Presentation on theme: "Inversion Transforming the apparent to « real » resistivity. Find a numerical model that explains the field measurment."— Presentation transcript:
Inversion Transforming the apparent to « real » resistivity. Find a numerical model that explains the field measurment.
Direct prob. / Inverse problem Measure or data Parameters or model d m
Problem to solve Error on measurment, sub sampling Field constraints Miss choose of relevant parameters Over simplified physical model or « law » Non unicity of the solution A priori knowledge to be included Cost in time, money …..
Search for solution Minimise the error (y) between the measred data (d) and the reproduction of these data ( đ ) from a synthetic model (m): Least square (norm L 2 ) : Robust inversion (norm L 1 ) : (filtering ouliers)
The mean square approach Linear case : solution : Non linear case : Gauss-Newton method J = jacobian matrix : Initial model :
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