harmonica

---
name: "harmonica"
description: "Harmonica uses a right-handed coordinate system: - Easting (x): positive east - Northing (y): positive north - Upward (z): positive up (heights positive, depths negative)"
license: "MIT"
---

# Harmonica - Gravity and Magnetics

## Quick Reference

```python
import harmonica as hm
import numpy as np

# Forward model - prism gravity
prism = [-500, 500, -500, 500, -2000, -500]  # (west, east, south, north, bottom, top)
gravity = hm.prism_gravity(coordinates, prism, density=500, field='g_z')

# Terrain correction
layer = hm.prism_layer((easting, northing), surface=topo, reference=0,
                        properties={'density': 2670})
terrain_effect = layer.gravity(coordinates, field='g_z')

# Equivalent source gridding
eqs = hm.EquivalentSources(depth=10000, damping=10)
eqs.fit(coordinates, gravity_data)
grid = eqs.grid(spacing=5000, data_names=['gravity'])

# Upward continuation (requires gridded xarray)
upward = hm.upward_continuation(gravity_grid, height_displacement=1000)
```

## Key Functions

| Function | Purpose |
|----------|---------|
| `point_gravity` | Gravity from point masses |
| `prism_gravity` | Gravity from rectangular prisms |
| `tesseroid_gravity` | Gravity from spherical prisms (regional/global) |
| `prism_magnetic` | Magnetic anomaly from prisms |
| `prism_layer` | Create layer of prisms from topography |
| `EquivalentSources` | Grid scattered data with equivalent sources |
| `upward_continuation` | FFT-based upward continuation |
| `bouguer_correction` | Simple Bouguer plate correction |

## Essential Operations

### Forward Model - Rectangular Prism
```python
# Define prism: (west, east, south, north, bottom, top) in meters
prism = [-500, 500, -500, 500, -2000, -500]
density = 500  # kg/m3 density contrast

# Observation grid
x_obs, y_obs = np.meshgrid(np.linspace(-5000, 5000, 100), np.linspace(-5000, 5000, 100))
z_obs = np.zeros_like(x_obs)

# Calculate gravity (mGal). Fields: 'g_z', 'g_north', 'g_east', 'potential'
gravity = hm.prism_gravity((x_obs.ravel(), y_obs.ravel(), z_obs.ravel()),
                           prism, density, field='g_z')
```

### Terrain Correction
```python
import xarray as xr

topo = xr.open_dataarray('dem.nc')
layer = hm.prism_layer((topo.easting.values, topo.northing.values),
                       surface=topo.values, reference=0,
                       properties={'density': 2670})
terrain_effect = layer.gravity((obs_easting, obs_northing, obs_height), field='g_z')
bouguer_anomaly = free_air_anomaly - terrain_effect
```

### Equivalent Source Gridding
```python
import verde as vd

# Project to Cartesian
projection = vd.get_projection(longitude, latitude)
easting, northing = projection(longitude, latitude)

eqs = hm.EquivalentSources(depth=10000, damping=10)
eqs.fit((easting, northing, altitude), gravity_mgal)
grid = eqs.grid(spacing=5000, data_names=['gravity'])
```

### Magnetic Forward Model
```python
prism = [-500, 500, -500, 500, -2000, -500]
magnetization = hm.magnetic_vector(intensity=5.0, inclination=60, declination=10)
b_total = hm.prism_magnetic(coordinates, prism, magnetization, field='b_total')
```

### Derivative Filters
```python
dx = hm.derivative_easting(gravity_grid)
dy = hm.derivative_northing(gravity_grid)
dz = hm.derivative_upward(gravity_grid)

thg = np.sqrt(dx**2 + dy**2)  # Total horizontal gradient
tilt = np.arctan2(dz, thg)     # Tilt angle
```

## Coordinate System

Harmonica uses a **right-handed coordinate system**:
- **Easting** (x): positive east
- **Northing** (y): positive north
- **Upward** (z): positive up (heights positive, depths negative)

Units are SI: meters for distance, kg/m3 for density, mGal for gravity.

## When to Use vs Alternatives

| Use Case | Tool | Why |
|----------|------|-----|
| Gravity/magnetic forward modelling | **Harmonica** | Purpose-built, Fatiando ecosystem |
| Potential field inversion | **SimPEG** | Full inversion framework with regularization |
| Commercial gravity processing | **Oasis Montaj** | Industry-standard GUI, proprietary formats |
| Simple Bouguer corrections only | **Custom numpy** | Fewer dependencies for one-off calculations |
| Equivalent source gridding | **Harmonica** | Best open-source option for potential fields |
| Regional/global scale | **Harmonica** (tesseroids) | Handles spherical geometry natively |
| Magnetic data reduction to pole | **Harmonica** | FFT-based filters for gridded data |
| Teaching/prototyping | **Harmonica** | Clean API, good documentation |

**Choose Harmonica when**: You need open-source gravity/magnetic processing with
forward modelling, terrain corrections, or equivalent source gridding. It integrates
well with Verde for projections and gridding. Part of the Fatiando a Terra ecosystem.

**Choose SimPEG when**: You need to invert potential field data for subsurface
property distributions (density or susceptibility models).

**Choose Oasis Montaj when**: You work in an industry setting that requires
proprietary formats, commercial support, or GUI-based interactive processing.

## Common Workflows

### Process Gravity Survey with Terrain Correction and Gridding
- [ ] Load raw gravity observations and station coordinates
- [ ] Apply latitude, free-air, and tidal corrections
- [ ] Load DEM and build prism layer with `hm.prism_layer()`
- [ ] Compute terrain effect at observation points
- [ ] Subtract terrain effect from free-air anomaly to get Bouguer anomaly
- [ ] Project coordinates to Cartesian with `verde.get_projection()`
- [ ] Block-reduce data if station density is uneven
- [ ] Fit equivalent sources with `hm.EquivalentSources()`
- [ ] Grid the Bouguer anomaly onto a regular grid
- [ ] Apply `vd.distance_mask()` to mask areas far from data
- [ ] Apply derivative filters (horizontal gradient, tilt angle) for interpretation
- [ ] Perform upward continuation to enhance regional features
- [ ] Export gridded data to NetCDF

## Common Issues

| Issue | Solution |
|-------|----------|
| Wrong gravity sign | Check z-axis convention (positive upward) |
| Poor equivalent source fit | Adjust `depth` and `damping` parameters |
| Slow terrain correction | Reduce DEM resolution or use larger prisms |
| Edge effects in FFT filters | Pad grid before applying `upward_continuation` |
| Coordinate mismatch | Ensure consistent use of projected vs geographic coords |

## Tips

1. **Use projected coordinates** (meters) for local surveys
2. **Use tesseroids** for regional/global scale modelling
3. **Equivalent sources** handle irregular data spacing well
4. **Choose appropriate density** (2670 kg/m3 typical for upper crust)
5. **Check sign conventions** - depths are negative z values

## References

- **[Gravity/Magnetic Corrections](references/corrections.md)** - Standard corrections and anomalies
- **[Forward Modeling](references/forward_modeling.md)** - Detailed forward modeling methods

## Scripts

- **[scripts/gravity_processing.py](scripts/gravity_processing.py)** - Process gravity survey data