states (quartz and duralumin) under confining pressure of 20MPa has been performed using

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1 Effects of Strain Amlitude on Relaxation Sectra of Wave Attenuation in Rock E. I. Mashinskii Institute of Petroleum Geology and Geohysics, Siberian Branch of the RAS, ros. Akad. Kotyuga 3, Novosibirsk, , Russia Abstract The laboratory study of wave attenuation in sandstone and the atomic elastic solid states (quartz and duralumin) under confining ressure of 20MPa has been erformed using the reflection method on ulse frequency of 1 MHz. This study resents the develoment of researches conducted in works [(1-3, 5, 7-9]. The exeriments have shown the unusual results in the behavior of the relaxation sectra of attenuation in deendence on strain amlitude. The atomic elastic solid states have been used as suosed standards for comarison with rock. The relaxation strength of attenuation in rock and standards is nonlinearly deendent on the frequency and strain amlitude in the range ~ ( ) Influence of changing amlitude on value of the relaxation strength for all materials is identical. With increasing strain amlitude, the value of the relaxation strength (and attenuation on the incident frequency) always decreases. Figure 1 shows the deendence of comeressional and shear wave attenuation on strain amlitude on six amlitude values. Attenuation is inversely to the strain amlitude: 1/Q ~ 1/ε o, where ε o is strain amlitude. Background of such behavior of attenuation was made in works studying the deendence of wave velocity on strain amlitude and the amlitude-deendent stress-strain relations [4, 6]. Simultaneously the relaxation curve descends endwise attenuation axis to a smaller value. At the same time with amlitude change, some transformations in the character of relaxation sectrum Q 1 ( f ) occur. On the ( ) ( ) 1 constant amlitude, Q f of sandstone, Q 1 f and Q 1 ( f ) of quartz are resented in the s form of the relaxation eak. As distinct from them in duralumin, Q 1 ( f ) resents the monotonically descending (negative-going) curve without a relaxation eak, but Q 1 ( f) s has the imlicit attenuation eak. The increasing or decreasing of amlitude leads to the

2 dislacement of the eak frequency along frequency axis. Direction of frequency shift deends from location of the incident frequency f incident with resect to the eak frequency f eak. When f incident is located on the low-frequency side of the eak then the dislacement of eak goes to high frequencies, and when f incident is located on the high-frequency side, the dislacement goes to low frequencies. With increasing amlitude, f eak of P- wave in sandstone shifts towards the higher frequencies, Figure 2. In quartz, the shift of f eak on P- wave is absent, but on S- wave the shift occurs towards the lower frequencies, Figure 3. In duralumin, the shift of the eak frequency in S- wave is the same as in quartz. Moreover, the eak is very asymmetric with a tendency to formation of the following eak. With increasing amlitude the symmetry of relaxation curve is imroves. The amlitude-deendent behavior of relaxation sectra of attenuation is exlained by feature of the joint action of viscoelastic and microlastic mechanisms. The exeriments have shown that the so-called atomic elastic standard is not the standard in reality as the micro-imerfectness is the significant reason in attenuation. These results can be used as fundamental singularity for imroving methods of geological interretation of seismic data. Key words: inelasticity, nonlinear stress-strain relation, hysteresis, inelastic seismic arameters, relaxation sectrum, amlitude deendence of wave velocity and attenuation References 1. Dvorkin J, Walls J, Taner T, Derzhi N and Mavko G 2003 Attenuation at Patchy Saturation A Model EAGE 65 th Conference & Exibition Stavanger, Norway, 2 5 June Jackson I, Fitz Gerald J D, Faul U H and Tan B H 2002 Grain-size sensitive seismic wave attenuation in olycrystalline olivine J. Geohys. Res. 107 B Klimentos T 1995 Attenuation of P- and S-waves as a method of distinguishing gas and condensate from oil and water Geohysics Mashinskii E I 2004 The variants of the strain-amlitude deendence of elastic wave velocities in the rocks under ressure J. Geohys. Eng

3 5. Mashinskii E I 2005a Exerimental study of the amlitude effect on wave velocity and attenuation in consolidated rocks under confining ressure J. Geohys. Eng Mashinskii E I 2005b Non-linear stress-strain relation in sedimentary rocks and its effect on seismic wave velocity Geohysica Mavko G M 1979 Friction Attenuation: An Inherent Amlitude Deendence J. Geohys. Res Mavko G M, Mukerji T and Dvorkin J 1998 Rock Physics Handbook, Cambridge University ress. 9. Mavko G and Dvorkin J 2005 P- wave Attenuation in reservoir and non-reservoir rock EAGE 67 th Conference & Exibition Madrid, Sain, June Figure 1. Comressional and Shear wave Attenuation as function of Strain Amlitude 0,09 0,07 1/Q and 1/Q s 0,05 0,03 sandstone-p quartz-p quartz-s duralumin-p duralumin-s 0,01 0 0,5 1 1,5 2 2,5 Amlitude (microstrain)

4 Figure 2. Comressional-wave attenuation as a function of frequency in sandstone Comressional-wave Attenuation (1/Q ) 0,12 0,11 0,1 0,09 f eak (A 1 ) shift f eak (A 6 ) Amlitude2 f min (A 1 ) shift f min (A 6 ) f incident 0,08 Figure 3. Shear-wave attenuation as a function of frequency in quartz Shear-wave Attenuation (1/Q s ) 0,08 0,06 0,04 f incident f eak (A 3 -A 6 ) f eak (A 1,2 ) shift of eak frequency Amlitude2 0,02

5 Figure 4. Shear-wave attenuation as a function of frequency in duralumin Shear-wave Attenuation (1/Q s ) 0,021 0,02 0,019 0,018 0,017 shift of eak frequency f eak (A 6 ) f eak (A 1 ) f incident Amlitude2 0,016