We consider two dimensional topological Landau-Ginzburg models. In order to obtain the free energy of these models, and to determine the Kähler potential for the marginal perturbations, one needs to determine flat or 'special' coordinates that can be used to parametrize the perturbations of the superpotentials. This paper describes the relationship between the natural Landau-Ginzburg parametrization and these flat coordinates. In particular we show how one can explicitly obtain the differential equations that relate the two. We discuss the problem for both Calabi-Yau manifolds and for general topological matter models (with arbitary central charges) with relevant and marginal perturbations. We also give a number of examples.

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The gravity gradient tensor (whose components are the second derivatives of the gravitational potential) is a symmetric tensor that, ignoring the constraint imposed by Laplace's equation, contains only six independent components. When measured on a horizontal plane, these components generate, in the spectral domain, six power spectral densities (PSDs) and fifteen cross-spectra. The cross-spectra can be split into two groups: a real group and a pure imaginary group. If the source distribution is statistically stationary, 1D spectra can be found from the 2D spectra via the slice theorem. The PSDs form two power-sum rules that link all gradient components. The power-sum rules, in combination with further equalities between the power and crossspectra, reduce the number of independent spectra to 13, a number reduced to seven if the power spectrum of the potential is assumed isotropic. The power-sum rules, cross-spectral phases, and coherence between components all provide information on the internal consistency of a set of gradiometry measurements. This information can be used to assess the noise, to determine the isotropy, and, for a self-similar source, to calculate the scaling factor and average depth. When applied to a data set collected in the North Sea, the power-sum rules reveal high-frequency noise that is distributed among only three of the gradient components; additionally, the coherences reveal the source to be anisotropic with a nonzero correlation length.