A method of hydrocarbon exploration, comprising: a. receiving, at a computer processor, a seismic dataset representative of a subsurface volume of interest and a prior model specification; b. performing, via the computer processor, full waveform inversion of the seismic dataset, which generates an ensemble of sampled earth models that adapt to the spatial resolution of the seismic dataset; c. generating, via the computer processor, an ensemble of seismic images from the seismic data and the ensemble of sampled earth models; d. performing an uncertainty analysis, via the computer processor, of the ensemble of seismic images using the ensemble of sampled earth models and the seismic data; e. using the ensemble of seismic images, the ensemble of sampled earth models, and the uncertainty analysis to appraise the subsurface volume of interest and determine locations to drill wells and produce hydrocarbons from the subsurface volume of interest, the method being characterized in that: the full waveform inversion uses a tree-based Bayesian sampling approach, which uses the prior model specification in reduced dimensions, and automatically adapts model complexity; the full waveform inversion uses a reduced model basis on a tree structure for model compression; the reduced model basis and the model compression use discrete wavelet transforms, DWT; and prior coefficient bounds are specified by finding minimum and maximum DWT coefficients at each level of the tree, and the bounds for coefficients at each level are set to be above and below the minimum and maximum in order to restrict prior models to being within only a given range of feasible models. a. receiving, at a computer processor, a seismic dataset representative of a subsurface volume of interest and a prior model specification; b. performing, via the computer processor, full waveform inversion of the seismic dataset, which generates an ensemble of sampled earth models that adapt to the spatial resolution of the seismic dataset; c. generating, via the computer processor, an ensemble of seismic images from the seismic data and the ensemble of sampled earth models; d. performing an uncertainty analysis, via the computer processor, of the ensemble of seismic images using the ensemble of sampled earth models and the seismic data; e. using the ensemble of seismic images, the ensemble of sampled earth models, and the uncertainty analysis to appraise the subsurface volume of interest and determine locations to drill wells and produce hydrocarbons from the subsurface volume of interest, the method being characterized in that: the full waveform inversion uses a tree-based Bayesian sampling approach, which uses the prior model specification in reduced dimensions, and automatically adapts model complexity; the full waveform inversion uses a reduced model basis on a tree structure for model compression; the reduced model basis and the model compression use discrete wavelet transforms, DWT; and prior coefficient bounds are specified by finding minimum and maximum DWT coefficients at each level of the tree, and the bounds for coefficients at each level are set to be above and below the minimum and maximum in order to restrict prior models to being within only a given range of feasible models. the full waveform inversion uses a tree-based Bayesian sampling approach, which uses the prior model specification in reduced dimensions, and automatically adapts model complexity; the full waveform inversion uses a reduced model basis on a tree structure for model compression; the reduced model basis and the model compression use discrete wavelet transforms, DWT; and prior coefficient bounds are specified by finding minimum and maximum DWT coefficients at each level of the tree, and the bounds for coefficients at each level are set to be above and below the minimum and maximum in order to restrict prior models to being within only a given range of feasible models.