Patent ID: 7675818

Claim:
A computer-implemented method for transforming geophysical data to a physical properties model of a subsurface region, comprising: (a) obtaining measured data from a geophysical survey of the subsurface region; (ab) developing a linear system of tomographic equations expressed in matrix form as Ax=b, where x is a vector whose components parameterize the model of said physical properties in a first representation of said subsurface region, b contains information derived from the measured data and sensitive to said physical properties, and A relates said physical properties within said subsurface region to said data; (c) selecting a second representation of the subsurface region in which the model of the same physical properties is parameterized by the components of a vector y, for which representation there exists a linear mapping matrix M that maps the first representation, x, to the second representation, y, such that x=My; (d) using a computer to perform the matrix multiplication C=AM; and (e) using a computer to invert the matrix equation Cy=b to solve for the physical properties parameterized by y.