# Wolfram Mathematica

## Ranges of Values of the Earth's Magnetic Field

The new functions CoordinateBounds and CoordinateBoundingBox allow you to find the extrema values in each dimension of a multidimensional array. This example finds the ranges of values of the Earth's magnetic field in a given region.

Define a region near the North Pole from its latitudes and longitudes.

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```lat = {65, 85}; lon = {-30, 30};```

Plot this region on a world map.

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```GeoGraphics[GeoBoundsRegion[{lat, lon}], GeoGridLines -> Automatic, GeoZoomLevel -> 5]```
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Generate the data of the Earth's magnetic field in this region.

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`data = GeomagneticModelData[Transpose[{lat, lon}], GeoZoomLevel -> 1]`
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Extract from this data the components of the Earth's magnetic field.

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```components = {"NorthComponent", "EastComponent", "DownComponent"}; arr = Lookup[data, components]```
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Convert the list of arrays into an array of 3-vectors.

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`qa = Transpose[QuantityArray[arr], {3, 1, 2}]`
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These are the ranges of the components of the Earth's magnetic field in the specified region.

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`Thread[components -> CoordinateBounds[qa]]`
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