A method for spectral analysis of seismic data obtains imaged seismic data and generates orthogonally shifted imaged seismic data gathers. The orthogonally shifted imaged seismic data gathers are processed to generate a spectrally processed imaged seismic data. Alternatively, the imaged seismic data are obtained using a spectral processing filter that is a function of a magnitude of a total wavenumber of the imaged seismic data in three dimensions and a spatially variable velocity function.

Systems and methods for geological medium exploration are provided herein. A method of geological medium exploration may include generating vibrations in a geological medium and recording wave-fields at a surface and in a borehole. Additionally, the method may include obtaining a wave field modification operator and applying the wave-field operator to a full range of seismic data to achieve a spectrally-modified wave field.

A method for determining earth property data from field vertical seismic profiling (VSP) data. The method includes obtaining a survey dataset regarding a geological region of interest encompassing a set of drilled wells. The survey dataset includes VSP data and well data corresponding to the drilled wells. The method also includes: extracting, from the VSP data, a first wavelet; constructing a set of pseudo-wells; determining a reflectivity series for each pseudo-well based on the well data; and generating a first synthetic seismic dataset for each pseudo-well based on its reflectivity series and the first wavelet. The method further includes training a set of machine learning models to predict earth property data given a VSP dataset using the first synthetic seismic dataset and target data. The method further includes determining, with the set of machine learning models, predicted earth property data from a field VSP dataset and planning a wellbore path.