Geodetic Inversion Package for MATLAB

This package performs kinematic finite-fault slip inversion using multi-source geodetic observations:

• InSAR phase & phase gradients
• POT/MAI (azimuth offsets)
• GNSS displacements
• Optical displacement measurements

The framework supports flexible data combinations and complex fault geometries while maintaining computational efficiency.

---

Directory Structure

Geodetic_Inversion/
├── example/
│   └── Ridgecrest/
│       ├── input/          # GNSS, InSAR, phase-gradient observations
│       └── model/          # Inversion configuration files and slip model
└── src/
    ├── Subsample.m            # Data subsampling
    ├── main_inv.m             # Main inversion entry
    └── main_inv_ridgecrest.m

📊 Data Preparation

Perform quality control and preprocessing before inversion. All coordinates use WGS84 datum.

📡 InSAR Phase/Phase Gradient Data

File format (space/tab-delimited):

Column	Description	Units
1	Longitude	deg
2	Latitude	deg
3	Topography	m
4	Look vector (East component)	-
5	Look vector (North component)	-
6	Look vector (Vertical component)	-
7	LOS displacement or phase gradient	mm/~
8	Sampling ratio (relative data weight)	-

Note: if not specified Sampling ratio (relative data weight), set 1 is ok

🧭 POT/MAI Data

File format (space/tab-delimited):

Column	Description	Units
1	Longitude	deg
2	Latitude	deg
3	Topography	m
4	Sampling ratio or std. error	mm

📡 GNSS Data

File format (space/tab-delimited):

Column	Description	Units
1	Longitude	deg
2	Latitude	deg
3	East displacement	mm
4	North displacement	mm
5	Vertical displacement	mm
6	East error	mm
7	North error	mm
8	Vertical error	mm
9	Topography	m

---

⚙️ Configuration (config.inv)

Dataset Definition

num_des_sources      = 2   # Descending InSAR datasets
num_asc_sources      = 1   # Ascending InSAR datasets
num_x_grd_sources    = 0   # West-East phase gradients
num_y_grd_sources    = 1   # South-North phase gradients
num_azi_sources      = 1   # POT/MAI datasets
num_gps_sources      = 3   # GNSS stations
phi1                 = 349.25 # Satellite track angle (degrees)

GNSS Component Selection

# Enable (1) or disable (0) components per dataset:
gps1h = 1   # Horizontal (E,N) for GNSS #1
gps1v = 0   # Vertical component disabled
gps2h = 1
gps2v = 1

Data File Assignment

Assign paths in the {data_files} block of config.inv:

des1 = t71_des.lltnde
asc1 = t64_asc_edit.lltnde
asc2 = t65_asc_alos2_new.lltnde
asc3 = t66_asc_alos2.lltnde

dec_grdx = Rc_ph_grdx_dec_masked.lltnde
asc_grdx = Rc_ph_grdx_asc_masked.lltnde
dec_grdy = Rc_ph_grdy_dec_masked.lltnde
asc_grdy = Rc_ph_grdy_asc_masked.lltnde

azi1 = t65_mai.llde

gps1 = GPS71_new.lldet
gps2 = GPS71_new.lldet

gov1 = optical_offset.lldeat

---

🌋 Fault Geometry (model block)

{model_params} num_of_sources = 8 poisson_ratio = 0.25 {origin} xo = -117.5990
yo = 35.7700 {trace1} x = -8.379680e+03 y = 1.216606e+04 z = 0.000000e+00 len = 1.686743e+04 wid = 2.000000e+04 dip = 90 strike = 1.357613e+02

Basic Parameters

num_of_source = 3    # Fault segments
xo = 142.365         # Epicenter longitude (deg)
yo = 38.322          # Epicenter latitude (deg)

Geometry Specification (Choose ONE method)

Option 1: Manual UTM Definition

Directly define patches in local UTM coordinates (advanced users).

Option 2: trace2patch Utility (Recommended)

% Define fault trace endpoints (geographic coordinates)
lon_endpoints = [lon1, lon2, lon2, lon3, ..., lon_n];
lat_endpoints = [lat1, lat2, lat2, lat3, ..., lat_n];
lon_epi = lon0;  % Epicenter longitude
lat_epi = lat0;  % Epicenter latitude

% Generate patches (default: 20km width, 90° dip)
[patch_params] = trace2patch(lon_endpoints, lat_endpoints, lon_epi, lat_epi);

Defaults: 20 km fault width, 90° dip angle. Modify in output files as needed.

---

🔧 Inversion Parameters (inversion block)

Discretization & Slip Constraints

top_patch_width        = 500    # Min patch width (m)
top_patch_length       = 500    # Min patch length (m)
patch_increment_factor = 1.5    # Resolution increase with depth

strike_slip = 1    # Enable strike-slip
dip_slip    = 1    # Enable dip-slip
normal_slip = 0    # Disable normal-slip (typical for most earthquakes)

Regularization

positivity_max          = 1000    # Max slip magnitude (m)
bottom_zero_constraint  = 1     # Enforce zero slip at bottom (1=yes)
smooth_factor           = 0.1   # Smoothing strength (1e-2 to 1e1)
smooth_between_segments = 1     # Cross-segment smoothing
smooth_dip_over_strike  = 0.5   # Dip vs. strike smoothing ratio

Data Weighting & Corrections

weight_phase  = 1.0   # InSAR phase weight
weight_ph_grd = 8000   # Phase gradient weight
weight_azi    = 0.1   # POT/MAI weight
weight_gps    = 0.1   # GNSS weight

remove_ramp          = 1  # Remove orbital/ionospheric ramps
consider_topography  = 0  # Ignore topography effects (0=no)
switch_phase         = 1  # Phase sign convention (+1/-1)

---

🔗 Advanced Constraints

Inter-Segment Smoothness (smooth block)

num_seg_smooth = 2       # Adjacent segment pairs
smo1 = [1, 2]            # Smooth between seg1 & seg2
smo2 = [2, 3]            # Smooth between seg2 & seg3

num_inter_smooth = 1     # Complex fault connections
smoi1 = [1, 3, 2]        # Connect seg1-seg3 with type-2 smoothing (artificial connection)

Fault Edge Constraints (edge_constraints block)

bot = 1       # Zero slip at bottom edge
top = 0       # No constraint at top edge
side = 1      # Enable side constraints
num_side = 2  # Segments with side constraints
side1 = [1, 1, 0]  # Segment1: left-edge=constrained, right-edge=free
side2 = [3, 0, 1]  # Segment3: left-edge=free, right-edge=constrained

---

▶️ Running the Inversion

1. Configure config.inv with your parameters
2. Set file paths in main_inv.m:

    earthquake = 'Ridgecrest';  %
    input_path = ['/home/path/to/Geodetic_Inversion/example/',earthquake,'/input/'];
    model_path = ['/home/path/to/Geodetic_Inversion/example/',earthquake,'/model/'];
    addpath '/home/path/to/Geodetic_Inversion/src'

3. Execute the inversion:

   main_inv.m; % Start computation

---

📚 References

1. Core Methodology
   Xu, X., Tong, X., Sandwell, D. T., Milliner, C. W., Dolan, J. F., Hollingsworth, J., ... & Ayoub, F. (2016). Refining the shallow slip deficit. Geophysical Journal International, 204(3), 1867-1886.

2. Phase-Gradient Constraints
   Zhang, Y., & Xu, X. (2024). Constraining shallow slip deficit with phase gradient data. Geophysical Journal International, 236(1), 123-145.