Joint Interpretation of Body and Surface Waves Data for a District in Middle Asia

Transcription

1 Geophys. J. R. Soc. (1966) 11, Joint Interpretation of Body and Surface Waves Data for a District in Middle Asia A. L. Levshin, T. M. Sabitova and V. P. Valus Summary An ambiguity in the solution of the inverse problem in seismology can be reduced by a joint interpretation of several types of data, particularly on body and surface waves. A numerical example of such an inversion carried out by use of a computer is given. This example deals with a velocity distribution in the crust between Dushanbe and Andizhan (Middle Asia). Travel times of P and S waves for epicentral distances 5&350 km and phase velocities of the fundamental Rayleigh mode in the range of periods 12-36s are used. Two types of parametrization which correspond to the crust with or without a velocity discontinuity at the interface were investigated. The Monte Carlo method was used to obtain individual velocity distributions for parameters within prescribed bounds. Theoretical travel times and phase velocities were computed for each distribution and compared with observed data. A set of velocity distributions was found corresponding to the observed data. This set is essentially narrow as compared with the original distributions. In particular a narrow range of average velocities is obtained. However, a significant ambiguity in many. important parameters (e.g. crust thickness) remains after the discussed procedure. 1. Introduction The ambiguity of numerical inversion for any seismological data is one of the main difficulties in determining the Earth s crust and upper mantle structure. There are many velocity distributions (referred to as 0.d.) essentially different from geologist s and geophysicist s point of view but fitting within limits of standard errors the same observat ional data. As it was shown in (1,2,4,9) there is a possibility of reducing the ambiguity combining several types of data (such as travel times, amplitudes, dispersion curves) in the process of interpretation. This paper presents a numerical example of such interpretation carried out by use of a computer. The travel times of P and S waves for epicentral distances up to 350 km and Rayleigh wave phase velocities for periods to 36s were used to tind a velocity distribution in the crust between Dushanbe a nd Andijan (in the Middle Asia). Two types of a parametrization with (or without) a velocity discontinuity inside the crust were tested. The Monte Carlo method was used to find the sets of velocity distributions fitting observational data within prescribed bounds for parameters. The obtained sets are essentially narrow as compared with original ones. In particular, they have 57

2 58 A. L. Levshin, T. M. Sabitova and V. P. Valus a short range of average velocities. However the signi ticant ambiguity still presents in many important parameters. 2. Observational data Travel time curves for this district are available thanks to the seismological expedition of the Institute of Physics of the Earth (6,7,8). We used P and S wave travel times from (7) only for epicentrical distances 5CL350 km with standard errors equal to 1 s for P waves and f 2 s for S waves. Phase velocities of Rayleigh mode in the range of periods 12-36s were determined by phase correlation method (3) from seismograms of Karnchatka and Kuril islands shocks obtained in Duschanbe and Andijan with Kirnos vertical seismometers. The standard error was estimated as f0.05 km/s. The data on travel times and phase velocities are given in Tables 1 and 2. Table 1 Travel times of body waves 4km) t,(s) tsb) Table 2 Phase velocities of Rayleigh waves T(s) UR,(km/s) Parametrization Two types of a parametrization, I and 11, for a velocity distribution in crust were chosen. The parametrization was based on general properties of observational data and some geophysical hypotheses on the crustal structure in mountain regions. The principles of choice of parametrization are discussed in (1). Both types correspond to crust formed by two inhomogeneous layers with constant but different

3 Joint interpretation of body and surface waves data for a district in Middle Asia 59 velocity gradients, overlaying the mantle with small positive gradients of longitudinal and shear velocities. There is a thin sedimental layer in the upper part of a crust. The main difference between two types of the parametrization is in the condition at the interface of crustal layers. The first parametrization allows only a discontinuity of velocity gradients. The second one permits the positive jump in velocities as well as a discontinuity in gradients. The minor differences relates to longitudinal and shear velocity ratio, density distribution and existence of a zone of negative velocity gradients. Bounds of possible values of parameters as velocities, densities and depths of boundaries are presented in Tables 3 and 4 and shown on Figs. 1-3 by dash lines. The parameters of the sedimental layer and mantle are fixed. As we use narrow ranges of periods and epicentral distances, the inaccuracy in data on these parts of a o.d. can not lead to essential errors in determination of crustal structure. For Z, = Z,+O, Z2, Z3-0; Table 3 Parametrization I 1.65h(Z,) < u(z,) < 1.85h(Z,) Depth Longitudinal velocity Shear velocity z (km) a (kmis) b (km/s) Z, = 0 u(z0) = 4.0 b(2,) = 2.0 Z1 = 3 u(zi-0) = 5.0 b(z1-0) = < u(z, +0) < < b(z, +0) < < Z, < < u(zj < < b(z2) < < Z3 < < u(z~-0) < < b(z3-0) < 4.25 U(Z3+0) = 8.1 b(z3 +0) = 4.6 Z, = 370 u(z,) = 9.0 b(z4) = 4.95 Density Layer P (s/cm3) p(z0) = 2.1 Sediments p(z1-0) == 2.3 p(zl+o) = 2.65 Crust 1 p(zz) = 2.65 p(z3-0) = 2.85 Crust 2 p(z,+o) = 3.35 Mantle p(z,) = 3.85 Let us note the bounds of the most important parameters in domains I and 11, as determined by Tables 3, 4*. A total thickness of the crust may vary from 40 to 70 km, a thickness of the first consolidated layer, from 7 to 22 (27) km. A shear velocity at the top of this layer may vary from 3 to 3.4 (3.5) km/s. A shear velocity at the bottom of the crust may change from 3.7 (3.5) to 4.25 km/s. On the whole it is quite evident that each domain includes the set of velocity distributions which differ significantly from geologist s and geophysicist s point of view. 4. Procedure of inversion The inversion procedure is the following : 4.1. Individual ~.d.s are chosen by turn within domain I or I1 by the Monte Carlo. method The corresponding theoretical curves, tp(a), ts(a) and uri(t) are computed for the chosen distribution The deviation of computed curves from observational ones are determined. $Ve use the mean square deviation 0; and the modulus of the maximum deviation * The values for the piiriitnc~i-i~ii~ion II ai-c presentcd in brackets when direrent fro m I.

4 Layer 9 5' -1 Sediments s Crust 2 to a < a Mantle 2 E Table 4 Parametrization II For Z, = Z,+O, ZZ-Q Z,+O, Z3-0; 1.7b(Z,) < n(z,) < I%b(Z,) Depth Longitudinal velocity z (km) a (km/s) zo = 0 a(z,) = 4 z, = 3 a(z,-o) = 5 5 < a(z,+0) < 6 10 < Z2 < 30 u(z, +0) < u(z, -0) < < a(zz-0) 6 < a(z,+o) < 7 a(z, + 0) < a(z, -0) < a(z, + 0) < Z3 < 70 6 < a(z3-0) a(z3 +O) = 8.1 Z4 = 370 a(z4) = 9 Downloaded from at Pennsylvania State University on Se Shear velocity Density b ( Ws) P (g/cm3) b(2,) = 2 p(z,) = 2.2 b(2,-0) = 3 p(2,-0) = < b(z,+o) < 3.5 b(z,+o) < b(z2-0) < , < b(z2-0) 3.5 < b(z2+0) < 3.85 p(zi) = a(Z,) b(z2+0)-0.1 < b(z3-0) < b(z2+0) < b(z3-0) b(2, +0) = 4.6 p(z3+0) = 3.35 b(2,) = 4.95 p(z4) = 3.85

5 I.? (kml FIG. 1. The results of the model test for parametrization 11. The outer dash lines show the bounds of possible values of shear and longitudinal velocities in the crust. The thick line represents the u.d. A. The other inner lines are the selected 0.d.s fitting to all observational data. The hatching shows the zone of c.d.s fitting to body wave data only. Downloaded from at Pennsylvania State University on Se

6 - / I '\J 4 \ / I I I /-- E x d -r;; ru

7 Joint interpretation of body and surface waves data for a district in Middle Asia 63 FIG. 3. The results of inversion of observational data for parametrization 11. The designations are the same as in Fig. 1.

8 64 A. L. Levshin, T. M. Sabitova and V. P. Valus Dj both normalized by standard errors, as measures of deviation for the curve with index j(j = t,, t,, vr,) The values of oj and Dj for each v.d. are compared with prescribed limits 5; and Dj. If ~j < 6; and Dj < Dj for all j, this distribution would be considered as a possible solution of the inversion problem and printed with all deviations. If at least one of the conditions for any j is not satisfied this u.d. will be excluded. We use the same values 6; and Dj, namely 1.5 and 2.0, for all j. They correspond to the following maximum individual deviations: < 2 s, < 4 s, 16u,,l < 0.10 km/s. The maximum average deviations determined by 5; are approximately 1.5 times less than maximum individual ones The described process must prolong until the domain of possible parameters will be completed. It needs of course rather a great amount of sampling. Then all possible essentially different solutions will be presented among printed u.d.-s. To realize such, and similar, procedures by a computer a special compiler programme was written by one of authors (V. P. Valus, unpublished). It includes as subroutines the programmes of Yanovskaya & Asbel for travel times and amplitudes (9) and Neigaus, Andrianova & Shkadinskaya for dispersion curves (2,5). This compiler programme permits an inversion of an arbitrary set of observatioiidl data on travel times and amplitudes of body waves and dispersion curves of surface waves. Various criteria to estimate the velocity or density distributions may be used. 5. Model test To estimate the abilities of described procedure a model test was carried out. The velocity distribution A, was chosen in the central part of the domain 11. The travel times tp(a), t,(a) and phase velocities u,,(t) were computed for A exactly for the same A and T as in observations. In addition the fundamental Love mode phase velocities were computed for the range of periods s. All these computed data were further supposed to be observational with the same standard errors prescribed as real ones. The values of 5; and Dj were chosen to be even less than for real data inversion, namely 1.2 and 1.5 for any j. 6. Discussion and conclusion The information about a number of tested and selected u.d.s is given in Table 5. The results of the model tests are shown in Fig. 1. The u.d.s corresponding to real data for parametrization I and I1 are shown in Figs. 2 and 3 respectively. Table 5 Stutistics of tests Number of Number of v.d. Number of v.d. Parametrization tests fitted to body fitted to all wave data data I, experimental data , experimental data t, model test The following conclusions may be derived from analysis of obtained sets of distributions : 6.1. The applied method converges since there are several velocity-depth curves in Fig. 1 which differ insignificantly from A.

9 Joint interpretation of body and surface waves data for a district in Middle Asia The v.d.s fitting only body wave data cover in domain I and I1 more area than ones fitting all data. Therefore it is possible to reduce the ambiguity using different types of data There is more information about crustal structure in obtained sets than in original ones, as determined by Tables 3 and 4. For exampie the range of the possible crustal thickness becomes narrow-namely 4-60 km instead of km in the beginning. The average velocities for selected distributions are within narrow bounds, km/s for shear velocity. The shear velocities at the depth from km to km are essentially less than maximum possible ones in domains I and 11. The difference equals approximately to km/s The set of used observational data is still not sufficient to obtain the unique solution. Indeed, there are the v.d.s in Fig. 1, whose important parameters, as a crustal thickness, a jump of velocity at the boundary inside crust, are essentially different from A. The similar ambiguity still presents after inversion of real data. In particular, it is impossible to choose a type of parametrization to fit observations the best, i.e. to include or exclude existence of a sharp velocity discontinuity inside the crust. It is only possible to obtain a very rough estimation for the crustal thickness, i.e km The reasonable increasing of the observational accuracy does not reduce the ambiguity significantly. Thus further investigations in this field must be devoted to a treatment of additional information which could reduce the obtained set of solutions (such information ;IS amplitudes, later phases of body waves, higher modes of surface waves). Soviet Geophysical Committee, Moscow June. References 1. Azbel, I. J., Keilis-Borok, V. I. & Yanovskaya, T. B., A technique of a joint interpretation of travel-time and amplitude-distance curves in the upper mantle studies, Paper presented at the Second Symposium on Theory and Computers, Rehovot, Grophys. J. R. astr. Soc., 31, Andrianova, Z. S., Keilis-Borok, V. I., Levshin, A. L. & Neigauz, M. G., Love surface waves (in Russian). Izd. Nauka, Moscow. 3. Brune, J., Nafe, J. & Oliver, J., A simplified method for the analysis and synthesis of dispersed wave train, J. geophys. Rex, 65, Ivanova, Z. S., Keilis-Borok, V. I., Levshin, A. L. & Neigauz, M. G., Love waves and the structure of the upper mantle, Geophys. J. R. astr. Soc., 9, Keilis-Borok, V. I., Neigauz, M. G. & Shkadinskaya, G. V., Application of the theory of eigenfunctions to the calculations of surface wave velocities, Rev. Geophys., 3, Nersessov, I. L. & Rautian, T. G., Cinematics and dynamics of seismic waves for epicentral distances up to 3500 km (in Russian), Proceedings of Institute of Physics of the Earth, No. 32, p Riznichenko, Ju. V. (ed;), The methods of detailed study of seismicity (in Russian), Proceedings of Institute of Physics of the Earth, No. 9, p. 176.

10 66 A. L. Levshin, T. M. Sabitova and V. P. Valus 8. Ulomov, V. I., Results of seismological studies of crustal structure in Middle Asia (in Russian), Izr. Akud. Nauk SSSR Ser. geophys., No Yanovskaya, T. B., The determination of the velocity distribution in the upper mantle by travel time curve as inverse mathematical problem (in Russian), Izv. Akad. Nauk SSSR Ser. geophys., No. 8.