Comparing Geostatistical Seismic Inversion Based on Spectral Simulation with Deterministic Inversion: A Case Study

Iranian Journal of Oil & Gas Science and Technology, Vol. 3 (2014), No. 1, pp. 01-14 http://ijogst.put.ac.ir Comparing Geostatistical Seismic Inversion Based on Spectral Simulation with Deterministic Inversion: A Case Study Hamid Reza Ansari1, Reza Motafakkerfard1*, and Mohammad Ali Riahi2 1 Department of Petroleum Exploration, Petroleum University of Technology, Abadan, Iran 2 Institute of Geophysics, University of Tehran, Tehran, Iran Received: May 28, 2013; revised: August 05, 2013; accepted: December 29, 2013 Abstract 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. Keywords: Geostatistical Seismic Inversion, Deterministic Inversion, Spectral Simulation, Geostatistics 1. Introduction Acoustic impedance (AI) is an important rock property that can be obtained from seismic data during seismic impedance inversion. Most of seismic inversion methods are based on minimizing differences between synthetic seismic and real seismic responses. Synthetic seismic responses are the result of convolution of wavelet and earth reflectivity. Earth reflectivity is a rock property, which is a function of acoustic impedance. The inversion methods which operate in minimizing error are known as “deterministic inversion.” Deterministic seismic inversion such as sparse spikes or model-based inversion is smooth in results, which is due to its limitations. Francis discussed some of these limitations (Francis, 2006). The significant limitation is missing low frequency information due to the band-limitation of real seismic data. Since the source wavelet is band-limited and does not cover all frequencies, low and high * Corresponding Author: Email: 2 Iranian Journal of Oil & Gas Science and Technology, Vol. 3 (2014), No. 1 frequency components are hidden in the seismic responses. Missing the low frequency is important due to the fact that low frequency components contain critical information about the absolute impedances values (Francis, 2010). Low frequency information can be obtained from well log data. For adding log data to seismic data, one may encounter a serious problem, which is known as the support of scale measurement of data. Well data have a high vertical resolution versus the seismic data. In deterministic methods, the scale-up of well data to larger support measurements is used. Scale-up is an averaging method, which reduces variability of measurements, when they are scaled up to larger supports. To overcome these problems, seismic data in a geostatistical framework are inverted. Geostatistical seismic inversion (GSI) is a method introduced to improve deterministic inversion results. GSI was introduced and tested by Haas et al. (Haas et al., 1994) for the first time in 1994. They employed a sequential Gaussian simulation (SGS) to produce impedance realizations in inversion process. In each grid node, a random large trace realization from seismic and log data is generated and then the best trace, which becomes data conditioning, is selected. Grijalba-Cuenca et al. offered another GSI algorithm, which worked grid by grid cell, instead of trace by trace (Grijalba-Cuenca et al., 2000). This algorithm estimated a local probability density function (PDF) from the PDF of the available control points by a kriging technique. The stratigraphic and structural information is incorporated in this method. This information is available in the form of time horizons. The final result is selected in simulated annealing method. Simulated annealing and SGS perform in an accepting or rejecting stage. Francis offered a new method of geostatistical inversion based on spectral simulation (Francis, 2005). Spectral simulation is performed in frequency domain and its main advantage is its fast run-time, due to the fact that a global density spectrum is calculated once and the inverse Fourier transform is performed only once to generate a realization (Yao et al., 2004). Recovering absolute impedance values is important when we should detect the thin bed (Zhang et al., 2012 and Merletti et al., 2003) or obtain other reservoir properties by high accuracy. In this study, at first, the deterministic inversion method is performed on a carbonate field from Iran and then a geostatistical seismic inversion based on spectral simulation (Francis, 2010 and Francis, 2005) is accomplished in this field. 2. Geological setting This paper is focused on a portion of an Iranian gas field in the Persian Gulf basin. The structure of this field is dome shaped, which has a gentle dip on the flanks. Kangan (Triassic) and upper Dalan (Permian) are two main formations in this field; each formation is divided into two different layers. From top to bottom, K1, K2, K3, and K4 are four reservoir layers in this field (Figure 1). K2 and K4 are two main gas reservoirs (Tavakoli et al., 2011). This field is a heterogeneous carbonate-evaporate reservoir in which dolomite, limestone, and anhydrite are the key lithology of the formations. The available data sets of this study belong to four wells and 3D post-stack seismic data. Well logs data consist of sonic and density logs, which are used to construct acoustic impedance log (Figure 2). Moreover, three interpreted time horizon surfaces termed Dashtak-S7, K1, and K4, are available in these data sets. H. R. Ansari et al. / Geostatistical Seismic Inversion … 3 Figure 1 Stratigraphic chart of the studied field; K1 to K4 are reservoir zones (modified from NIOC documents, 2004). 3. Data preparation The seismic d (...truncated)