# 4.8.2.1. Edit Options for Gravity Inversion Objects¶

## 4.8.2.1.1. Grav3D Inversion¶

This functionality is responsible for setting all inversion parameters pertaining to the 3D gravity inversion codes; see GRAV3D background theory. The edit options window is comprised of 3 tabs:

Sensitivity:Sets the mesh, observed data, topography, sensitivity weighting and wavelet compression

Inversion:Sets protocols for the trade-off parameter (\(\beta\)) and all parameters pertaining to the model objective function (alphas, cells weights, upper and lower bounds, active cells, reference models and starting models)

Blocky model norms (ver 5.1 and above):can be activated to recover sparse and blocky models; see sparse and blocky norms

### 4.8.2.1.1.1. Units¶

**Inputs:**

Observed data:gravity anomaly data given in units of milliGal (mGal)

Reference/background density model:\(g/cm^3\)

**Outputs:**

Recovered anomalous density model:\(g/cm^3\)

### 4.8.2.1.1.2. Sensitivity Tab¶

Mesh:mesh for the recovered model

Observed data:observed data including uncertainties

Topography:a topography data object. Leave asnullfor flat topography at an elevation of 0 m.

Weighting:set the type and parameters for sensitivity weighting. The parameters which define the sensitivity weighting are described in the Grav3D manual .

Type:Depth or distance. The choice determines the expression used for the weighting

Exponent:Given by \(\alpha\) in the manual. This parameter hasdefault= 2 to reflect the fact the fields fall of as \(1/r^2\)

Z0 or R0:These constants are defined by equations in the manual.R0andZ0are small and generally chosen to be 1/4 the length of the smallest cell dimension

Wavelet parameter:wavelet compression of the sensitivity matrix is used reduced the memory requirements for storing the sensitivity matrix and improve the speed of the inversion algorithm. The details of this are described in the Grav3D manual

Type:sets the type of wavelet transform applied to the rows of the sensitivity matrix

Mode:

Relative error:the level of wavelet compression is specified by a relative threshold (default= 0.05)

Threshold:the level of wavelet compression is specified an absolute threshold

Threshold:user specified value based on choice inmode

### 4.8.2.1.1.3. Inversion Tab¶

Inversion Mode:Sets the protocol for the trade-off parameter (\(\beta\) )

Discrepancy:sets the stopping criteria for the inversion using the discrepancy principle.Chi-factordetermines the stopping criteria andtolerancesets how close to the ideal stopping criteria before the inversion is terminated.

User Input:the user specifies the exact value for the trade-off parameter (beta)

Weighting:Sets the weights for smallness and smoothness regularization in x, y and z; for relevant equations see manual .

Default:Sets the values ofalpha S,alpha X,alpha Yandalpha Zbased on cell dimensions

Alphas:Sets specific values foralpha S,alpha X,alpha Yandalpha Z

Lengths:User sets valuesLen E,Len NandLen Zwhich define the values ofalpha X,alpha Yandalpha Zrelative toalpha S. These relationships are given by \(L_x = \sqrt{\frac{\alpha_x}{\alpha_s}}\), \(L_y = \sqrt{\frac{\alpha_y}{\alpha_s}}\) and \(L_z = \sqrt{\frac{\alpha_z}{\alpha_s}}\).

Weighting object:Specify additional cell weights. Usenullif no additional model weights are supplied.

Reference model options:

Value:use a constant value to define the reference model

Object:use a GIFmodel as the reference model

Role in objective function:the user selectsSMOOTH_MODorSMOOTH_MOD_DIF. IfSMOOTH_MODis selected, the reference model is included only in the smallness term in the model objective function. IfSMOOTH_MOD_DIFis selected, the reference model is included in the smallness and smoothness terms in the model objective function. Further explanation of this is found in fundamentals of inversion.

Initial model:

Value:use a constant value to define a homogeneous starting model

Object:use a GIF model as the starting model

Lower bounds:

Value:set a constant value for the lower bounds for all cells

Object:use a GIF model to supply cell-specific lower bounds

Upper bounds:

Value:set a constant value for the upper bounds for all cells

Object:use a GIF model to supply cell-specific upper bounds

Active cells:Specifies which cells lying below the surface topography are active during the inversion. All other cells remain fixed-valued (equal to starting model). Usenullto set all cells lying below surface topography as active.

Sensitivity matrix:

Default:If this option is chosen, the code will generate the sensitivity matrix and save it to the working directory.

Already exists:If the sensitivity matrix for your problem has already been created, this option allows the user to point to the sensitivity file and avoid recomputation

### 4.8.2.1.1.4. Blocky Model Norms Tab (ver. 5.1 and 6.0)¶

Sparse and blocky model norms are explained in fundamentals of inversion. Below are parameter descriptions for fields within *edit options*.

Lp exponent:

Value:set as a constant value \(p \in (0,2]\)

Object:use a GIF model to supply cell-specific values for \(p\)

Null:a default value of \(p=2\) or \(q=2\) is used

Lq exponent (Easting, Northing or Vertical):

Value:set as a constant value \(p \in (0,2]\) or \(q \in (0,2]\)

Object:use a GIF model to supply cell-specific values for \(p\) or \(q\)

Null:a default value of \(p=2\) or \(q=2\) is used

Lp/Lq scaling:the nature of these parameters are discussed in fundamentals of inversion

Lp vs Lq scale:the user alter the weighting between smallness and smoothness while performing the sparse inversion.Default= 1.

Lp epsilon:see fundamentals of inversion

Lq epsilon:see fundamentals of inversion