M.Sc. Student of Geophysics, Earth Physics Department, Institute of Geophysics, University of Tehran, Iran
Assistant Professor, Earth Physics Department, Institute of Geophysics, University of Tehran, 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.
In the current study, the algorithm of stochastic inversion is modified to estimate the porosity instead of acoustic impedance. According to this algorithm, neutron porosity logs have been used to prepare local realizations of pseudo-porosity log. These pseudo-porosity logs are then converted to acoustic impedance to be able to setup synthetic seismograms. The synthetic seismograms will be compared with real ones and then using an accept-reject command, the best local realization will be selected at each grid nodes. This procedure is repeated for all the grid nodes to prepare a 3D estimated model (realization) of porosity.
Therefore, the workflow for the single-step inversion of porosity data will be expressed as follows:
- A random path is selected through the seismic grid.
- At each node, using the original and previously inverted porosity logs, a pseudo-porosity log is simulated
- The simulated porosity log is converted into a impedance log by means of relations that has been previously established between porosity and acoustic impedances at well locations.
- The converted impedance log is convolved with the extracted wavelet to produce a synthetic seismogram.
- The synthetic seismogram is compared with the original seismogram to measure the misfit.
- If the calculated misfit is less than a threshold value, the simulated porosity 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-porosity log will be simulated until an allowable porosity log is created.
- The above procedure is repeated for all grid nodes of the selected path until the seismic grid is filled with acoustic impedance logs.
The results of application of the above procedure to create 3D realizations of porosity exhibit an acceptable match with real porosity logs.