Very recently a new inversion method has been developped to analyze the intergalactic medium seen in absorption in quasar spectra (the so-called Lyman-alpha forest). This method is applied to recover the temperature of the gas and the underlying density field. Using constraints from the Lyman-beta forest, it is possible to recover this field up to over-densities delta=10. By inverting the HI and CIV absorptions together it has been shown that the CIV/HI ratio varies through the profile of strong lines, beeing larger in the wings. The method can be applied to reconstruct the 3D density field from multiple lines of sight and is shown to give good results up to mean separations of 3 arcmin. Results from a survey of QSO pairs performed with HST/STIS and VLT/UVES-FORS are summarized.
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