Two_Layers.md

Two Layers

This example is devoted to demonstration of interface geometry optimization (interface inversion) applied to a simple synthetic model consisting of two layers.

Description

Original model

The original (or true) model contains two bodies (layers) of identical sizes: an upper body with zero density (an air layer) and a lower body (a subsurface layer) with density of 200 kg/m^3, separated by a horizontal plane at a depth of 5 km (see Figure below).

Both bodies are 20 \times 20 km horizontally and 5 km thick.

Input data

The original model was used to create a gravity dataset calculated for a set of 6561 stations regularly placed on the plane at a zero depth level (see Figure below).

Bouguer anomaly modelled above a simple two-layer model measured with a regularly spaced set of stations placed at a zero depth level.

Stations cover the area 40 \times 40 km, exceeding the model edges by 10 km in each direction. For simplicity, there is no extension of the bodies beyond the model boundaries, and the edge effect is clearly visible in the dataset.

The described dataset was used as an input measured gravity data for inversion.

Starting model

In order to have a starting model which would differ from the original model, additional vertices have been added on the boundary between the two bodies and then manually moved up or down (see Figure below).

From a 3D view of the starting model one can see that the boundary is modified at each of the 5 working sections (see Figure below).

Download

The input data required for this example as well as the two models are available for download here.

The share contains 3 files:

• Two_Layers_Measured_Gravity.csv: the input measured gravity data in CSV format
• Two_Layers_Original.zip: the original IGMAS+ model of two layers separated with a horizontal plane used to calculate the input gravity data
• Two_Layers_Inversion.zip: the IGMAS+ model used for inversion consisting of two timeline steps:
  • starting model: a model where the boundary between the two layers was distorted
  • final model - a model after application of the interface inversion to the starting model

The input gravity data file Two_Layers_Measured_Gravity.csv is in CSV format and has 4 data columns: "x" "y" "z" "measured z component" and 6561 data rows corresponding to stations. The values in columns are delimited with space.

The two models are zip archives with IGMAS+ projects. Simply unpack and load projects in IGMAS+.

Modelling

!!! abstract "Goal" The goal of this modelling example is to apply interface geometry optimization to the starting model in order to demonstrate how it can be iteratively inverted to a final model close to the true one based on the input gravity data, assuming that densities are known.

The interface geometry optimization functionality is provided by the Interface Inversion plugin. With this plugin it is possible to iteratively optimize the geometry of an interface using the misfit between the measured and calculated (at each iteration) field.

Open the starting model

• Start IGMAS+

- Select ++"File"++ --> ++"Open Project"++ - Select the folder `Two_Layers_Inversion` - In the Timeline window select the earliest timeline - this is the starting model (see Figure on the right)
- The starting model will open in the 3D view - However, there are no stations - for that you need to load the input gravity data.

Load input gravity data

• Select ++"File"++ --> ++"Import"++ --> ++"Stations"++
• Navigate to the folder with Two_Layers_Measured_Gravity.csv file
• Change the file type to [csv|xyz] - Comma Separated Values to see the file

• Now you can see the files with .csv and .xyz extensions
• Click on the Two_Layers_Measured_Gravity.csv file
• Information on the units that will be used for input is visible on the right
• Click ++"Open"++

- The preview window will show the data from the file distributed in columns - Click ++"Finish"++

• The loaded data will be displayed on top of the model together with stations
• The data will also appear as measured data ("meas Gz") in the Object Tree under "Fields" --> "Gravity: z-component"
• Now it is necessary to calculate the gravity field for the loaded.

Calculate gravity field

• First, triangulate the model using ++"Edit"++ --> ++"Model Triangulation"++ or by clicking
• Then calculate the anomaly of the model using ++"Tools"++ --> ++"Calculate Anomalies"++ or by clicking
  • Select "Calc Gz"
  • Click ++"Finish"++

• Open 2D View using ++"Add View"++ --> ++"2D View"++ or by clicking
• The curves above the vertical cross section shows the misfit between the measured and calculated gravity anomalies for the starting model
• In the Object Tree under "Fields" select "Gravity: z-component"
• Click on the Property Editor Tab and uncheck "Auto Shift": it is better to run inversion without the autoshift.
• Now, before starting the inversion, it is necessary to add the inversion category.

Add inversion category

• In the Object Tree, click ++"right mouse button"++ on "Interfaces" and select ++"Add Category"++
• In the dropdown list choose "Inversion" and click ++"OK"++
• A new "Inversion" entry will appear in "Interfaces"

• Add an interface to the "Inversion" category
  • In the [Object Tree] under "Interfaces" find the interface between the upper and lower bodies called "Unten <> Oben"
  • Pick this interface with ++"left mouse button"++ and drag it to the "Inversion"
• The interface "Unten <> Oben" will be copied under the "Inversion" (see Figure on the right)
• Now you are ready to start the interface inversion.

??? tip The model at this stage can be opened from the middle timeline of the Two_Layers_Inversion model.

Start interface inversion

• Open the interface inversion wizard using the start icon

- Interface inversion settings window will open (see Figure on the right) - Select the "Optimizer" to be "Optimizer no-check" - Adjust the "Standard Deviation" to be in the range from `0.15` to `0.05` - this is the initial standard deviation for variation of depth coordinates of the interface vertices. The more the value, the larger is the initial variation. We recommend to keep 0.1 here. - Adjust the "Stop-Quality SD" to be in the range from `0.1` to `0.002`. The less the value is, the longer the inversion will last and the better the fit will be in the end. A recommended value for the "Stop-Quality SD" to reach an optimal accuracy in a reasonable time is 0.05. - Make sure the "Use Triangle Effect" is **checked**: it involves calculation of gravity effect for the triangulated bodies - Make sure the "Use Voxel Effect" is **unchecked**: there are no voxel cubes and we don't need to involve it - Once ready, click ++"Next"++