11 Inversion of Surface Waves: AReview Barbara Romanowicz University of California, Berkeley,California, USA 1996/07/11 21:46:39.7 h = 15.0 km ∆ =109.7° = 32.3° 1. Introduction Station: CMB Burma–China Border Region M = 6.8 Channel: LHZ W In what follows, we attempt to review progress made in the last R1 R few decades in the analysis of teleseismic and regional surface 1 wave data for the retrieval of earthquake source parameters and global and regional Earth structure. This review is by no means R2 exhaustive. We will rapidly skip over the early developments of R2 R3 R the 1950s and 1960s that led the foundations of normal mode 4 R R 5 6 R7 R8 and surface wave theory as it is used today. We will not attempt to provide an exhaustive review of the vast literature on surface wave measurements and the resulting models, but rather focus on describing key theoretical developments that are relevant and have been applied to inversion. Since surface wave theory is closely related to that of the Earth's normal modes, we will discuss the latter when appropriate. However, we make no attempt to extensively review normal mode theory, as this 02468101214 Time (h) subject is addressed in a separate contribution (see Chapter 10 by Lognonne and CleÂveÂdeÂ). FIGURE 1 Example of vertical component record showing many Earth-circling mantle Rayleigh wave trains over a time window of 14 h. This record was recorded at station CMB of the Berkeley 2. Background Digital Seismic Network (BDSN) and corresponds to a channel with a sampling rate of 1 sample/sec. The earthquake is shallow and the Most of the long-period energy (periods greater than 20 s) epicentral distance Á 109.7 . Because the distance is close to 90 generated by earthquakes and recorded at teleseismic distances the wave packets corresponding to even and odd order trains are well separated from each other. (Courtesy of Joseph Durek and Lind Gee.) propagates as surface waves. Most clearly visible on long- period seismograms are the successive, Earth-circling, dis- persed wave trains of the fundamental mode. For moderate size produce a spectrum of the Earth's free oscillations by Fourier earthquakes recorded at teleseismic distances (M 5.5), only analysis of long time-series. the surface waves propagating along the direct great circle path Most studied are fundamental mode Rayleigh waves, which between the epicenter and the station have signi®cant signal-to- correspond to P±SV energy and have elliptical particle motions noise ratio, mostly between 20 and 100 s period, and the dis- in the vertical plane containing the direction of propagation. persive and attenuative properties of these wave trains have These waves are well recorded on the quieter vertical com- been used extensively, since the 1950s to infer crust and upper ponent seismographs (Fig. 2). On the other hand, Love waves, mantle structure in different regions of the Earth. For earth- which carry SH energy, and are polarized horizontally in a quakes of magnitude 7 or larger, successive Earth-circling direction perpendicular to the direction of propagation, require surface wave trains can be followed for many hours (Fig. 1), rotating the two horizontal records to extract the transverse and are then either analyzed individually or combined to component of motion. Love wave studies have suffered, INTERNATIONAL HANDBOOKOFEARTHQUAKE AND ENGINEERING SEISMOLOGY,VOLUME 81A ISBN: 0-12-440652-1 Copyright # 2002 by the Int'l Assoc. Seismol. & Phys. Earth's Interior Committee on Education. All rights of reproduction in any form reserved. 149 150 Romanowicz Station: CMB 1996/07/12 15:46:59.8 h =15.0 km ∆ = 88.7° = 47.4° 1/23/1997 Southern Bolivia SUR Comp L Dist 8419 km Mb 6.4 MW 7.1 dep 276 km Loyalty Islands Region MW = 6.4 Surface wave Vertical harmonics R1 arrival S Rayleigh Longitudinal P arrival P Love Transverse 0 102030405060 500 1000 1500 2000 2500 3000 3500 Time (min) Time (sec) FIGURE 2 Three-component seismograms observed at station FIGURE 3 Example of longitudinal component seismogram CMB for a shallow earthquake at a distance of Á 88.7. The hor- recorded at IRIS/GSN station SUR showing the arrivals of multiply izontal components have been rotated to the longitudinal and trans- re¯ected body wave phases forming a higher-mode Rayleigh wave verse directions, clearly exhibiting fundamental mode Love and train in front of the fundamental mode (R1). The Airy phase, corre- Rayleigh waves on the transverse and vertical/longitudinal compo- sponding to the group velocity minimum around 230 sec, is well nents, respectively. (Courtesy of Joseph Durek and Lind Gee.) visible in the R1 train. The event occurred on 14 Jan. 1997 in southern Bolivia, at a depth of 276 km. The epicentral distance is 8419km. The especially in the early days of analog recordings, from the seismogram has been bandpass ®ltered with cut-off frequencies at more complex data processing required, and from the higher 35 and 400 sec. (Courtesy of Yuancheng Gung.) levels of background noise on horizontal components at long periods, due primarily to the in¯uence of atmospheric pres- 1959; Ben-Menahem, 1961; Kanamori, 1970). At that time, sure variations, inducing ground tilts. Fundamental mode the theoretical formulation for the excitation of surface Love and Rayleigh waves are generally well separated from waves and normal modes of the Earth was developed (Sato other phases on the seismograms, and well excited by shallow, et al., 1962; Harkrider, 1964; Haskell, 1964), much stimulated crustal earthquakes, while overtones travel at higher group by the occurrence of the great Chilean earthquake of 22 May velocities, appear as packets of mixed overtones (e.g., X 1960, and more quantitative studies of the effects of the phases, Jobert et al., 1977), and are better excited by deeper earthquake source on spectra of surface waves followed. earthquakes (Fig. 3). The association of a normal mode formalism (e.g., Gilbert, Surface waves recorded at teleseismic distances contain 1971) to compute dispersion and excitation of surface waves information about both the characteristics of the earthquake (and complete seismograms) with a moment tensor formal- source and the structure of the Earth along the source station ism to describe the earthquake source (e.g., Backus and path. Separating these two effects has been one of the long- Mulcahy, 1976; Mendiguren, 1977) has led to the present- standing challenges faced by seismologists. day commonly used expressions and to a rapid develop- Studies of the structure of the crust and upper mantle pro- ment of source studies based on surface waves in the 1980s. gressed rapidly in the 1950s and early 1960s, as the tools to A computational method (Takeuchi and Saito, 1972), follow- measure group and phase velocities, and interpret them in ing the theoretical approach of Saito (1967) based on Runge± terms of layered mantle and crust models, became readily Kutta matrix integration, has long been the main reference available (e.g., Ewing et al., 1957; Brune et al., 1961a,b; for the practical calculation of excitation for surface waves Alsop, 1963). In these studies, source effects were generally and normal modes in laterally homogeneous, elastic, ¯at or eliminated by considering propagation between two or more spherical Earth models. Later, different schemes, using stations aligned along the same great circle path, or, at longer different mathematical approaches (variational method) were periods, observation of consecutive Earth-circling wave developed (Wiggins, 1976; Buland and Gilbert, 1984). trains at the same station. On the other hand, in early studies Today, another widely used code for spherical geometry and of earthquake sources, propagation effects were assumed to be ef®cient to relatively short periods (10 s) is based on a pro- known, and amplitudes were ``equalized'' to obtain the pagator matrix approach, in which minors of sets of solutions source radiation pattern and infer information about the fault are used (Gilbert and Backus, 1966; Woodhouse, 1980a, orientation (e.g., Aki, 1960) and its directivity (Alterman et al., 1988). Inversion of Surface Waves 151 These theoretical advances were ®rst applied to the analog surface wave at distance Á, azimuth , and angular frequency data of the World Wide Standard Seismic Network (WWSSN) !. Following Kanamori and Stewart (1976), and Nakanishi accumulated in the 1960s and 1970s. The IDA (International and Kanamori (1982): Deployment of Accelerometers) network, established in the mid-1970s (Agnew et al., 1976), provided the ®rst long-period U Á, , !Us , !S ÁUp Á, , !F !, 0D !I ! 2 digital data, along with several stations installed and operated where Us is the source spectrum, Up contains propagation by the French (Jobert and Roult, 1976). The digital recording effects, I is the instrument response, S(Á) the geometrical greatly facilitated the simultaneous analysis of many records, spreading term, and F and D express the source process as paving the way for large-scale tomographic studies of global clari®ed below. structure and systematic teleseismic source studies. A major The propagation term Up can be expressed as (e.g., drawback, however, was the limited dynamic range of the Romanowicz and Monfret, 1986) IDA instruments, so that ®rst-arriving low-frequency R1 and 1 G1 wave trains would saturate for large earthquakes. This Up Á, , ! exp i=4 exp im=2 problem disappeared in the 1980s with the deployment by sin Á1=2 France of the high dynamic range, digital broadband GEO-  expÀi!Á=C !, expÀ !, Á 3 SCOPE network (Romanowicz et al., 1984, 1991) and by the United States of the IRIS Global Seismic Network (e.g., where m denotes the number of polar passages and C(!, ), Smith, 1986), gradually complemented by many broadband (!, ) are, respectively, the average phase velocity and stations contributed by other countries through the Federation attenuation coef®cient along the source±station path.