Method for attenuation compensation utilizing non-stationary matching filters

A method of generating an attenuation-compensated model of a subsurface region, comprising:

• (a) computing an attenuation-compensated gradient of the subsurface region based on field data and a subsurface model;
• (b) computing a search direction based on the attenuation-compensated gradient;
• (c) searching for an improved model;
• (d) checking the improved model for convergence;
• and
• (e) in the absence of convergence:
• updating the subsurface model with the improved model;
• and
• repeating (a)-(e).

An improved method for generating an image of a subsurface region, the improvement of which comprises:

• utilizing a viscoelastic wave propagation operator with forward modeling, while utilizing an elastic wave propagation operator with adjoint modeling, the method comprising:
• computing an initial image of the subsurface region utilizing the elastic wave propagation operator and based on field data and a subsurface model;
• generating forward-modeled data utilizing the viscoelastic wave propagation operator and based on the initial image;
• computing a secondary image by migrating the forward-modeled data with the elastic wave propagation operator;
• computing a non-stationary matching filter based on the initial image and the secondary image;
• and
• applying the non-stationary matching filter to the initial image to generate the attenuation-compensated image.