Estimation of Q curve by the constrained spectrum ratio matrix method Zhen Cui 1, 2* , Siyuan Cao 1, 2 , Wei Liu 1, 2 , Yuanyuan Ma 1,2 , Jianhong Zhang 1,2 , 1 State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, China 2 CNPC Key Laboratory of Geophysical Prospecting, China University of Petroleum, Beijing, China Summary Quality factor Q is the parameter that describes the characteristic of the wave attenuation in the subsurface media and it has important applications in reservoir prediction and description. The fitting K-Δt method can obtain the equivalent single layer Q. But it doesn't work in the multilayer Q curve estimation because the estimation of Q from the deep formation by the fitting method contains shallow Q information. We establish an optimization problem between the time difference and the spectrum ratio to estimate the quality factor Q curve. In this method the control parameter  and the prior information  ref are introduced to constrain the solution of the optimization. The tests show that estimation of Q curve by the constrained spectrum ratio matrix method is reasonable and reliable. Introduction The energy attenuation will occur when the seismic waves propagate through the subsurface medium. Non-intrinsic attenuation and intrinsic attenuation are two kinds of attenuation factors. Non-intrinsic attenuation is independent of frequency including reflection and transmission losses, inter particle scattering and spherical divergence etc. The intrinsic attenuation is frequency-dependent. The higher the frequency is, the more serious the absorption is. Meanwhile, the phase of the seismic wavelet changes due to the velocity dispersion. The intrinsic attenuation causes the dominant frequency of seismic wave decreasing and the bandwidth narrowing. Quality factor Q is the key parameter that represents the absorption and attenuation of medium. The smaller the Q is, the stronger the attenuation is. The previous studies have shown that the Q is related with the petro physical properties, porosity, fluid type and fluid saturation. Therefore, Q can be used to reservoir prediction. When the stratum contains gas, the Q will become smaller and the obvious abnormal phenomenon will occur. Moreover, inverse Q compensation with the subsurface Q field is an effective means of improving data resolution. Thus, the accurate estimating of Q is important to high precision interpretation, reservoir prediction and reservoir description. The conventional estimation methods of quality factor Q can be divided into two categories: time domain and frequency domain. The most famous method (Ward R W, 1979) is logarithmic spectrum ratio method which utilizes the relationship between the frequency ratio and Q to estimate Q. the characteristics of this approach is that stable frequency has a higher Q precision. Subsequently, the scholars proposed centroid frequency shift method(Quan Y and Harris J M,1997), peak frequency shift method(Zhang C and Ulrych T J,2002) and spectrum attributes method (Cao,2012) etc. All those methods improve Q accuracy by extracting more accurate change of frequency or amplitude during propagating. In recent years, because the microlog has better stimulate coupling and higher SNR, it is widely used for near surface Q and other parameters estimation. The conventional method is to estimate equivalent Q by different depth spectrum ratio fitting (or other parameter differences). The multilayer Q curve is obtained using the relation between equivalent Q and multilayer. The shortcoming of this method is that the estimation of Q from the deep layer contains shallow Q information which causes the inaccuracy of deep Q estimation. The spectrum ratio matrix method In the microlog data, the SNR of the far offset traces is low and the energy among shot gathers is inconformity. So we apply the frequency ratio between two common receiver gathers to estimate Q. However, the distance between receivers will influence the wave travelling path and result in the frequency ratio in the deep containing the shallow area information. Concerning this issue, we use the matrix solution to obtain the Q curve. (a) (b) (c)