Image appraisal for 2D and 3D electromagnetic inversion

Abstract

Linearized methods are presented for appraising image resolution and parameter accuracy in images generated with two and three dimensional non-linear electromagnetic inversion schemes. When direct matrix inversion is employed, the model resolution and model covariance matrices can be directly calculated. The columns of the model resolution matrix are shown to yield empirical estimates of the horizontal and vertical resolution throughout the imaging region. Plotting the square root of the diagonal of the model covariance matrix yields an estimate of how the estimated data noise maps into parameter error. When the conjugate gradient method is employed rather than a direct inversion technique (for example in 3D inversion), an iterative method can be applied to statistically estimate the model covariance matrix, as well as a regularization covariance matrix. The latter estimates the error in the inverted results caused by small variations in the regularization parameter. A method for calculating individual columns of the model resolution matrix using the conjugate gradient method is also developed. Examples of the image analysis techniques are provided on a synthetic cross well EM data set.