Simple Basin¶

This example contains a detailed description on how to create a simple model of a sedimentary basin based on synthetically generated gravity anomaly data using interactive geometry modification in IGMAS+.

Description¶

Input data¶

To create the input gravity dataset we used a simple model of a sedimentary basin with densities of 2300 kg/m $^3$ for the sediments and 2700 kg/m $^3$ for the basement.
A set of 1938 gravimeters are placed on a flat Earth's surface above the sedimentary basin.

The Figure below shows the measured gravity (Bouguer anomaly with values in the range from approximately -33 to 0 mGal:

A simulation of Bouguer anomaly above a sedimentary basin measured with a regularly spaced set of stations on a flat Earth's surface. — A simulation of a typical Bouguer anomaly above a sedimentary basin measured with a regularly spaced set of stations on a flat Earth's surface.

Download¶

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

The share contains 3 files:

Simple_Basin_Measured_Gravity.csv: the input gravity data in CSV format
Simple_Basin_2D.zip: the resulting 2D IGMAS+ model together with intermediate timeline steps (for comparison)
Simple_Basin_3D.zip: the resulting 3D IGMAS+ model together with intermediate timeline steps (for comparison)

The input gravity data file Simple_Basin_Measured_Gravity.csv is in CSV format and has 4 data columns: "x" "y" "z" "calculated z component" and 1938 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¶

Goal

The goal of this modelling example is to determine the depth and extent of sedimentary basin based on the input gravity data and known densities.

The modelling is carried out in three steps:

1D interpretation: Perform a quick initial estimate of the maximal depth of the sediments using the simple Bouguer Plate.
2D interpretation: Build a 2D model through the gravity minimum. Use a single section with mirrors, its direction should be West-East, which is perpendicular to the North-South striking of the anomaly. Use IGMAS+ for this task.
3D interpretation: Extend the 2D model in IGMAS+ to a 3D model by adding more sections north and south of the 2D model. Do not use more than 5 sections in total.

1D interpretation¶

We start with a quick initial estimate of the maximum sediments depth using a simple Bouguer Plate approach.

The formula for Bouguer Plate correction,

$\delta g_{max} = 2\pi G \Delta\rho h_{max},$

reformulated for $h_{max}$ reads

$h_{max} = \frac{\delta g_{max}}{2\pi G \Delta\rho},$

where:

$\delta g_{max}$ is the maximum absolute gravity anomaly value
$\Delta\rho$ is the density difference between the basement and the sediments
$G$ is the gravitational constant.

Question

What is the approximate maximum sediment thickness based on the quick 1D estimate?

Tip

Using the maximum absolute gravity anomaly of 33 mGal and density difference of 400 kg/m $^3$ , this estimation results in a maximum sediment thickness of approximately 2 km.
Here is how it can be calculated:

$h_{max} \approx \frac{33~mGal}{4.19358\times10^{−5}~mGal~m^2~kg^{−1}\cdot400~kg~m^{-3}} \approx 1967~m \approx 2~km$

Answer

Based on the 1D theoretical estimate, the sediment thickness is approximately 2 km.

2D interpretation¶

Here we build a 2D model through the gravity minimum. We use a single West-East oriented section, perpendicular to the North-South strike of the anomaly.

1. Import the measured anomaly¶

Start IGMAS+
Open the import dialogue: File → Import → Stations
Select the measured anomaly file Simple_Basin_Measured_Gravity.csv
Specify the unit of the coordinates: "km"
Program will automatically generate a model domain with 8 km depth for the area covered by stations (see Figure below), but without any working sections.

A 3D view of the model in IGMAS+ created after loading of the measured gravity.

2. Add a working section¶

Add a single working section along $y$ =10 km (West-East):

Open sectioning dialogue: Edit → Add Sections
Adjust the Count of sections to 1
Press Preview
Click right mouse button on the South West node (bottom-left white dot) of the section area rectangle (see Figure below)
Leave -3 in field X, change field Y value to 10 and click OK
Click Finish

Adding a single West-East oriented section in IGMAS+

3. Mirror the section¶

Now add mirrors to the working section:

Select the section in the Object Tree and add 100 (km) to "mirror+" and "mirror-" in the Section Mirror dropdown:

This creates a pseudo-3D model extending 100 km on either side of the profile.
Now triangulate the model using Edit → Model Triangulation.
Click to clip to model bounds and view the entire model:

A pseudo-3D model created using section mirrors.

4. Assign densities¶

Now create bodies for the sediments and the basement and assign the densities:

In the Body Manager Tab use Add Parameter and select "Density"
Rename the "new_body" body to "Basement" (double click the name to rename it)
Add a body with name "Sediments" using Add Body
Assign a density of 2.7 t/m $^3$ to the "Basement" and 2.3 t/m $^3$ to the "Sediments"
Assign the "reference" body with the density of 2.7 t/m $^3$ to avoid any edge effect

5. Define the "Sediments" body and adjust its geometry¶

There is still just one body ("Basement"), no "Sediments" body in the triangulated geometry.

Add the 2D view with or Add View → 2D View
You must now cut off the upper part of the model block to build the "Sediments" body. There are several possibilities. The simplest is to insert 2 vertices on the surface to the left and right of the centre (A and B) and then move the central vertex upwards:
- To insert a vertex, hold I and click left mouse button on the border of a polygon. A new vertex will appear in this position.
- To shift a vertex, hold Shift and drag the desired vertex with left mouse button
- Now divide the polygon between the new vertices A and B by holding D and dragging the left mouse button:

Double left mouse button click on the upper part, use right mouse button and select Set Body → "Sediments"
New triangulation is necessary after this step: Edit → Model Triangulation
Now insert some points along the interface between "Sediments" and "Basement": hold I and click left mouse button:

Move the new vertices to form a basin structure: hold Shift and drag the desired vertex with left mouse button:

Delete or shift down the central uppermost vertex. To delete, hold I and click left mouse button on the undesired vertex
Again, new triangulation is necessary: Edit → Model Triangulation
Now there are both "Basement" and "Sediments" bodies in the triangulated geometry and both have assigned densities.

6. Fit the anomaly¶

Now calculate the anomaly of the model using or Tools → Calculate Anomalies.

To fit the calculated anomaly to the measured better, adjust the positions and/or add/remove the subsurface vertices
A constant shift may remain due to additional stations in the file:

Constant shift between the calculated and measured anomaly

You can switch off Auto Shift (see Figure below):

Select "Gravity: z-component" under "Model" → "Fields" in the Object Tree.
Open Property Editor Tab
Uncheck "Auto Shift" checkbox

Adjusting the geometry of the "Sediments" body to fit the measurements

Question

What is the approximate maximum sediment thickness based on the anomaly fit in 2D?

Answer

Based on the anomaly fit in 2D, the sediment thickness is approximately 2.9 km.

3D interpretation¶

Here we extend the 2D model to a 3D model by adding more sections north and south of the 2D model. We use not more than 5 sections in total:

Save a copy of the 2D model: Files → Save as...
- Create an empty folder and select it
- Click Save: your 2D model has been saved and now you can use the current project to create the 3D model
Add more sections:
- Open the sectioning dialogue with Edit → Add Sections
- Change the area to be sectionized by changing the position of the points (marked red in the Figure below) using right mouse button:
  - Enter X = -3 and Y = 0 for the lower point
  - Enter X = -3 and Y = 20 for the upper point
  - Use 5 for the "Spacing" between the sections
  - Click Preview and then Finish.

Tip

Instead of using the function Edit → Add Sections you can use the function “Copy and Shift” four times using the shift 10, 5, -5, and -10 km to copy the central section.

Remove mirrors from the first section (this is the central section number 0 at $y$ =10) by setting them to 0.
Perform new triangulation: Edit → Model Triangulation
Use or Tools → Re-Calculate Anomalies to recalculate the anomalies.

Open 2D View and step through the model – all sections are identical and they should be modified to mitigate the discrepancy between the measured and the calculated anomalies.
The goal is to get the residual field as low as possible (see Figure below). In this case residuals are below 3.4 mGal in absolute value.

Residual between the measured and calculated anomalies for the final 3D model

After the adjustments one can estimate the maximum depth of the sediments using the 2D view:

Section with the largest sediment thickness for the 3D model and the corresponding anomaly fit

The final resulting sedimentary basin can be seen from the 3D view:

The resulting shape of the sedimentary basin derived with the 3D gravity modelling

Question

What is the approximate maximum sediment thickness based on the anomaly fit in 3D?

Answer

Based on the anomaly fit in 3D, the sediment thickness is approximately 3.3 km.

Question

What is the maximum extent of the sedimentary basin in North-South and East-West directions?

Answer

Based on the maximum extent of the sedimentary basin in North-South direction is about 20 km and in the East-West directions it is about 13 km.