In this chapter, we introduce two kinds of deterministic analyses of coda waves, that is, inversion analyses of coda envelopes and seismic array observations, and we show several studies that effectively estimate the inhomogeneous structures in the crust and uppermost mantle. The first one analyzes wave data obtained by local or regional seismographic networks. Nishigami (1991) presented an inversion analysis of coda waves from local earthquakes, to estimate 3-D distribution of relative scattering coefficients. The deviation of coda envelopes from average decay curves is measured as the observational data, assuming a single isotropic scattering model. This method was applied to central California and the inhomogeneous structure around the San Andreas fault system was revealed (Nishigami, 2000). Asano and Hasegawa (2004) revised this method to estimate the absolute scattering coefficients. Revenaugh (1995a) proposed another analysis method, called Kirchhoff coda migration, in which the forward-scattered energy in teleseismic P coda observed by a regional seismographic network is stacked. The second approach is seismic array observation with station spacing shorter than the wavelength of seismic waves. We first summarize several analysis methods of seismic waves propagating through the array. For example, scattered waves with weak energy can be detected by beam-forming techniques. Coda waves are also decomposed into wave trains with various ray directions using analyses such as multiple signal classification or semblance coefficients. The energy of scattered waves in the coda can be evaluated by processing the slant-stacked waveforms under the assumption of a single-scattering model. For example, Matsumoto et al. (1998) applied this method to the source area of the 1995 Kobe earthquake (M7.3), and revealed the existence of strong scatterers just beneath the hypocenter of the mainshock. These studies analyzing the seismic network or array observation data seem to be effective to estimate the Earth's inhomogeneous structures.