Repository: fatiando/harmonica

Issue:
Inverted sign in upward derivative filter
**Description of the problem:**
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The upward derivative returned has an inverted sign. It looks OK when inspecting plots because a lot of us are used to the sign convention of positive downwards. But since we use heights (and thus positive upward), the sign should be the opposite of what we expect. This is meant to improve consistency between small-scale and global data (which often has a "radial" component that is positive upward).

The fix should be relatively simple. Just add a minus sign to https://github.com/fatiando/harmonica/blob/main/harmonica/filters/_filters.py#L63

**Full code that generated the error**
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```python
import harmonica as hm
import verde as vd
import numpy as np
import matplotlib.pyplot as plt

model = [
    [35e3, 40e3, 50e3, 55e3, -6e3, -1e3],
]
magnetization = [
    hm.magnetic_angles_to_vec(20, -40, 15),
]
inc, dec = -40, 15
fe, fn, fu = hm.magnetic_angles_to_vec(1, inc, dec)
region = [0, 100e3, 0, 80e3]
coordinates = vd.grid_coordinates(region, spacing=500, extra_coords=1000)

be, bn, bu = hm.prism_magnetic(coordinates, model, np.transpose(magnetization), field="b")
anomalia = fe * be + fn * bn + fu * bu

grid = vd.make_xarray_grid(coordinates, anomalia, data_names="tfa", extra_coords_names="upward")
grid["d_up"] = hm.derivative_upward(grid.tfa)

fig, axes = plt.subplots(1, 2, layout="constrained", figsize=(10, 3))
grid.tfa.plot(ax=axes[0])
grid.d_up.plot(ax=axes[1])
```

**Full error message**


This produces the following result:

![image](https://github.com/fatiando/harmonica/assets/290082/8ec8fbf2-b293-434c-96b1-d7f0d6036124)

If we use positive upward, then the positive parts of the anomaly should be decreasing towards 0 (negative derivative) and the negative parts of the anomaly should be increasing towards 0 (positive derivative).


**System information**

* Operating system: Linux
* Python installation (Anaconda, system, ETS): Miniforge
* Version of Python: 3.11
* Version of this package: current main ([bbaf5a1](https://github.com/fatiando/harmonica/commit/bbaf5a191c7a3ccf9835a2d3b565be26a3500d26))
* If using conda, paste the output of `conda list` below: Not using conda.

<details>
<summary>Output of conda list</summary>
<pre>

PASTE OUTPUT OF CONDA LIST HERE

</pre>
</details>


Comments:

Patch:
diff --git a/harmonica/filters/_filters.py b/harmonica/filters/_filters.py
index defe9e8..a561cef 100644
--- a/harmonica/filters/_filters.py
+++ b/harmonica/filters/_filters.py
@@ -60,7 +60,7 @@ def derivative_upward_kernel(fft_grid, order=1):
     k_easting = 2 * np.pi * freq_easting
     k_northing = 2 * np.pi * freq_northing
     # Compute the filter for upward derivative in frequency domain
-    da_filter = np.sqrt(k_easting**2 + k_northing**2) ** order
+    da_filter = (-np.sqrt(k_easting**2 + k_northing**2)) ** order
     return da_filter
 
 


Test patch:
diff --git a/harmonica/tests/test_filters.py b/harmonica/tests/test_filters.py
index 035af9d..1a699fc 100644
--- a/harmonica/tests/test_filters.py
+++ b/harmonica/tests/test_filters.py
@@ -261,15 +261,14 @@ def test_derivative_upward_kernel(sample_fft_grid, order):
     """
     # Load pre-computed outcome
     expected = (
-        np.array(
+        -np.array(
             [
                 [0.00756596, 0.00565487, 0.00756596],
                 [0.00502655, 0.0, 0.00502655],
                 [0.00756596, 0.00565487, 0.00756596],
             ]
         )
-        ** order
-    )
+    ) ** order
     # Check if the filter returns the expected output
     npt.assert_allclose(
         expected, derivative_upward_kernel(sample_fft_grid, order=order), rtol=2e-6
diff --git a/harmonica/tests/test_transformations.py b/harmonica/tests/test_transformations.py
index 16c5b84..78d4592 100644
--- a/harmonica/tests/test_transformations.py
+++ b/harmonica/tests/test_transformations.py
@@ -260,17 +260,20 @@ def test_derivative_upward(sample_potential, sample_g_z):
     # Calculate upward derivative and unpad it
     derivative = derivative_upward(potential_padded)
     derivative = xrft.unpad(derivative, pad_width)
-    # Compare against g_z (trim the borders to ignore boundary effects)
+    # Compare against g_up (trim the borders to ignore boundary effects)
     trim = 6
     derivative = derivative[trim:-trim, trim:-trim]
-    g_z = sample_g_z[trim:-trim, trim:-trim] * 1e-5  # convert to SI units
-    rms = root_mean_square_error(derivative, g_z)
-    assert rms / np.abs(g_z).max() < 0.015
+    g_up = -sample_g_z[trim:-trim, trim:-trim] * 1e-5  # convert to SI units
+    rms = root_mean_square_error(derivative, g_up)
+    assert rms / np.abs(g_up).max() < 0.015
 
 
 def test_derivative_upward_order2(sample_potential, sample_g_zz):
     """
     Test higher order of derivative_upward function against the sample grid
+
+    Note: We omit the minus sign here because the second derivative is positive
+    for both downward (negative) and upward (positive) derivatives.
     """
     # Pad the potential field grid to improve accuracy
     pad_width = {