Cross-Gradient Tool

The Cross Gradient Method is a geophysical joint inversion technique that enhances geological consistency by enforcing structural similarity between different physical models. It utilizes the cross-product constraint of model gradient vectors to achieve structural coupling without relying on prior petrophysical relationships.

Usage Guide

Running the Demo:

python demo_cross_gradient.py

cg_solver = CrossGradient()
cg_solver.dx_dz(
    model_A, 
    model_B,
    a_b='ab',      # Similarity mode
    ni=300,        # Iterations (default:300)
    tol_=1e-20,    # Convergence tolerance (default:1e-20)
    smooth=True,   # Smoothing switch
    coef_x=2,      # X-direction smooth factor (default:2)
    coef_y=2       # Y-direction smooth factor (default:2)
)

Key Parameters

a_b Behavior Modes

Mode	Description
'ab'	Bidirectional structural similarity between Model A and B
'a'	Unidirectional constraint: Model A adapts to match Model B's structure
'b'	Unidirectional constraint: Model B adapts to match Model A's structure
'No'	Disable cross-gradient constraints

Dependencies

• NumPy >= 1.21
• SciPy >= 1.7
• Matplotlib >= 3.5

Authors

Original Author

Diego Domenzain

• GitHub Repository: diegozain/alles

Python Implementation Author

Bai Lige

• GitHub: gebai7