AMGEM - Adaptive Mesh Generator for Geophysical Electromagnetic Modeling

A companion preprocessing tool for PETGEM.
Automates the generation of simulation ready tetrahedral FE meshes for 3D CSEM surveys.

Overview

AMGEM bridges the gap between raw geophysical survey data and a simulation ready mesh for PETGEM (Parallel Exascale Toolkit for Geophysical Electromagnetic Modeling). Starting from a base Gmsh boundary mesh, it executes a fully automated pipeline:

1. Multi-surface topography interpolation — displaces mesh nodes on any number of geological faces (bathymetry, basement, etc.) to conform to real survey data in gridded or XYZ coordinate format.
2. Laplacian mesh smoothing — iteratively repositions interior nodes to the centroid of their neighbours, improving element quality after interpolation.
3. Skin-depth computation — reads a 3D resistivity model (SEG-Y) and computes the electromagnetic skin-depth across the domain to derive physically motivated element sizes.
4. Background mesh generation — produces a Gmsh .pos file that encodes spatially varying target element sizes: globally driven by the minimum skin-depth and locally refined near survey sources and receivers using a bin grid spatial index.

The output background mesh file is passed directly into a Gmsh .geo script to drive adaptive tetrahedral mesh generation, completing the data preparation workflow for PETGEM.

Prerequisites

Dependency	Version	Notes
CMake	≥ 3.25
C compiler	C23	GCC / Clang
segyio	1.9.14	Included as a Git submodule
GNU Scientific Library (gsl)	≥ 2.0

Install GSL on Debian/Ubuntu:

sudo apt install libgsl-dev

Install GSL on Fedora/RHEL/CentOS Stream:

sudo dnf install gsl-devel

Install GSL on Arch Linux:

sudo pacman -S gsl

Install GSL on macOS (Homebrew):

brew install gsl

Getting started

Clone the repository with submodules:

git clone --recurse-submodules https://github.com/dfmeretzki/interpolate-topography.git

If you cloned without submodules:

git submodule update --init --recursive

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Build

Build the program using cmake from the root directory of the project

cmake -S . -B build
cmake --build build

Or use one of the provided presets for debug and release builds. For debug builds use

cmake --preset debug
cmake --build --preset debug

and for release builds use

cmake --preset release
cmake --build --preset release

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Usage

./<build_directory>/amgem <config_file>

example:

./out/build/release/amgem config.in

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Configuration file

All parameters are supplied through a plain text file using key = value syntax. Lines beginning with # are comments. Multi-value parameters use comma separated lists.

# AMGEM configuration file

# -- Mode of operation --------------------------------------------------------
# Valid values: all, interpolate, background_mesh
# interpolate = only perform topography interpolation and smoothing
# background_mesh = only perform background mesh generation using the input mesh and resistivity model
mode = all

# -- Topography ---------------------------------------------------------------
# Paths to topography data files, one per geological surface.
# Mapped to surfaceMeshFaces in order: 1st file → 1st face, 2nd → 2nd, etc.
topoFiles = data/bathymetry.dat, data/basement.dat

# Interpolation grid resolution (number of sample points along each axis)
nx = 150
ny = 180

# -- Mesh I/O -----------------------------------------------------------------
skinMeshFileIn  = meshes/skin.msh
skinMeshFileOut = meshes/skin_modified.msh

# -- Surface interpolation ----------------------------------------------------
# Face identifiers in the mesh corresponding to the geological surfaces
surfaceMeshFaces = 6, 11

# -- Smoothing ----------------------------------------------------------------
# Face indices where Laplacian smoothing is applied after interpolation
meshFacesToSmooth = 1, 2, 3, 4, 5
# Convergence parameters (defaults: 200 and 0.01)
iterMaxSmooth = 200
tolerSmooth   = 0.01

# -- Resistivity model --------------------------------------------------------
# Minimum resistivity in ohm-m, if not specified, it will be extracted from the SEG-Y file
minResistivity = 0.1
# SEG-Y file with 3D resistivity distribution (used for skin-depth calculation)
resistivityFile = data/resistivity.segy

# -- Sources / receivers ------------------------------------------------------
# Source and receiver positions as (x, y, z) triplets, one per line
sourcesFile = data/sources.dat

# -- Background mesh output ---------------------------------------------------
backgroundMeshFile = meshes/background.pos

# -- EM survey parameters -----------------------------------------------------
# Signal frequency in Hz (default: 1.0)
frequency = 0.25

# Global element size = min_skin_depth / rSkinDepth  (default: 2.0)
rSkinDepth = 2.0

# Emitter dipole length in metres (default: 1.0)
emitterLength = 1.0

# Local element size near sources = emitterLength / rsFactor,
# capped at the global skin-depth size (default: 10.0)
rsFactor = 10.0

# Geometric growth factor for element size away from sources (default: 1.25)
# Element size grows by this factor each layer away from sources center, up to the global size limit with a maximum distance of 3.0 * global element size
growthFactor = 1.25

# Optional scaling factor applied to all element sizes in the background mesh (default: 1.0, no scaling)
elemSizeScale = 1.0

Parameter reference

Parameter	Required	Default	Description
mode	no	all	Operation mode: all, interpolate, background_mesh
topoFiles	yes	—	Comma-separated paths to topography files
nx, ny	yes	—	Interpolation grid resolution
skinMeshFileIn	yes	—	Input boundary mesh (Gmsh .msh v1)
skinMeshFileOut	yes	—	Output mesh file path
surfaceMeshFaces	yes	—	Face IDs to interpolate topography onto
meshFacesToSmooth	no	—	Face IDs where Laplacian smoothing is applied
iterMaxSmooth	no	200	Maximum smoothing iterations
tolerSmooth	no	0.01	Smoothing convergence tolerance
minResistivity	yes/no*	—	Minimum resistivity in ohm-m (overrides SEG-Y extraction)
resistivityFile	yes/no*	—	SEG-Y resistivity model
sourcesFile	yes	—	Source/receiver positions (XYZ, one per line)
backgroundMeshFile	yes	—	Output Gmsh background mesh (.pos)
frequency	no	1.0	EM survey frequency in Hz
rSkinDepth	no	2.0	Global element size factor (relative to min skin-depth)
emitterLength	no	1.0	Emitter dipole length in metres
rsFactor	no	10.0	Source local refinement factor
growthFactor	no	1.25	Geometric growth factor for element size away from sources
elemSizeScale	no	1.0	Optional scaling factor applied to all element sizes in the background mesh
*either minResistivity or resistivityFile must be provided to compute skin-depths.If both are provided, minResistivity will be used.

Topography file format

Grid format for regularly sampled datasets:

<nx> <ny>
<x_1> <x_2> ... <x_nx>
<y_1> <y_2> ... <y_ny>
<z_1,1> <z_2,1> ... <z_nx,1>
...
<z_1,ny> <z_2,ny> ... <z_nx,ny>

XYZ format for irregularly spaced survey points:

<x_1> <y_1> <z_1>
<x_2> <y_2> <z_2>
...

The same XYZ format is used for sourcesFile.

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Mesh refinement strategy

Element sizes are determined by two levels:

• Global size: derived from the minimum skin-depth across the resistivity model:

  $\displaystyle h_\text{global} = \frac{503\sqrt{\rho_\text{min} / f}}{r_\text{skin}}$

• Local size: applied near each source/receiver within a radius of $3 \times h_\text{global}$, defined as:

  $\displaystyle h_\text{local}(d) = \min\left(\frac{L_\text{emitter}}{r_s}, h_\text{global}\right)\cdot{growthFactor^{\lfloor{d}/{h_\text{global}}\rfloor}}$

Size grows geometrically with distance d from the source with a factor growthFactor per layer.