Seismic inversion is a method that extracts acoustic impedance data from the seismic traces. Source wavelets are band-limited, and thus seismic traces do not contain low and high frequency information. Therefore, there is a serious problem when the deterministic seismic inversion is applied to real data and the result of deterministic inversion is smooth. Low frequency component is obtained from well log data; however, but when well log and seismic data are used together, it faces a problem which is a function of the support of scale of measurements. Well log data have a high vertical resolution while seismic data represent low details in vertical direction. Geostatistical seismic inversion (GSI) is a method to overcome the aforementioned limitations. GSI uses well log and seismic data together in the geostatistical frameworks. In this study, a new approach of geostatistical inversion based on spectral geostatistical simulation is used. This approach is performed in frequency domain and stochastic framework. Distinct from sequential simulation, spectral simulation method is a direct method, which does not require an acceptance/rejection step. Hence, GSI algorithm based on spectral simulation is fast. This approach is performed in a case study of an Iranian gas field in the Persian Gulf basin. The upper-Dalan and Kangan are two main formations of this field. The results of GSI are compared with deterministic inversion and it is concluded that, as opposed to deterministic inversion, GSI can recover low frequency components.