Despite the efforts reported in the literature to explain contrasting experimental observations, the evolution of seismic attributes (velocity and attenuation) of rocks across the saturation range remains ill understood. In a comparative study, we monitored the evolution of ultrasonic P wave attributes in a porous sandstone subjected to two experiments of moisture adsorption and water spontaneous imbibition. Both experiments highlighted a significant (i.e., by 1 order of magnitude) and similar drop in P waves amplitudes, although the maximum saturations reached in each experiment is very different (i.e., about 2% vs. 70%). However, only moisture adsorption leads to a dramatic elastic softening (velocity reduction). This difference might be explained by the coupling between two competing physical mechanisms taking place during water imbibition, namely, elastic softening driven by water adsorption at the grain contact and elastic stiffening driven by full saturation of the grain contacts, at the ultrasonic frequency of the measurement.

We tested on a data set including 12 different rocks the assumption that, during water imbibition experiments, the interaction between direct P waves and reflected P waves on the imbibition front could explain the early P wave amplitude variation occurring before any velocity variation. Our calculations show that (i) the observed distance between the water front and the ultrasonic sensors is always larger than the estimated critical distance below which the first peak amplitude is impacted by the reflected P wave, (ii) the magnitude of the coefficients of reflection is generally very small, and (iii) using simulations of composite waveforms, an impact on the first peak amplitude is expected only in 25% of the tested samples. P wave interaction is definitively a mechanism which can lead to amplitude variations, but it is very likely that such a mechanism is not responsible for the early amplitude variation detected in most of the tested rocks. Moisture diffusion is still a very relevant mechanism to account for our observations on P wave amplitude variations during capillary rise.

Full-waveform inversion for borehole seismic data is an ill-posed problem and constraining the problem is crucial. Constraints can be imposed on the data and model space through covariance matrices. Usually, they are set to a diagonal matrix. For the data space, signal polarization information can be used to evaluate the data uncertainties. The inversion forces the synthetic data to fit the polarization of observed data. A synthetic inversion for a 2D-2C data estimating a 1D elastic model shows a clear improvement, especially at the level of the receivers. For the model space, horizontal and vertical spatial correlations using a Laplace distribution can be used to fill the model space covariance matrix. This approach reduces the degree of freedom of the inverse problem, which can be quantitatively evaluated. Strong horizontal spatial correlation distances favor a tabular geological model whenever it does not contradict the data. The relaxation of the spatial correlation distances from large to small during the iterative inversion process allows the recovery of geological objects of the same size, which regularizes the inverse problem. Synthetic constrained and unconstrained inversions for 2D-2C crosswell data show the clear improvement of the inversion results when constraints are used.