3d inversion of deep resistivity measurements with constrained nonlinear transformations

A system to generate a first inverted 3D model of a subsurface formation, the system comprising:

• a processor;
• and
• a machine-readable medium having program code executable by the processor to cause the processor to,
• set a value of a formation parameter for the subsurface formation;
• create an initial three-dimensional (3D) model of the subsurface formation based on the formation parameter;
• apply a constrained transformation to one or more inversion variables of the initial 3D model to create a variable-constrained 3D model of the subsurface formation;
• apply an unconstrained minimization operation to the variable-constrained 3D model to generate a first transformed 3D model;
• and
• invert the first transformed 3D model to generate the first inverted 3D model of the subsurface formation.

One or more non-transitory machine-readable media comprising program code to generate a first inverted 3D model of a subsurface formation, the program code to:

• set a value of a formation parameter for the subsurface formation;
• create an initial three-dimensional (3D) model of the subsurface formation based on the formation parameter;
• apply a constrained transformation to one or more inversion variables of the initial 3D model to create a variable-constrained 3D model of the subsurface formation;
• apply an unconstrained minimization operation to the variable-constrained 3D model to generate a first transformed 3D model;
• and
• invert the first transformed 3D model to generate the first inverted 3D model of the subsurface formation.