## 1 Introduction  
One critical issue in petroleum industry economics is an estimation of hydrocarbon volume. The existence of hydrocarbons is determined by the petrophysical properties of the reservoir. Petrophysical data sets are key information during the production phase and are needed for determining the recovery factor after long-term production of a reservoir. Advanced reservoir study, e.g., reservoir simulation, used petrophysical data as a basis of study [1; 2]. Such process and study need reliable petrophysical data from which the hydrocarbon reservoir will be characterized in detail. The reservoir distribution that includes the reservoir thickness, areal extent and spatial variability needs to be delineated, and the hydrocarbon volume has to be quantitatively estimated. It is important to accurately estimate the reservoir's petrophysical properties to support the reservoir characterization. The areal extent of the reservoir is determined from seismic data. A comprehensive reservoir description is achieved through the integration of the well petrophysical properties log and three-dimensional seismic data. Such integration is needed in order to understand, as much detail as possible, the deployment of the rock petrophysical parameters of the reservoir. Seismic inversion is one method to integrate the well log and seismic data. Seismic inversion aims to transform seismic data into the rock and fluid properties of the earth. Acoustic impedance inversion is the most basic seismic inversion [3]. It calculates the acoustic impedance (product of compressional velocity and density) of the earth layer from which the geological properties of the earth can be predicted. With the proper use of acoustic impedance and/or integration with other methods, acoustic impedance inversion can be conducted for advanced reservoir characterization, such as reservoir properties distribution and discrimination between lithology, porosity and fluid effects. Recently, [PERSON] et al. [4] used advanced constrained sparse spike inversion (CSSI) to identify the spatial sand ratio distribution of a tight sand gas reservoir. They successfully distinguished the tight sand from coal and mudstone facies by analyzing the acoustic impedance volume inverted by CSSI. Using further analysis, they also successfully interpreted the presence of the environment of depositional, i.e., thick fluvial braided channels and braided bars where the tight sandstone is accumulated and the inter-distributary channels where the mudstone facies are present. [PERSON] et al. [5] integrated petrophysical, geostatistical analysis and rock physics with CSSI to characterize the heterogeneity of a clastic reservoir through the inverted acoustic impedance volume analysis. They showed that the integration was able to precisely characterize the reservoir parameter within the zone of interest shown by the well delineation of the lithofacies distribution and its heterogeneity. However, [PERSON] et al. [5] suggested that to invert the acoustic impedance, density and \(\mathrm{Vp}/\mathrm{Vs}\) ratio using elastic impedance inversion, which is capable of extracting numerous petroelastic parameters that are evidently vital from stratigraphic and sedimentological perspectives. Elastic impedance (EI) inversion aims to invert not only acoustic but also elastic characteristics of the earth layer. Different from acoustic impedance inversion, which uses single reflection (normal or zero angle incidence reflection), elastic impedance inversion uses either normal (zero angle incidence) or non-normal (non-zero angle incidence) reflection seismic data to characterize the earth layer geology. EI inversion showed that the zero angle incidences seismic signature respond the acoustic properties and the non-zero angle incidences signature respond the elastic properties from where the earth lithology and fluid information can be characterized. There are two ways to collect or gather the non-zero angle incidence seismic data from those that are common azimuth and variable azimuth.