Method for 3-d gravity forward modeling and inversion in the wavenumber domain

A method for determining spatial distribution of a physical property within a volume of subsurface rock formations, comprising:

• deploying at least one sensor above the volume and/or at least one sensor in at least one wellbore penetrating the volume;
• obtaining measurements of a physical parameter having a potential field from the at least one deployed sensor;
• generating an initial model of spatial distribution of the physical property using available data, the data related to spatial distribution of the physical property within the volume;
• generating a forward model in the wavenumber domain of spatial distribution of a potential field;
• entering as input to an interpolation measurements of the physical parameter having a potential field from the at least one deployed sensor;
• generating a revised model of spatial distribution of the potential field by interpolating the measurements above the volume and/or in the at least one wellbore to a plurality of positions within the volume, the interpolating performed in the wavenumber domain;
• and
• generating a revised model of spatial distribution of the physical property by inversion in the wavenumber domain of the revised potential field model.

A method for determining spatial distribution of a physical property within a volume of subsurface rock formations, comprising:

• generating an initial model of spatial distribution using available data, the data related to the physical property distribution within the volume;
• generating a forward model in the wavenumber domain of spatial distribution of a potential field;
• and
• inverting the forward model in the wavenumber domain to generate a model of spatial distribution of the physical property within the volume.

A method for determining spatial distribution of density within a volume of subsurface rock formations, comprising:

• generating an initial model of spatial distribution of density using available data, the data related to the density distribution within the volume;
• generating a forward model in the wavenumber domain of spatial distribution of gravity;
• entering as input to an interpolation measurements of gravity obtained at spaced apart locations above the volume and/or in at least one wellbore penetrating the volume;
• generating a revised model of spatial distribution of gravity by interpolating the measurements above the volume and/or in the at least one wellbore to a plurality of positions within the volume, the interpolating performed in the wavenumber domain;
• and
• generating a revised density model by inversion in the wavenumber domain of the revised gravity model.