Effects of porosity on the attenuation of wave propagation are studied. The effects of pore fluids and porous structures are significant on changing the shapes of propagating wavelets. The waveform change of a propagating wavelet is much more sensitive to porosity than intrinsic attenuation. The attenuation occurred in natural rocks may largely due to these porous effects in addition to the internal friction of the solid represented by the intrinsic quality factor Q. The waveform of a propagating wavelet is quantitatively associated with attenuation, porosity, and fluid content, and is characterized by three parameters: the porosity , the quality factor Q, and the center frequency f0. Estimations of attenuation, porosity, and fluid content can be made by optimal wavelet analysis. High-resolution mapping of subsurface structures can be achieved by solving the integral equation with the nonlinear optimization of the time-variant wavelets. The inversion and the optimization schemes have been applied to study the porous sea floor and the crustal axial magma chamber (AMC) on the East Pacific Rise. These results provide porosity, attenuation information, and the highly resolved wave events, for further evaluation of compressional and shear wave velocities and other physical properties such as crack density and aspect ratio.