PolyBodyGrav — 规则体重力正演系统

Gravity forward modeling for regular-shaped bodies. Compute and visualize gravity anomalies and full tensor gravity gradiometry (FTG, 7 components) for 7 body types — analytical formulas for cuboids and spheres, hybrid analytical-numerical solutions for the rest, with multi-body superposition and parameter sensitivity analysis.

Overview

PolyBodyGrav is a MATLAB desktop application for forward gravity modeling of regular geometric bodies. It covers the complete workflow from geometry setup, forward computation, multi-body combination, sensitivity scanning, to GIS-standard format export.

Supported Body Types

Body	Formula	Gravity	FTG (7 components)	3D Color
Sphere	Point-mass analytical	✓	✓ (analytical)	Gold
Cuboid	Nagy/Plouff (1976) prism	✓	✓ (analytical)	Red
Vertical Cylinder	Axial + geometric attenuation	✓	✓ (finite difference)	Green
Horizontal Cylinder	Finite line mass (Blakely 1996)	✓	✓ (finite difference)	Blue
Tilted Cylinder	Blakely (1996) line integral	✓	✓ (finite difference)	Cyan
Ellipsoid	Gauss-Legendre (32-node) + Z-Y-X Euler rotation	✓	✓ (finite difference)	Purple
Frustum	Thin-disk trapezoidal integration	✓	✓ (finite difference)	Orange
Multi-body	Linear superposition	✓	✓	Mixed

FTG Components

All 7 gravity gradient tensor components available in all body types:

$$V_z, \quad V_{xx}, V_{yy}, V_{zz}, \quad V_{xy}, V_{xz}, V_{yz}$$

• Cuboid & sphere: analytical FTG via Plouff formula (satisfies Laplace $V_{xx}+V_{yy}+V_{zz}=0$)
• Other bodies: Vz analytical + gradient via 3-layer finite difference with free-space Laplace constraint

Units

Quantity	Unit	Conversion
Gravity Vz	μGal	$1\ \mu\text{Gal} = 10^{-8}\ \text{m/s}^2$
Gradient tensor	Eötvös (E)	$1\ \text{E} = 10^{-9}\ \text{s}^{-2}$
Density	g/cm³ (UI) → kg/m³ (SI)	× 1000

Features

Forward Modeling

• 7 body types with analytical / hybrid-analytical formulas
• 7 FTG components per body type
• Constant or topographic observation surface (load external DEM as .asc/.grd/.dat/.txt/.xlsx)
• Gouraud-lit 3D visualization + plan-view contour map

Parameter Sensitivity Analysis

• Select any scannable parameter as X-axis variable
• Define Min/Max range and step count
• Curve-family support with colon notation multipliers (e.g., 0.5:0.5:2.5)
• Multi-curve output with 3D model preview

Multi-Body Superposition

• Combine arbitrary numbers of bodies (sphere, cylinder, cuboid, ellipsoid, frustum)
• Per-body editable name, color, and parameters
• Linear superposition of gravity fields

Persistence & Exchange

• JSON parameter export/import: Full parameter serialization across sessions
• Auto-persistence: Automatic save/restore of all inputs (app_settings.mat)
• GIS-standard export: ESRI ASCII Grid (.asc), Surfer 6 Grid (.grd), XYZ columnar (.dat)
• Columnar data export: TXT / XLSX formats

Test Data (35 files, 7 terrain types × 5 formats)

Terrain	Description	Grid
valley	V-shaped valley	201×201 @ 10m
mountain	Conical peak	201×201 @ 10m
slope_x	X-direction slope	201×201 @ 10m
basin	Basin depression	201×201 @ 10m
complex	2 peaks + 1 valley	201×201 @ 10m
flat	Zero-elevation plane	201×201 @ 10m
random	Random topography	201×201 @ 10m

Parameter presets: preset_sphere.txt, preset_cuboid.txt, preset_vertical_cylinder.txt, preset_multibody.txt

Technical Principles

Sphere — Point Mass (Analytical)

$$V_z = G \cdot M \cdot \frac{-dz}{r^3} \times 10^8 \quad (\mu\text{Gal})$$

$$V_{zz} = G M \frac{3dz^2 - r^2}{r^5} \times 10^9 \quad (\text{E})$$

Cuboid — Nagy/Plouff Prism (Analytical)

8-corner sign-alternating kernel summation:

$$V_z = -G\rho_{si} \sum_{i=1}^{2}\sum_{j=1}^{2}\sum_{k=1}^{2} (-1)^{i+j+k} \cdot GH(\xi_i, \eta_j, \zeta_k)$$

$$G_{xx} = G\rho \sum \pm \arctan\frac{yz}{xR}, \quad G_{xy} = -G\rho \sum \pm \ln|z+R|$$

Other Bodies — Hybrid (Analytical Vz + Finite-Difference Gradients)

1. Compute Vz analytically at 3 elevations: z₀, z₀±dz (dz=1.0m)
2. Vzz = (Vz_top − Vz_bottom) / (2·dz) × 10⁹
3. Vxz = ∂(Vz)/∂x, Vyz = ∂(Vz)/∂y (MATLAB gradient)
4. Free-space Laplace constraint: Vxx = Vyy = −Vzz/2, Vxy ≈ 0

Gravitational Constant

CODATA 2018: $G = 6.67430 \times 10^{-11}\ \text{m}^3\cdot\text{kg}^{-1}\cdot\text{s}^{-2}$

System Requirements

Component	Requirement
OS	Windows 10/11 (64-bit)
Runtime	MATLAB Runtime R2025a
Memory	8 GB recommended

Download

Get the latest installer from Releases.

Screenshots

Sphere Forward Modeling

Parameter Panel

3D Visualization

Multi-Body Setup

Parameter Sensitivity Analysis

Large Grid Result

Cuboid Forward Modeling

Contour Map & 3D View

Cylinder Forward Modeling

Frustum Forward Modeling

Documentation

Document	Content
软件说明书 (Technical Manual)	Complete formulas for all 7 body types, finite-difference gradient theory, unit conversion, JSON parameter schema, file format specifications

ScreenShots

Spherical body forward modeling with Gouraud-lit 3D visualization and plan-view contour

Parameter sensitivity analysis curve family

Z-Axis Convention

• UI: Z upward positive, downward negative (ground = 0, subsurface bodies Z < 0)
• Computation kernel: Auto-converted internally

References

• Blakely, R. J. (1996). Potential Theory in Gravity and Magnetic Applications. Cambridge University Press.
• Nagy, D., Papp, G., & Benedek, J. (2000). The gravitational potential and its derivatives for the prism. Journal of Geodesy, 74, 552–560.
• Plouff, D. (1976). Gravity and magnetic fields of polygonal prisms. Geophysics, 41(4), 727–741.
• Werner, R. A. & Scheeres, D. J. (1997). Exterior gravitation of a polyhedron. Celestial Mechanics and Dynamical Astronomy, 65, 313–344.

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Forward modeling for exploration geophysicists — analytical where possible, numerical where necessary.