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Ambient seismic noise or microtremor observations used in spatial auto-correlation (SPAC) array methods consist of a wide frequency range of surface waves from the frequency of about 0.1 Hz to several tens of Hz. The wavelengths (and hence depth sensitivity of such surface waves) allow determination of the site S-wave velocity model from a depth of 1 or 2 m down to a maximum of several kilometres; it is a passive seismic method using only ambient noise as the energy source. Application usually uses a 2D seismic array with a small number of seismometers (generally between 2 and 15) to estimate the phase velocity dispersion curve and hence the S-wave velocity depth profile for the site. A large number of methods have been proposed and used to estimate the dispersion curve; SPAC is the one of the oldest and the most commonly used methods due to its versatility and minimal instrumentation requirements. We show that direct fitting of observed and model SPAC spectra generally gives a superior bandwidth of useable data than does the more common approach of inversion after the intermediate step of constructing an observed dispersion curve. Current case histories demonstrate the method with a range of array types including two-station arrays, L-shaped multi-station arrays, triangular and circular arrays. Array sizes from a few metres to several-km in diameter have been successfully deployed in sites ranging from downtown urban settings to rural and remote desert sites. A fundamental requirement of the method is the ability to average wave propagation over a range of azimuths; this can be achieved with either or both of the wave sources being widely distributed in azimuth, and the use of a 2D array sampling the wave field over a range of azimuths. Several variants of the method extend its applicability to under-sampled data from sparse arrays, the complexity of multiple-mode propagation of energy, and the problem of precise estimation where array geometry departs from an ideal regular array. We find that sparse nested triangular arrays are generally sufficient, and the use of high-density circular arrays is unlikely to be cost-effective in routine applications. We recommend that passive seismic arrays should be the method of first choice when characterizing average S-wave velocity to a depth of 30 m (V(s)30) and deeper, with active seismic methods such as multichannel analysis of surface waves (MASW) being a complementary method for use if and when conditions so require. The use of computer inversion methodology allows estimation of not only the S-wave velocity profile but also parameter uncertainties in terms of layer thickness and velocity. The coupling of SPAC methods with horizontal/vertical particle motion spectral ratio analysis generally allows use of lower frequency data, with consequent resolution of deeper layers than is possible with SPAC alone. Considering its non-invasive methodology, logistical flexibility, simplicity, applicability, and stability, the SPAC method and its various modified extensions will play an increasingly important role in site effect evaluation. The paper summarizes the fundamental theory of the SPAC method, reviews recent developments, and offers recommendations for future blind studies.