As I’ve illustrated in a number of posts, Mathematica is developing a number of useful and relatively easy way to construct maps. One of the most frustrating issues with the implementation is that the default latitude tick marks are not in degrees (along with the ever-present problem that they have no idea how long a tick mark should be in a quality plot). In this post I describe a simple function to create tick marks for the Mercator projection maps, and the code is relatively easily generalized to work with other projections.

[If you simply want correct ticks and don’t care about the map projection, select the “Equirectangular” projection and use Mathematica’s default frame ticks. Map ticks are correct for that projection (only). If you need to use a more traditional map projection, read on – CJA, 12 Oct, 2023.]

GeoGraphics – Incorrect Ticks Marks

Let’s start with a simple map of the location of the 2015 Nepal (Gorkha) Earthquake.

(* set up the earthquake information *)
cat = {607208674, "CSEM", "2015-04-25", "06:11:26.30", 28.28, 84.79, 
       "     ", "", "GCMT", "MW", 7.9};
eloc = {#[[5]], #[[6]], #[[11]]} & /@ {cat}
eqradius[m_] := N[10^(0.5*m - 2.25)]
scaleFactor = 1;
(* plot the map *)
GeoGraphics[{Polygon[Entity["Country", "Nepal"]], 
  GeoStyling[Opacity[0.25], EdgeForm[Black], FaceForm[Red]],
  GeoDisk[{#[[1]], #[[2]]}, (scaleFactor*Quantity[eqradius[#[[3]]], "km"]) ] & /@ eloc},
  GeoRange -> {{26.25, 29.75}, {82.5, 88.5}}, Frame -> True,
  FrameTicks -> {Automatic, Automatic},
  BaseStyle -> {18, FontFamily -> "Helvetica"},
  PlotLabel -> Style["Gorkha, Nepal Earthquake, 2015-04-25 06:11:26.30 UTC, Mw 7.9", {16}],
  GeoZoomLevel -> 8, FrameStyle -> AbsoluteThickness[1.2],
  GeoScaleBar -> {"Imperial", "Metric"},
  ImageSize -> 600] // Print

Here is the output

Mathematica map of the 2015 Nepal earthquake epicenter plotted with the default FrameTicks. Those are not latitudes on the vertical axis.

The map looks pretty good, but those are not latitude tick marks. Worse yet, in this example, they happen to be close enough to actual latitudes that they could fool you. The latitude of the center of the red circle is 28.28N, the tick marks lead you to believe the location is at roughly 29.5N. Technically, the tick marks are not wrong, they are simply in the practically useless transformation coordinate system. To get the correct tick marks, you need to specify them yourself, convert to projection coordinates, and label appropriately.

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