Seismic-Derived Rock True Resistivity (R) Revisited. Part I: Reformulation Of Combined Gassmann – Shaly Sand Models

The last decade has observed frantic efforts by geoscientists to extract as much information as possible from seismic data. From the traditional role of establishing subsurface structural geometry, seismic processing and interpretations have evolved into an ever increasing role in providing rock physical properties such as acoustic impedance (AI) and porosity (0). The more common use of 3-D seismic surveys, in both exploration and development stages, have fur- ther underlined the role of seismic data as provider of inter-well rock property data. Further developments in the petrophysics-related seismic interpretation have also shown efforts to ex- tract information related to contents of formation rocks. From the widely acknowledged brightspot analysis for detecting presence of gas-bearing porous rocks in the last decades of the 20 century to the later efforts to extract information regarding fluid saturation in reservoir. Actually, as early as in mid- 1960s have scientists started to investigate the relations between acoustic signals and fluid saturation (e.g King, 1966; Domenico, 1976; Gregory, 1976). However, due to the fact that the then commonly used of 2-D seismic was considered as having insuf- ficient resolution for any practical uses in the field, the efforts remained mainly for academic purposes only. Rapid developments in technology of 3-D seis- mic survey and processing, as well as its more com- mon use at present have prompted attentions back to the investigations aimed at extracting fluid saturation information from seismie data. In 1990s have Widarsono and Saptono (1997) started a series of investigation through laboratory measurements and modeling using core samples. This was followed by more works not only at laboratory level but at larger levels of well and field scales (e.g. Widarsono Saptono, 2000a, 2000b, and 2001; and Widarsono et al, 2002a, 2000b). Other investigators (e.g. Furre Brevik, 2000; Wu, 2000; Zhu et al, 2000; and more recently Wu et al, 2005) have also devoted some works to achieving the same goal. Other paths of development have incorporated other supporting tech- niques such as non-linear regression (e.g.Balch et al, 1998) and artificial neural network (e.g. Poupon Ingram, 1999; Oldenziel et al, 2000).From various investigations using seismic waves as the sole data for fluid saturation extraction, short- comings were soon felt in the form of 'narrow bands' of acoustic signals (ie P-wave velocity, V, and acoustic impedance, AI) that are influenced by varia- tions in fluid saturation. In other words, V, and AI are not too influenced by variation in fluid saturation. This reduces the effectiveness of seismic-derived V and Al as fluid saturation indicators. Efforts were then devoted to link V, and AI to other parameters such as rock true resistivity (R), a parameter known to be very sensitive to variation in fluid saturation. Widarsono and Saptono (2003, 2004) provide laboratory verifications and first field trial with some degree of succes. However, certain assump- tions (i.e. constant/uniform porosity) in the theoreti- cal formulation were still adopted in the above works, which in turn reduced the validity of the resulting formula produced and used. In this paper, the first part of a three-part work, is devoted to reformulating the combination of Gassmann theory and shaly sand water saturation models of Poupon and Hossin. These are to replace the shale-free Archie model used in the above works, which is considered as invalid for most field uses. With this reformulation, it is hoped that a more robust model/formula of resistivity as a function of acoustic impedance (R, = fAI)) is achieved, hence a more reliable resistivity could be extracted from seismic- derived acoustic impedance. Summarily, the objectives of the works a part of them presented in this paper are - To establish a model/method to obtain formation rock true resistivity (R) from seismic-derived acoustic impedance (AI), and To provide correction/modification onto previous works reported in Widarsono Saptono (2003, 2004).