Seabed loging data curve fitting using cubic splines

Abstract

Deep water and deep target environment for Seabed Loging (SBL) has been a challenge, and the better delineation method is needed. This paper describes the curve fitting methods namely smoothing spline and piecewise cubic Hermite interpolating polynomial (PCHIP) to give better delineation. In this work we simulated five geophysical layers namely air (500m), sea water (2000m), over burden (1000m), hydrocarbon (100m) and under burden (1000m) respectively. Target depth was increased gradually by 500m from 1000m to 3000m at constant frequency of 0.125Hz and 1250A current. Due to the weak electromagnetic signal from deep target of SBL we had chosen curve fitting methods to describe hydrocarbon reservoir. The results show that smoothing spline is quantified as compare to the PCHIP due to the existence of various noises in the SBL data. Several numerical results will be presented.

Cubic spline interpolation for petroleum engineering data

“…Data fitting, data approximation and data interpolation are important in visualization of the data that may be obtained from numerical experiment or data collection from well drilling, petroleum etc. Karim and Yahya [1] has discussed in details the used of cubic spline smoothing for oil and gas data interpretation. The Seabed Loging Data (SBL) is used for their purposed.…”

“…One of the main reasons why cubic spline is the most utilizing basis function for data interpolation is that it is the lower degree splines that can achieve the 2 C continuity [2 -9]. Besides the used of cubic spline interpolation there exist another cubic spline called as PCHIP but is only has 1 C continuity and usually data that being interpolated by PCHIP is overshoot at certain interval [2,8,9]. This unwanted overshoot is not visual pleasing and may remove the important characteristics of the data.…”

“…This paper is continuation from the work of Karim and Yahya [1]. The main different is that in this paper both cubic splines interpolation and PCHIP will be used to interpolate the given data sets, meanwhile in [1] the cubic smoothing spline and PCHIP are used for SBL data fitting (smoothing) and data interpolation. Furthermore an error analysis for data interpolation by using cubic spline interpolation and PCHIP also will be discussed in details.…”