The simulation of migrated and inverted data is hampered by the high computational cost of generating 3D synthetic data, followed by processes of migration and inversion. For example, simulating the migrated seismic signature of subtle stratigraphic traps demands the expensive exercise of 3D forward modeling, followed by 3D migration of the synthetic seismograms. This computational cost can be overcome using a strategy for simulating migrated and inverted data by filtering a geologic model with 3D spatial-resolution and angle filters, respectively. A key property of the approach is this: The geologic model that describes a target zone is decoupled from the macrovelocity model used to compute the filters. The process enables a target-oriented approach, by which a geologically detailed earth model describing a reservoir is adjusted without having to recalculate the filters. Because a spatial-resolution filter combines the results of the modeling and migration operators, the simulated images can be compared directly to a real migration image. We decompose the spatial-resolution filter into two parts and show that applying one of those parts produces output directly comparable to 1D inverted real data. Two-dimensional synthetic examples that include seismic uncertainties demonstrate the usefulness of the approach. Results from a real data example show that horizontal smearing, which is not simulated by the 1D convolution model result, is essential to understand the seismic expression of the deformation related to sulfate dissolution and karst collapse.

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In geophysical exploration different types of measurements are used to probe the same subsurface region. In this paper we show that the wavelet transform can aid the process of linking different data types. The continuous wavelet transform, and in particular the analysis of amplitudes along wavelet transform modulus maxima lines, is a powerful tool to analyze the characteristic properties of local variations in a signal. The amplitude-versus-scale curve of a particular transition in a signal can be seen as its fingerprint. Hence, local variations in different data types can be linked by comparing their fingerprints in the wavelet transform domain. Insight in the physics underlying the different types of measurements is required to 'tune' the different wavelet transforms in such a way that a particular geological transition in the Earth's subsurface leaves the same fingerprint in the wavelet transform of each data type. We discuss the wavelet transform as a tool for geophysical data integration for three situations. First we discuss how one can link the scale-dependent properties of outliers in borehole data to those of reflection events in surface seismic data. We use wave theory to derive relations between the two data types in the wavelet transform domain. Next we analyze the relation between the wavelet transforms of detailed geological models and (simulated) migrated seismic data, with the aim of improving the geological interpretation. A spatial resolution function provides the link between the wavelet transforms of the geological model and the migrated seismic data. Finally we consider the integration of geotechnical (cone penetration test) data with shallow shear wave seismic data. We illustrate with a real data example that specific geological features of the shallow subsurface can be identified in the wavelet transforms of both data types. We conclude that the wavelet transform can be used as a tool that aids the integration of different types of data.

Using a combined Forward and Inverse operator (resolution function), a fast method is presented to construct a simulated migrated seismic section from a geological depth model. Unlike the 1D convolution model, the resolution function expresses both vertical and horizontal resolution. This gives an interpreter a powerful tool to create simulated migrated seismics, which includes migration effects. Further due to its low computational costs, different geological models can rapidly be evaluated.