Single-step estimation of porosity using stochastic inversion algorithm in a south-western oil field of Iran

In exploration seismology، estimation of elastic parameters of rocks using seismic amplitudes is considered as inverse problems. Nowadays، model-based and more generally optimization-based algorithms are of the most common methods of seismic inversion. These algorithms which are known as deterministic methods، are suffering from two main problems; First، vertical resolution of outputs is very low. The estimated outputs of these methods contain the same frequency content as the seismic bandwidth. So the resolution of estimates will be same as that of seismic data. Second، these methods are not able to prepare any estimation of uncertainty in calculation of output model. That because the deterministic methods generate only one realization of acoustic impedance that is considered as the most probable model. In addition to these problems، the output model of deterministic methods is very smooth estimation of acoustic impedance which makes it inappropriate for continuity evaluation of events and volumetric calculations. In order to solve these shortcomings of deterministic methods، a new algorithm known as stochastic inversion has been proposed which in most common situations، uses Sequential Gaussian Simulation (SGS) of acoustic impedance logs to prepare multiple realizations of acoustic impedance، in such a way that all these realizations are compatible to seismic data. According to this method، first of all a random path is selected through the seismic path. In each grid node of the selected path a pseudo-acoustic impedance log is simulated by SGS method. This pseudo-log is then convolved with the extracted wavelet to produce a synthetic seismogram. In the next stage the synthetic seismogram is compared with the real one to measure the misfit. If the calculated misfit is less than a threshold value، the simulated impedance log will be selected and added to the data set to be used for simulation of future nodes. On the other hand، if the simulated log does not satisfy the maximum allowable misfit، then a new pseudo-impedance log will be simulated until an allowable impedance log is created. This procedure is repeated for all grid nodes of the selected path until the seismic grid is filled with acoustic impedance logs. The above procedure is then repeated using different random paths. As a result، multiple realizations of acoustic impedance will be created that all of them are compatible with original seismic data. Since the output realizations of stochastic inversion are fundamentally simulated models of well logs، it would be obvious that the resolution of these models will be controlled by well logs which are highly more resolvable than seismic data. The ability of stochastic inversion in generation of multiple realizations، make it possible to evaluate uncertainties in estimations.