International audienceThe aim of inverting seismic waveforms is to obtain the “best” earth model. The best model is defined as the one producing seismograms that best match (usually under a least‐squares criterion) those recorded. Our approach is nonlinear in the sense that we synthesize seismograms without using any linearization of the elastic wave equation. Since we use rather complete data sets without any spatial aliasing, we do not have the problem of secondary minima (Tarantola, 1986). Nevertheless, our gradient methods fail to converge if the starting earth model is far from the true earth (Mora, 1987; Kolb et al., 1986; Pica et al., 1989)

The approximate ray Green's tensor in 3-D heterogeneous elastic media combined with the first-order Born approximation lead to new explicit equations for solving, modelling and inverse scattering problems. Individual wave scattering: contributions (PP. PS, SP. SS) are represented for four different linear approximations (i.e. parameter linearizations). The first-order Born appoximation yields a scattered wavefield which is linearly related to medium parameter perturbations. The linearized inverse scattering problem is solved in the space-time domain and consists of minimizing a cost function within the I , norm with a one-step conditioned gradient procedure. From uni-or multicomponent data and a reference heterogeneous background model representing adequately either the long spatial wavelengths of the medium (i.e. the smooth model), and/or its principal features (i.e. the macro-model), this operation reduces to: (1) pre-stack depth-migrating the scattered data yielding three intermediate images; and (2) deconvolving these images by an elastic Hessian correction which produces final high-resolution images representing the medium's short spatial wavelength variations convolved with the source function (e.g. P and S impedances and density maps). If the reference model and data are satisfactory, typical artefacts are due to limited aperture or insufficient coverage. Use of high-frequency and Born approximations require certain constraints. For example, the dominant wavelength must always be smaller than the characteristic length of the reference medium, but larger than the scatterer characteristic length. To increase computational efficiency, the high-frequency approximate Green's tensor is calculated by the paraxial ray method. 2-D elastic synthetic examples for surface reflection and cross-hole experiments show the ability of such a technique to delineate subsurface structure and to recover local changes in elastic properties. However, density variations are more difficult to resolve than P and S impedance or velocity changes.

Locating groundwater in deep-seated karst aquifers is inherently difficult. With seismic methods, we studied the upper epikarst and the underneath low-permeability volume (LPV) of several karst systems located in the southern Quercy and Larzac regions of France and found that refraction tomography was effective only in the epikarst and not in the LPV. We evaluated a 3D case study using a combination of surface records and downhole receivers to overcome this limitation. This 3D approach unveiled a set of elongated furrows at the base of the epikarst and identified heterogeneities deep inside the LPV that may represent high-permeability preferred pathways for water inside the karst. To achieve the same result when no borehole was available, we studied seismic amplitudes of the wavefield, recognizing that wave-induced fluid flow in low-permeability carbonates is a driving mechanism of seismic attenuation. We developed a workflow describing the heterogeneity of the LPV with spectral attributes derived from surface-consistent decomposition principles, and we validated its effectiveness at benchmark locations. We applied this workflow to the 3D study and found a low-amplitude signal area at depth; we interpreted this anomaly as a water-saturated body perched above the aquifer.