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We develop methods for the modeling and inversion of the power‐density spectrum from magnetic anomaly data assuming that the crustal magnetic field is caused by an ensemble of vertical‐sided and uniformly magnetized prisms. The solution of the forward problem is achieved in the wavenumber domain, where a synthetic spectrum is given by the product of the mathematical expectations of single‐valued functions that describe depth, thickness, and horizontal dimensions of prisms in the ensemble. We use Gaussian and uniform distributions to describe the ensemble and provide a variety of functions from which different statistical models can be obtained. The solution of the inverse problem is achieved iteratively, starting from an initial set of model parameters. It is based on the ridge‐regression algorithm, and its usefulness is assessed in a number of examples with numeric, synthetic and real data spectra. The methods are first tested on the spectrum obtained from a simple artificial magnetic anomaly and on the artificial spectrum caused by an ensemble of source bodies and are found to be capable of recovering the source parameters. Next, the methods are applied to marine magnetic data from a survey offshore of the Yucatán Peninsula, Mexico. The results of this last application are consistent with the crustal structure observed at Chicxulub hole.

The gravity effect produced by two and three‐dimensional bodies with nonuniform density contrast has been treated by several authors. One of the first attempts in this direction made by Cordell (1973), who developed a method to compute the gravity effect due to a two‐dimensional prism whose density decreases exponentially with depth. A different approach was proposed by Murthy and Rao (1979). They extended the line‐integral method to obtain the gravity effect for bodies of arbitrary cross‐sections, with density contrast varying linearly with depth. Chai and Hinze (1988) have derived a wavenumber‐domain approach to compute the gravity effect due to a vertical prism whose density contrast varies exponentially with depth. Recently, Rao (1990) has developed a closed expression of the gravity field produced by an asymmetrical trapezoidal body whose density varies with depth following a quadratic polynomial.

New methods for 2-D modeling of gravity anomaly data are developed following an approach that uses both analytic and numerical methods of integration. The forward‐model solution developed here is suitable to calculate the gravity effect caused by a 2-D source body bounded either laterally or vertically by continuous functions. In our models, the density contrast is defined by a second‐order polynomial function of depth and distance along the profile. We present several examples to show that our models are capable of accommodating a broad variety of geologic structures.

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