Xi’an Jiaotong University 1 Quality Factor Inversion from Prestack CMP data using EPIF Matching Jing Zhao, Jinghuai Gao Institute of Wave and Information, Xi’an Jiaotong University

Xi’an Jiaotong University 2 introduction ◊ why to estimate Q? ● Lithology identification ● Inversing Q filtering to Improve the resolution of seismic imaging ● Predicting the fluid properties

Xi’an Jiaotong University 3 ◊ The developed methods ►Time domain methods ►Frequency domain methods —the logarithm spectral ratio (LSR,1981) —centroid frequency shift (CFS,1993) —peak frequency shift (PFS,2002) —Modeling method (MF,1980) —the IF matching (IFM) method(1995) ►Time-Frequency domain methods ►Inversion methods introduction

Xi’an Jiaotong University 4 ◊ Why is pre-stack CMP data? Pre-stack seismic data doesn’t process by NMO correction and the frequency information is not destroyed, so the Q estimation is available. We further developed Mathneey and Nowack’s work, and propose a method for estimating Q from pre-stack data based on envelope peak instantaneous frequency matching analysis. introduction

Xi’an Jiaotong University 5 The EPIF matching method — Instantaneous frequency (IF) matching at a wavelet envelope peak ◊ The principle In a media of horizontally layered anelastic with a frequency-independent Q, we can determine the wavefield of a source wavelet traveling through a distance by: (1) wavefield of the source signature the factor which is independent of frequency and attenuation Phase velocity Travel distance

Xi’an Jiaotong University 6 the source wavelet can be approximated by (2) The EPIF is defined as: (3) ◊ The principle ■ Pick up the EPIF (observation signals ) The EPIF matching method modulating frequency energy decay factor amplitude spectrum

Xi’an Jiaotong University 7 ◊ The principle The EPIF matching method records IF IAIF = EPIF cosine roll-off window

Xi’an Jiaotong University 8 ◊ The principle ■ Calculate the velocity The EPIF matching method In the mini-spread and little offsets case, according to the geometrical relationship shown in figure 1, the average velocity is expressed as follows: Fig. 1 Seismic wave propagation scheme (4)

Xi’an Jiaotong University 9 For zero-offset trace, the interval velocities can be approximately determined by the average velocities: (5) ◊ The principle ■ Calculate the velocity The EPIF matching method

Xi’an Jiaotong University 10 For the first event, the amplitude attenuation factor is: (6) For the multilayer model, the amplitude attenuation factor is: (7) ◊ The principle ■ Amplitude attenuation factor (Calculate the attenuated reference signals ) The EPIF matching method error accumulation effect attenuation esti- mated above the Nth layer attenuation to be estimated

Xi’an Jiaotong University 11 ◊ The principle ■ Optimization Algorithm The EPIF matching method the objective function is defined as: the EPIF of observation signal of the jth trace the EPIF of the attenuated reference signal of the same trace

Xi’an Jiaotong University 12 For an arbitrarily given initial is adjusted by the following formula for each time series variable : ◊ The principle ■ Optimization Algorithm The EPIF matching method Namely the error of the (k+1)th step is modified along the negative gradient direction of the kth step error modification.

Xi’an Jiaotong University 13 ◊ The steps of implement.Define events of pre-stack CMP data according to the correlation..Cut off the reference wavelet in each reflection interface, and then calculate the parameters of the wavelets, average velocities and interval velocities..Cut off the wavelet along all offsets of each event, and then calculate IA and IF..Pick the EPIF from IA and IF sections..Each event cycles. Matching the EPIF of the obser- vation signals of all offsets with that of the attenuated reference signals to calculate Q. The EPIF matching method

Xi’an Jiaotong University 14 ◊ Find the event positions ■ Why? When the method is tested on the real dataset, the reflectivities information picked from post-stack data or log information are not coincident with the event positions of the pre-stack CMP data. ■ How? Using the correlation between adjacent traces of the pre-stack CMP data combining with priori layers information. The EPIF matching method

Xi’an Jiaotong University 15 The EPIF matching method Having correlation Having no correlation ■ How to find the event positions?

Xi’an Jiaotong University 16 Objective function is defined as: (10) ■ How to find the event positions? The EPIF matching method the number of chosen traces event position provided by priori layer information the weight of correlation coefficient event position determined by reference trace the event position of chosen traces of near offsets except the reference trace

Xi’an Jiaotong University 17 The steps of implement : ① Chose several neighboring traces. Calculate IA and IF of these traces, then pick the EPIF whose positions may be considered to be the event positions. ② Choose the reference trace. Calculate the correlation of the EPIF positions between the reference trace and other choosing traces. ③ If the correlation coefficient is greater than the given threshold, the weight sets nonzero; otherwise, nulling. ■ How to find the event positions? The EPIF matching method

Xi’an Jiaotong University 18 The steps of implement : ④ If the nonzero number of certain position is greater than another given threshold, the position is considered to be the reference event position. ⑤ Calculate the correlation of the event positions received at the forth step and that provided by priori reflectivities knowledge. Similarly, if correlation coefficient is greater than the given threshold, the weight sets nonzero; and the weight sets zero on the contrary. Then the position with nonzero is considered to be the event position. ■ How to find the event positions? The EPIF matching method

Xi’an Jiaotong University 19 ◊ Test on the synthetic data The EPIF matching method (a) The parameters and observation system of the three-layer model (b) the synthetic seismogram

Xi’an Jiaotong University 20 ◊ Test on the synthetic data The EPIF matching method The estimated Q curve using EPIF matching analysis

Xi’an Jiaotong University 21 ◊ Test on the synthetic data The EPIF matching method (a) The parameters and observation system of the five-layer model (b) the synthetic seismogram

Xi’an Jiaotong University 22 ◊ Test on the synthetic data The EPIF matching method The estimated Q curve using EPIF matching analysis

Xi’an Jiaotong University 23 Discussion and Conclusions If we don’t know the source wavelet parameters exactly, is the traveltime difference with the reference signal. The error is increasing from 7% of the first layer to the 15% of the third layer, so the error accumulation effects greatly. If we know the source wavelet parameters exactly, is the two-way traveltime of the received signal in the jth layer. This proves that the accuracy of the Q estimating depends on the accuracy of the wavelet parameters estimating and the traveltime picking.

Xi’an Jiaotong University 24 Discussion and Conclusions In this paper, we propose a method for Q inversion from pre-stack CMP records using envelope peak instantaneous frequency matching analysis. A test using synthetic pre-stack CMP data shows that the method is more stable, more accurate while getting proper parameters, since the error of each step while iterating is the average effect of every offset.. This method has great potential for seismic attenuation estimation and gas reservoir characterization.

Xi’an Jiaotong University 25 Future work Tomography to analyse complicated construction of the earth.

Xi’an Jiaotong University 26 Acknowledgments We thank National Natural Science Foundation of China ( , ), National 863 Program (2006A09A102-11) and National Science & Technology Major Project (2008ZX , 2008ZX ) for their support.

Xi’an Jiaotong University 27 Quality Factor Inversion from Prestack CMP data using EPIF Matching Jing Zhao, Jinghuai Gao Institute of Wave and Information, Xi’an Jiaotong University