diff --git a/pygmt/datasets/load_remote_dataset.py b/pygmt/datasets/load_remote_dataset.py
index c6f0471b8ee..e0a97a9ea73 100644
--- a/pygmt/datasets/load_remote_dataset.py
+++ b/pygmt/datasets/load_remote_dataset.py
@@ -592,11 +592,12 @@ def _load_remote_dataset(
                 kind=dataset.kind, outgrid=None, vfname=voutgrd
             )
 
-    # Full path to the grid if not tiled grids.
-    source = which(fname, download="a") if not resinfo.tiled else None
+    # Full path to the grid
+    source: str | list = which(fname, verbose="q")
+    if resinfo.tiled:
+        source = sorted(source)[0]  # get first grid for tiled grids
     # Manually add source to xarray.DataArray encoding to make the GMT accessors work.
-    if source:
-        grid.encoding["source"] = source
+    grid.encoding["source"] = source
 
     # Add some metadata to the grid
     grid.attrs["description"] = dataset.description
diff --git a/pygmt/tests/test_xarray_accessor.py b/pygmt/tests/test_xarray_accessor.py
index 11b184110f6..5422f6defcb 100644
--- a/pygmt/tests/test_xarray_accessor.py
+++ b/pygmt/tests/test_xarray_accessor.py
@@ -132,10 +132,13 @@ def test_xarray_accessor_sliced_datacube():
         Path(fname).unlink()
 
 
-def test_xarray_accessor_grid_source_file_not_exist():
+def test_xarray_accessor_tiled_grid_slice_and_add():
     """
-    Check that the accessor fallbacks to the default registration and gtype when the
-    grid source file (i.e., grid.encoding["source"]) doesn't exist.
+    Check that the accessor works to get the registration and gtype when the grid source
+    file is from a tiled grid, that slicing doesn't affect registration/gtype, but math
+    operations do return the default registration/gtype as a fallback.
+
+    Unit test to track https://github.com/GenericMappingTools/pygmt/issues/524
     """
     # Load the 05m earth relief grid, which is stored as tiles.
     grid = load_earth_relief(
@@ -144,17 +147,25 @@ def test_xarray_accessor_grid_source_file_not_exist():
     # Registration and gtype are correct.
     assert grid.gmt.registration is GridRegistration.PIXEL
     assert grid.gmt.gtype is GridType.GEOGRAPHIC
-    # The source grid file is undefined.
-    assert grid.encoding.get("source") is None
+    # The source grid file for tiled grids is the first tile
+    assert grid.encoding["source"].endswith("S90E000.earth_relief_05m_p.nc")
 
-    # For a sliced grid, fallback to default registration and gtype, because the source
-    # grid file doesn't exist.
+    # For a sliced grid, ensure we don't fallback to the default registration (gridline)
+    # and gtype (cartesian), because the source grid file should still exist.
     sliced_grid = grid[1:3, 1:3]
-    assert sliced_grid.gmt.registration is GridRegistration.GRIDLINE
-    assert sliced_grid.gmt.gtype is GridType.CARTESIAN
-
-    # Still possible to manually set registration and gtype.
-    sliced_grid.gmt.registration = GridRegistration.PIXEL
-    sliced_grid.gmt.gtype = GridType.GEOGRAPHIC
+    assert sliced_grid.encoding["source"].endswith("S90E000.earth_relief_05m_p.nc")
     assert sliced_grid.gmt.registration is GridRegistration.PIXEL
     assert sliced_grid.gmt.gtype is GridType.GEOGRAPHIC
+
+    # For a grid that underwent mathematical operations, fallback to default
+    # registration and gtype, because the source grid file doesn't exist.
+    added_grid = sliced_grid + 9
+    assert added_grid.encoding == {}
+    assert added_grid.gmt.registration is GridRegistration.GRIDLINE
+    assert added_grid.gmt.gtype is GridType.CARTESIAN
+
+    # Still possible to manually set registration and gtype.
+    added_grid.gmt.registration = GridRegistration.PIXEL
+    added_grid.gmt.gtype = GridType.GEOGRAPHIC
+    assert added_grid.gmt.registration is GridRegistration.PIXEL
+    assert added_grid.gmt.gtype is GridType.GEOGRAPHIC