees towards East. The geometry is meant to mimic a banded-iron formation.\n",
+    "\n",
+    "```{figure} ./images/fold_model.png\n",
+    "---\n",
+    "scale: 30%\n",
+    "---\n",
+    "```\n",
+    "\n",
+    "From this model, we simulate residual magnetic field data along an East-West survey, 200 m line spacing and a mean terrain clearance of 150 m. For simplicity, we use a vertical inducing field with a magnitude of 50,000 nT.\n",
+    "\n",
+    "```{figure} ./images/fold_model.png\n",
+    "---\n",
+    "scale: 30%\n",
+    "---\n",
+    "```\n",
+    "\n",
+    "The basic components (data, model and topography) to reproduce this example can be [downloaded here]()."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6bdbf088-2983-4975-99f5-cb1fba3d2741",
+   "metadata": {},
+   "source": [
+    "### Standard unconstrained inversion\n",
+    "\n",
+    "As a starting point, we invert the magnetic data with standard constraints (lower bounds and reference value of 0 SI). \n",
+    "The resulting smooth model shows clear breaks between the survey lines and poorly resolves the dip of the magnetic layer. The subsequent compact model further exacerbates these issues. \n",
+    "\n",
+    "\n",
+    "### Directional constraints\n",
+    "\n",
+    "To improve the continuity of the magnetic layer across lines and down-dip, we can provide trend information to the inversion from our structural control points.\n",
+    "\n",
+    "We interpolate the dip and dip direction data from the `structural markers` to the inversion mesh. We use the Radial Basis Function (RBF) application, but users may want to experiment with different interpolation algorithms.\n",
+    "\n",
+    "```{figure} ./images/fold_model.png\n",
+    "---\n",
+    "scale: 30%\n",
+    "---\n",
+    "```\n",
+    "\n",
+    "Following the instructions presented in the [previous section](rotated-gradients), we group the interpolated data as type `Dip Direction & Dip`. Users can validate the constraint by displaying the vectors onto sections of the mesh. Once created, the orientation information is provided to the inversion. \n",
+    "\n",
+    "```{figure} ./images/invert_fault_equal.png\n",
+    "---\n",
+    "scale: 30%\n",
+    "---\n",
+    "```\n",
+    "\n",
+    "The resulting model shows an improved \n",
+    "\n",
+    "\n",
+    "We can further improve this result by decreasing the relative weight applied to the gradient penalty perpendicular (z) to the rotated plane.\n",
+    "\n",
+    "```{figure} ./images/invert_fault_wz0p5.png\n",
+    "---\n",
+    "scale: 30%\n",
+    "---\n",
+    "```\n",
+    "\n"
+   ]
   }
  ],
  "metadata": {
@@ -116,7 +190,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.17"
+   "version": "3.10.19"
   }
  },
  "nbformat": 4,