Gravity anomalies of a trapezoidal model with quadratic density function

The decrease of density contrast with depth in sedimentary strata is approximated by a quadratic function. The anomaly equation of a trapezoidal model with the quadratic density function is derived. Nonlinear optimization technique using the Marquardt algorithm has been developed and used to interpret a synthetic anomaly profile of the trapezoidal model. The exact values of the coefficients of the quadratic density function are assumed to be known. The convergence of the method is shown by plotting the values of the objective function λ and the various parameters with respect to iteration number. θ and half-width of the trapezoidal model are found to be correlated. The method is also applied to interpret the gravity anomalies over San Jacinto graben, California. Finally, the use of modelling with quadratic density function is discussed.