The Saturation Estimation Of Gas Hydrate Based On Radial Basis Function Interpolation

Gas hydrate is an ice-like solid composed of water and natural gas. It is one of themost promising potential energy sources in the21century and beyond. Drillingexploration for gas hydrate in the Shenhu area was successfully completed byGuangzhou Marine Geological Survey in2007. It is important to be able to estimategas hydrate saturation based on available data for computing the reserves. We oftenuse chloride concentration of pore water, electrical resistivity, and P-wave velocity ofthe formation to estimate gas hydrate saturations. These methods play an importantrole in gas hydrate exploration. However, they also have shortcomings.This paper introduces a new method, Radial Basis Function (RBF) interpolation,which is used to estimate the hydrate saturation in the Shenhu area. Different from thetraditional methods, this approach is model-independent and only requires a database.The database is used to form a non-linear mapping function between the input and theoutput. Such a mapping function is then used for predicting the output when input isknown. This method has been developed by applied mathematicians forapproximating smooth and continuous multivariate functions over the past30years. Ithas been shown that RBF interpolation can solve geophysical problems wherephysical quantities are closely related but without explicit mathematical correlation.P-wave velocity comparatively increases in a layer when gas hydrate exists. Thisphenomenon is marked in Shenhu area.We define the velocity increment as theamount of actual velocity deviated from background velocity. Then we establish theRBF non-linear mapping function between P-wave velocity increment and gashydrate saturation. Finally we can predict the gas hydrate saturation through the RBFinterpolation method. The test results of this approach on the well SH2and well SH7in the Shenhu area are quite satisfying. The RBF interpolation method is a fast andefficient way for gas hydrate saturation prediction and allows us to bypasscomplicated physical models building and obtain a reasonable result. This method canbe applied to a large prospect where the P-wave velocity data are available fromseismic inversion.The width is an important parameter in the Gaussian RBFs which has a great effect on the result. For accurate approximations, the width should be of the order ofthe Euclidian nearest-neighbor distances in the input space. It also can be chosen to beproportional to the Euclidian NN distances. This paper analyzes the factors thatinfluence the interpolation results, including the radial basis function interpolationalgorithm, input quantities, database establishment, sample pretreatment andmulti-dimensional input. In practical application, to apply the RBF interpolationeffectively, these points are important. This method can be used to solve a broad rangeof estimation problems encountered in geophysics.