## Tau-p Transform for Noises Suppression

Presenter: Roma Widiyansari

Date: 2017/01/05

**Abstract**

There are 3 types of tau-p transforms: linear tau-p, parabolic tau-p, and hyperbolic tau-p transform. Basically radon (tau-p) transform is summing the data (t-x domain) along a certain trajectory i.e. linear, parabolic, hyperbolic) so that the original data are transformed into tau-p domain. On common midpoint point or common shot point (CSP) gathers, seismic events are likely hyperbolic than linear (reflections and diffractions are hyperbolic, refractions and direct waves are linear). The standard linear tau-p transform converts hyperbolas in the x-t domain into ellipses in the tau-p domain. This kind of transform does not really help much for suppressing noise in the form of multiples or for separating reflected P- and S-waves which also have hyperbolic trajectories in the x-t space. Therefore a hyperbolic tau-p transform which transforms the hyperbolic events on the seismic section into points is preferred to improves the resolution of the section by separating events. In particular, the multiples can be more easily isolated from the signals of interest. However, the direct hyperbolic tau-p transform is too expensive to realize because the transform is time variable (Hampson, 1986). To make the transform time-invariant, a t2-stretching (Yilmaz, 1989) or NMO correction (Hampson, 1986) is performed on the seismic data to make the events become parabolic. Then a parabolic tau-p transform is applied to the t2-stretched or NMO-corrected data set, and a better focused section can be obtained for suppressing the coherent noise. In the recent development Jiang et al. (2015) established time-domain hyperbolic radon transform with the computational cost can be kept reasonably low for practical application by applying the conjugate gradient algorithm during the inversion of hyperbolic radon transform. This method was tested with synthetic data and the feasibility also verified by a real field data example.

**Reference**

Zhou, B. and Greenhalgh, S. A., 1994, Linear and parabolic tau-p transforms revisited, GEOPHYSICS, VOL. 59, NO. 7 (JULY 1994); P. 1133-1149, 7 FIGS., 1 TABLE.

Jiang, Xiaoxue; Zheng, Fan; Jia, Haiqing; Lin, Jun; And Yang, Hongyuan, 2015, Time-domain hyperbolic Radon transform for separation of P-P and P-SV wavefields, Stud. Geophys. Geod., 60 (2016), 91-111, DOI: 10.1007/s11200-015-0735-y,Inst. Geophys. CAS, Prague