Extracting dispersion curve and filtering of acoustic data with wavelet transform

Overview & Synopsis

Dispersion curves of acoustic data carry important information about the acoustic state of the rock. By dispersion curves, we refer to the group and phase slowness (reciprocal of velocity) as a function of frequency. Because such information is critical to quantitatively understand the formation properties of rocks there is a need for robust and automatic method for extracting dispersion curves from acoustic waves received by an array of receivers to characterize the properties of the rocks surrounding a borehole. In this paper we propose an approach to automatically extract the slowness dispersion of acoustic waves received by an array of receivers. The method has been developed in order to achieve the dispersion extraction without the use of any physical model, but rather exploiting the time frequency localization of the propagating mode and the continuity of the dispersion curve as a function of frequency. After the dispersion curve extraction is performed, properties of the continuous wavelet transform allow the reconstruction of the mode corresponding to the extracted dispersion curve. This approach can then be done iteratively to extract various modes propagating across a receiver array. Examples on synthetic and real data will be presented to illustrate this methodology.