The three point problem

Summary

This video explains the 'three-point problem,' a technique geologists use to interpret subsurface structures based on borehole data. By examining three boreholes, the orientation and position of geological boundaries, such as a sandstone bed, can be accurately predicted. The video demonstrates how to map the surface by connecting points from wells at different depths, calculating elevation changes, and using structure contours to outline the topography. This method allows geologists to forecast the extent of geological layers in a region, providing valuable insights for mapping subsurface formations.

Takeaways

• 🛠️ Geologists use boreholes to make interpretations of the subsurface, using a method called the three-point problem.
• 📏 The three-point problem allows geologists to determine the orientation and position of geological boundaries based on three boreholes.
• 🌍 A plane is unconstrained by one point, can tip with two points, but is locked in a fixed orientation with three points.
• 🔍 The example focuses on mapping the top of a sandstone bed using three wells labeled A, B, and C.
• 📐 At each well, the depth of the sandstone bed below the surface is measured, and the elevation of the top of the bed is calculated.
• 📊 The process involves creating a triangle between the three points and determining structure contours by dividing the lines between these points.
• 🧮 Geologists calculate the dip and strike of the sandstone layer by measuring the elevation differences and the horizontal distances between points.
• 📡 The strike is measured using the trend of the structure contours, while the dip is calculated using trigonometry.
• 🗺️ The positions where structure contours intersect topographic contours mark the outcrop locations of the sandstone bed.
• 🎨 The final result is a geological map showing the extent of the sandstone bed, illustrating how subsurface structures can be forecasted using the three-point solution.

Q & A

What is the three-point problem in geology?

The three-point problem is a method used by geologists to determine the orientation and position of a geological boundary based on three boreholes. By knowing the position of three points in the subsurface, the orientation of the boundary, such as a sandstone layer, can be forecasted.

Why are three points necessary to define the orientation of a geological plane?

One point offers no constraints on a plane’s orientation, and two points allow it to tip in various directions. Three points, however, lock the plane into a specific orientation, making it possible to define the plane’s position and orientation precisely.

What do the borehole depths represent in the three-point problem example?

The borehole depths represent the distance below the surface to the top of the sandstone bed. For example, at well A, the top of the sandstone bed is 50 meters below the surface, meaning it is at an elevation of 250 meters above sea level.

How do you calculate the elevation of the sandstone bed at a well location?

To calculate the elevation of the sandstone bed at a well, subtract the depth to the sandstone bed from the surface elevation of the well. For example, in well A, the surface elevation is 300 meters, and the sandstone is 50 meters below the surface, giving an elevation of 250 meters for the bed.

How do structure contours help in understanding subsurface geology?

Structure contours represent lines of equal elevation on a geological surface, such as the top of a sandstone bed. They allow geologists to map the geometry of subsurface features by connecting points of equal elevation between wells and using them to infer the strike and dip of the layer.

What is the strike of a geological layer, and how is it determined from the map?

The strike is the direction of a horizontal line on the surface of a geological layer. In the example, it is determined by the angle between the structure contour lines and the north arrow. In the video, the strike is measured as 078 degrees.

What is the dip of the sandstone bed, and how is it calculated?

The dip is the angle of inclination of the geological layer relative to the horizontal plane. It is calculated using trigonometry by dividing the elevation change (vertical distance) by the horizontal distance between two points. In the video, the dip is calculated to be approximately 30 degrees.

How are the structure contours related to topographic contours in the map?

Structure contours intersect topographic contours where they represent the same elevation. These intersections indicate where the geological surface (e.g., the top of the sandstone bed) outcrops at the surface, helping to define the extent of the geological feature on the map.

What assumptions are made when using the three-point problem to map geological features?

The primary assumption is that the geological surface being mapped is planar. This means the structure contours will be parallel and equally spaced, making it possible to project and predict the subsurface geometry accurately based on the three points.

How can the extent of the sandstone bed be determined from the structure and topographic contours?

The extent of the sandstone bed is mapped by identifying where the structure contours intersect with the topographic contours at the same elevation. These points of intersection define the boundary of the sandstone bed, which can then be connected to outline the subsurface feature.