geology · structural
Three-Point Problem (Strike & Dip)
n = (B−A) × (C−A); dip = atan(√(a²+b²)/|c|); strike = dipDirection − 90°
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Inputs
ft
ft
ft
ft
ft
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ft
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ft
Description
Solves the classic three-point problem — given the position and elevation of three non-collinear points on a geologic surface (a formation top, unconformity, or other contact), finds the strike and dip of the best-fit plane through them. This is a foundational subsurface mapping technique used whenever scattered well picks or outcrop observations of the same surface need to be converted into an attitude.
Variables
| Symbol | Unit | Description |
|---|---|---|
| θstrike | ° | Strike Azimuth |
| δ | ° | True Dip |
| θdip | ° | Dip Direction (Azimuth) |
| xA | ft | Map easting (or local x-coordinate) of the first control point on the surface. |
| yA | ft | Map northing (or local y-coordinate) of the first control point on the surface. |
| zA | ft | Elevation of the surface at point A (e.g., formation-top or contact pick). |
| xB | ft | Map easting (or local x-coordinate) of the second control point on the surface. |
| yB | ft | Map northing (or local y-coordinate) of the second control point on the surface. |
| zB | ft | Elevation of the surface at point B (e.g., formation-top or contact pick). |
| xC | ft | Map easting (or local x-coordinate) of the third control point on the surface. |
| yC | ft | Map northing (or local y-coordinate) of the third control point on the surface. |
| zC | ft | Elevation of the surface at point C (e.g., formation-top or contact pick). |
Assumptions
- The three points lie on a single, genuinely planar surface between them — no folding or faulting is present within the triangle they define.
- The three points are non-collinear when projected onto the map — the problem is undefined if they fall on a single line.
- x and y are true horizontal map coordinates (e.g., UTM or a consistent local grid) in the same length unit as z (elevation).
Limitations
- Assumes strictly planar geometry — real structural surfaces are rarely perfectly planar over long distances, so the result is a local best-fit plane, not a guarantee of true planarity.
- Very gently dipping surfaces are highly sensitive to small errors in point position or elevation; a small pick error can swing the computed strike substantially.
- Does not validate that the three points are actually the same structural pick (e.g., the same formation top or the same fault surface) — that judgment call is the user's responsibility.
Use Cases
- → Mapping from scattered well picks: Determine the local structural dip and strike of a marker or unconformity from three nearby wells that each penetrate the same surface.
- → Outcrop or topographic contact mapping: Determine the attitude of a contact exposed at three locations of known elevation — the classic field-geology three-point problem.
Related Calculations
Region Notes
Global
The three-point method assumes the surface is planar between the three input points — in structurally complex settings (folds, unconformities, faulted panels) apply it only within a single fault block or panel of consistent dip.
References
Primary source
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