The methodology presented was developed for processing and mathematical interpretation of aeromagnetic data derived from two-dimensional sources. The inversion is based on the ridge regression technique as extended in Marquardt (1963) to nonlinear problems. The mathematical formulation provides a statistical approach for study of the efficiency of the solution.A procedure for data preparation is presented which includes a critical evaluation of the digital data obtained during the aerosurvey, joining of flight segments into a single line, and regional-residual separation for profile analysis to set up the initial model approximation.The forward model is analyzed using predictive diagnostics called sensitivity coefficients and parameter correlation matrix. The parameter confidence intervals take into account the measurements of the nonlinearity of the quadratic approximation to the object function. The initial approximation is determined by profile analysis and by the geologic information that defines the forward model and its constraints. The nonuniqueness of the solution results in an interpretation that can be refined as new geologic information is applied for additional model constraints.Synthetic models are used to test and study the convergence and statistical properties of the solution, and to show the ability of the method to resolve anomalies due to various sources. The procedure is also applied to data obtained from aerosurveys over an oil exploration area of the upper Amazon sedimentary basin of Brazil. The validity of the solution is discussed in terms of its compatibility with the geologic information and constraints, and in terms of the statistical properties of the model parameters used to explain the observed data.