Fix grammar and spelling mistakes

notebooks/03-gravity/inv_gravity_anomaly_3d.ipynb

@@ -411,7 +411,7 @@
    "source": [
     "### Starting/Reference Models\n",
     "\n",
-    "The **starting model** defines a reasonable starting point for the inversion and does not necessarily represent an initial estimate of the true model. Because the integral formulation used to solve the gravity forward simulation is linear, the optimization problem we must solve is a linear least-squares problem, making the choice in starting model insignificant. It should be noted that the staring model **cannot be vector of zeros,** otherwise the inversion will be unable to compute a gradient direction at the first iteration. For gravity inversion, the starting model is frequently a constant vector with a very small value.\n",
+    "The **starting model** defines a reasonable starting point for the inversion and does not necessarily represent an initial estimate of the true model. Because the integral formulation used to solve the gravity forward simulation is linear, the optimization problem we must solve is a linear least-squares problem, making the choice in starting model insignificant. 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. For gravity inversion, the starting model is frequently a constant vector with a very small value.\n",
     "\n",
     "The **reference model** is used to include a-prior information. The impact of the reference model on the inversion will be discussed in another tutorial. Assuming the contribution from all background structures has been removed from the gravity anomaly data, and assuming we have not a-priori information, the reference model for basic inversion of gravity data is zero.\n",
     "\n",
@@ -552,7 +552,7 @@
    "source": [
     "### Define the Optimization Algorithm\n",
     "\n",
-    "To understand the role of the optimization algorithm in the inversion, please visit this online resource. Here, we use the [InexactGaussNewton](myst:SimPEG#SimPEG.optimization.InexactGaussNewton) class to solve the optimization problem using inexact Gauss-Newton. 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."
+    "Here, we use the [InexactGaussNewton](myst:SimPEG#SimPEG.optimization.InexactGaussNewton) class to solve the optimization problem using inexact Gauss-Newton. 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."
    ]
   },
   {
@@ -592,7 +592,7 @@
     "\n",
     "Directives represent operations that are carried out during the inversion. Here, we apply common directives for weighted least-squares inversion of gravity data and describe their roles. These are:\n",
     "\n",
-    "- [UpdateSensitivityWeights](myst:SimPEG#SimPEG.directives.UpdateSensitivityWeights): apply sensitivity weighting to counteract the natural tendancy of potential field inversion to cluster recovered structures near the receivers. Because the 3D integral formulation is linear, the sensitivity weighting is independent of the model and does not need to be updated throughout the inversion, so we set `every_iteration=False`.\n",
+    "- [UpdateSensitivityWeights](myst:SimPEG#SimPEG.directives.UpdateSensitivityWeights): Apply sensitivity weighting to counteract the natural tendancy of potential field inversion to cluster recovered structures near the receivers. Because the 3D integral formulation is linear, the sensitivity weighting is independent of the model and does not need to be updated throughout the inversion, so we set `every_iteration=False`.\n",
     "\n",
     "- [UpdatePreconditioner](myst:SimPEG#SimPEG.directives.UpdatePreconditioner): Apply Jacobi preconditioner when solving optimization problem.\n",
     "\n",
@@ -633,7 +633,7 @@
    "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 instatiated 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"
+    "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"
    ]
   },
   {
@@ -810,7 +810,7 @@
    "source": [
     "## Iteratively Re-weighted Least-Squares (IRLS) Inversion on a Tree Mesh\n",
     "\n",
-    "Here, we provide a step-by-step best-practices approach for iteratively IRLS inversion of gravity anomaly data on a tree mesh. Many of the steps are the same as our previous approach. As a result, we will avoiding repeating information whenever possible. For the tutorial example, any datum whose normalized data misfit is outside of (-2, 2) will have its uncertainty decreased by a factor of 2.5. This choice was problem dependent!"
+    "Here, we provide a step-by-step best-practices approach for iteratively IRLS inversion of gravity anomaly data on a tree mesh. Many of the steps are the same as our previous approach. As a result, we will avoid repeating information whenever possible. For the tutorial example, any datum whose normalized data misfit is outside of (-2, 2) will have its uncertainty decreased by a factor of 2.5. This choice was problem dependent!"
    ]
   },
   {

notebooks/04-magnetics/inv_magnetics_induced_3d.ipynb

@@ -424,7 +424,7 @@
    "source": [
     "### Starting/Reference Models\n",
     "\n",
-    "The **starting model** defines a reasonable starting point for the inversion and does not necessarily represent an initial estimate of the true model. Because the integral formulation used to solve the magnetic forward simulation is linear, the optimization problem we must solve is a linear least-squares problem, making the choice in starting model insignificant. It should be noted that the staring model **cannot be vector of zeros,** otherwise the inversion will be unable to compute a gradient direction at the first iteration. For magnetic inversion, the starting model is frequently a constant vector with a very small value.\n",
+    "The **starting model** defines a reasonable starting point for the inversion and does not necessarily represent an initial estimate of the true model. Because the integral formulation used to solve the magnetic forward simulation is linear, the optimization problem we must solve is a linear least-squares problem, making the choice in starting model insignificant. 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. For magnetic inversion, the starting model is frequently a constant vector with a very small value.\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. Assuming the contribution from all regional structures has been removed from the magnetic data, and assuming we have not a-priori information, the reference model for basic inversion of magnetic data is zero or equal to the starting model.\n",
     "\n",
@@ -566,7 +566,7 @@
    "source": [
     "### Define the Optimization Algorithm\n",
     "\n",
-    "To understand the role of the optimization algorithm in the inversion, please visit this online resource. Here, we use the [ProjectedGNCG](myst:SimPEG#SimPEG.optimization.ProjectedGNCG) class to solve the optimization problem using projected Gauss-Newton with conjugate gradietn 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. Here, the `lower` property is set to 0 to ensure recovered susceptibility values are positive."
+    "Here, we use the [ProjectedGNCG](myst:SimPEG#SimPEG.optimization.ProjectedGNCG) class to solve the optimization problem using projected Gauss-Newton with conjugate gradietn 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. Here, the `lower` property is set to 0 to ensure recovered susceptibility values are positive."
    ]
   },
   {
@@ -606,7 +606,7 @@
     "\n",
     "Directives represent operations that are carried out during the inversion. Here, we apply common directives for weighted least-squares inversion of magnetic data and describe their roles. These are:\n",
     "\n",
-    "- [UpdateSensitivityWeights](myst:SimPEG#SimPEG.directives.UpdateSensitivityWeights): apply sensitivity weighting to counteract the natural tendancy of potential field inversion to cluster recovered structures near the receivers. Because the 3D integral formulation is linear, the sensitivity weighting is independent of the model and does not need to be updated throughout the inversion, so we set `every_iteration=False`.\n",
+    "- [UpdateSensitivityWeights](myst:SimPEG#SimPEG.directives.UpdateSensitivityWeights): Apply sensitivity weighting to counteract the natural tendancy of potential field inversion to cluster recovered structures near the receivers. Because the 3D integral formulation is linear, the sensitivity weighting is independent of the model and does not need to be updated throughout the inversion, so we set `every_iteration=False`.\n",
     "\n",
     "- [UpdatePreconditioner](myst:SimPEG#SimPEG.directives.UpdatePreconditioner): Apply Jacobi preconditioner when solving optimization problem.\n",
     "\n",
@@ -647,7 +647,7 @@
    "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 instatiated 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"
+    "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"
    ]
   },
   {
@@ -817,7 +817,7 @@
    "source": [
     "## Iteratively Re-weighted Least-Squares Inversion\n",
     "\n",
-    "Here, we provide a step-by-step best-practices approach for iteratively IRLS inversion of total magnetic intensity data on a tree mesh. Many of the steps are the same as our previous approach. As a result, we will avoiding repeating information whenever possible."
+    "Here, we provide a step-by-step best-practices approach for iteratively IRLS inversion of total magnetic intensity data on a tree mesh. Many of the steps are the same as our previous approach. As a result, we will avoid repeating information whenever possible."
    ]
   },
   {

notebooks/05-dcr/inv_dcr_1d.ipynb

@@ -412,7 +412,7 @@
    "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 staring model **cannot be vector of zeros,** otherwise the inversion will be unable to compute a gradient direction at the first iteration.\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",
@@ -548,7 +548,7 @@
    "source": [
     "### Define the Optimization Algorithm\n",
     "\n",
-    "To understand the role of the optimization algorithm in the inversion, please visit this online resource. 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."
+    "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."
    ]
   },
   {
@@ -588,7 +588,7 @@
     "\n",
     "Directives represent operations that are carried out during the inversion. Here, we apply common directives for weighted least-squares inversion of DC resistivity data and describe their roles. These are:\n",
     "\n",
-    "- [UpdateSensitivityWeights](myst:SimPEG#SimPEG.directives.UpdateSensitivityWeights): apply sensitivity weighting to counteract the natural tendancy of DC resistivity inversion to place materials near the electrodes. Since the problem is non-linear and the sensitivities are updated with every model, we set `every_iteration=True`.\n",
+    "- [UpdateSensitivityWeights](myst:SimPEG#SimPEG.directives.UpdateSensitivityWeights): Apply sensitivity weighting to counteract the natural tendency of DC resistivity inversion to place materials near the electrodes. Since the problem is non-linear and the sensitivities are updated with every model, we set `every_iteration=True`.\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",
@@ -629,7 +629,7 @@
    "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 instatiated 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"
+    "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"
    ]
   },
   {