#### 2.1. Study Region

[7] The study region is confined within latitudes 5°–55°N and longitudes 68°–150°E (Figure 1). This region contains oceanic and continental areas. The oceanic area includes a small part of the old northwest Pacific Ocean and young sea basins formed by back arc spreading, such as the Japan Sea and the Philippine Sea, as well as the Okinawa Trough, which is currently undergoing strong spreading. The subduction of the Pacific plate and the Philippine plate beneath Eurasia plays an important role in the modern geodynamic process of east Asia. In the land area, there are the world-famous Tibetan Plateau and other strongly uplifting areas such as Pamir, Tianshan, and Altai. There are also ancient platforms including Yangtze, Tarim, and Siberia, as well as reactivated platform areas like Shanxi graben and north China plain which show strong contemporary tectonic movement. On the whole, this region is tectonically very complicated and is one of the regions with strong tectonic movement and intensive seismicity in the world. The study of crust and upper mantle structure is of great importance for understanding the lithospheric dynamics.

#### 2.2. Data

[8] Rayleigh wave data recorded by digital seismograph stations in the study region were utilized in the tomographic study. Within China, there are 11 China Digital Seismograph Network (CDSN) stations; CDSN's earliest station, BJI, started providing data in late 1987, and the latest station, XAN, started in 1994. Data also come from 22 digital stations in the surrounding areas (Figure 1), including some stations no longer in operation, such as KAAO and SHIO. Some of the stations (SRO stations) started in the 1970s, but most of them were built in the 1990s. To improve path coverage, we also used some records from the FREESIA network of Japan and the long-period data from portable stations in Tibet deployed by a Sino-U.S. joint research project during 1992–1993. These stations are marked as open triangles in Figure 1.

[9] For earthquake locations and origin times we used International Seismological Centre reports for events before June 1998 and preliminary determination of epicenter reports for events between 1998.6 and 2000.1. To improve the dispersion measurement at short periods, we included recordings of moderate earthquakes, some below magnitude 5, in the data set. The average epicentral distance over all periods is ∼3000 km. It is 2400 km at 10 s and increases with period to 3900 km at 184 s.

#### 2.3. Dispersion Measurement

[10] Rayleigh wave group velocity dispersions between 10 and 184 s periods were determined with our frequency-time analysis software. It is an interactive graphic program based mainly on the multiple filter technique [*Dziewonski et al.*, 1969; *Dziewonski and Hales*, 1972]. The program is designed to extract dispersion curves as efficiently and objectively as possible. It automatically reads the data following a work list, makes instrument response correction, makes high and low filtering, and sets an appropriate time window for Rayleigh waves. It then calculates the energy distribution on the time-frequency plane, picks out the energy peak and next five local maxima at each period, and displays them with different symbols. At shorter periods, there is generally more than one branch of incoming energy. The analyst needs to set the high and low period for usable dispersion range and to assign a quality flag to the dispersion curve. Sometimes the analyst may manually select a proper dispersion branch at short periods and smooth the dispersion curve if he/she deems it appropriate.

[11] After the dispersions along all paths were measured, dispersion curves along similar paths were grouped into composite paths. That is, we take the earthquakes within 15 km from a group center as a cluster and calculate average dispersion curves to be used in the inversion. After a preliminary inversion we discarded a small number of paths that have very large travel time residuals. The final path numbers in the period range 10–100 s are >2500 (counting a composite path as a single one), and above 125 s they decrease fast. For example, the path number is 2563 at 10 s, 3785 at 34.1 s, and 897 at 184 s.

[12] Figure 2 shows the path coverage at 34.1 and 158 s. Although the general situation is good, the path distribution is not even in the study region. The coverage is better in the eastern part of the study region. In the margins the path coverage is the worst, where the paths are generally in one direction without crossing each other. The northeast, southeast, and southwest corners are not covered with any path; these areas will be unshaded in the resulting velocity maps.

[13] During the inversion for group velocity distributions the computer automatically leaves those marginal nodes out of the inversion that do not have a single path passing by. However, inside the region, all nodes participate in the inversion even if some nodes have no paths passing by, so that there will be no holes inside the region. The velocities at these nodes will be the average value of surrounding nodes owing to the smoothness constraints used in the inversion.

#### 2.4. Inversion for Group Velocity Maps

[14] Assuming surface waves are propagated along great circle paths, the total travel time along a path is the sum of travel times spent on all elementary path segments. We divide the study region into a 1° × 1° grid. The velocities at the grid nodes represent the discrete group velocity model; velocities in between the nodes are calculated by bilinear interpolation. Thus the inversion problem is reduced to solving a linear equations system.

[15] In order to suppress the adverse effect of dispersion measurement errors and improper path coverage we adopted the Occam's inversion method proposed by *Constable et al.* [1987] and *deGroot-Hedlin and Constable* [1990]. This method seeks a smooth model that reasonably satisfies the observational data. Thereby we try to extract the major tectonic features of the study region while suppressing as much as possible artifacts caused by measurement errors, path coverage defects, and inadequacy of basic assumptions such as great circle propagation.

[16] This Occam's inversion method was elucidated by *Constable et al.* [1987] and *deGroot-Hedlin and Constable* [1990]. For completeness, we give a brief account of the method here. Denote the velocity model with *N* unknowns as *m* and the observation data of *M* paths as **d**, and put the observational errors in a diagonal matrix **W** = diag(1/σ_{1}, 1/σ_{2}, … 1/σ_{M}). There is a definite functional relation between the data and model parameters, denoted as **d** = *F*(**m**), and the corresponding partial derivative matrix is **J**. The smoothness of the model is described by roughness *R* defined as

where **δ**_{X}**m** and **δ**_{Y}**m** are vectors composed of first-order spatial partial derivatives in *x* and *y* directions, respectively. Parallels denote the modulus of a vector, and **δ**_{X} and **δ**_{Y} are *N* × *N* matrices in the following form:

Δ is the distance between neighboring nodes in *x* or *y* direction. If the node corresponding to a diagonal element is on the rim of the region, all the elements in that row are zeros. Otherwise there are two nonzero elements, and the position of the off-diagonal element depends on the numbering of nodes.

[17] The objective of inversion is to minimize the following functional:

The first term represents the fitting to observational data, the second term is the smoothness constraint, and μ is a smoothing factor. As μ becomes larger, the resulting model becomes smoother. In theoretical tests with synthetic data it was found that the best result was achieved when the decrease of residual started to slow down with decreasing μ. After that the residual reduced slightly, whereas the roughness of model increased rapidly [*Huang and Zheng*, 1998].

[18] In the present inversion, wave propagation is fixed along the great circle path; therefore the inversion problem is essentially linear. At each period we assume a uniform initial model with a velocity averaged over all paths at that period. If the initial model is m_{0}, the resulting model is

[19] The equation system is solved by the singular value decomposition method. This inversion method is robust, and a stable solution can be obtained even if the number of unknowns is much greater than the path number. As a consequence, we can use a much finer grid and basically eliminate the objectiveness in model discretization. Furthermore, the inversion result is improved in the margins and areas of poor paths coverage. On the other hand, the introduction of smoothness constraints into the inversion smears sharp velocity boundaries that may exist between tectonic blocks and reduces the power to resolve small-scale heterogeneities. The selection of μ value in the inversion of actual data depends largely on subjective judgment. The final model is the result of a compromise between having more details and maintaining a reasonable smoothness for the velocity model.

#### 2.5. Resolution

[20] Checkerboard tests were conducted to estimate the achievable resolution. Figure 3a shows a theoretical velocity model that is discretized into a 1° × 1° grid as the real model. The size of alternatively high- and low-velocity cells is 3°. Each cell has a constant velocity 5% above or below an average velocity of 3.5 km/s. Synthetic data of group velocities were calculated according to the actual paths at period 34.1 s, and then a random error in between +0.05 and −0.05 km/s was added to each path. The average absolute error was 0.025 km/s. Then the data were used to reconstruct the velocity model by the same inversion method and smoothing factor as used for actual data. The resulting model is shown in Figure 3b.

[21] It can be seen from Figure 3b that the resolving power is generally not bad in the Chinese territory and neighboring seas but it deteriorates toward the periphery. Figure 3c shows the result of a similar test with the path coverage at 158 s. In that case the theoretical velocity model has a 5° × 5° checkerboard pattern and is not shown here. The reconstructed velocity image is basically correct in most of China and neighboring seas.

[22] It should be pointed out that in these tests the theoretical travel times were calculated along great circle path, exactly like the calculations in the inversion. In reality, such is not the case, and the errors caused by off great circle propagation or multipathing are most likely systematic rather than random. Therefore the actual resolution should be worse than that in the tests. In view of this we would like to put, as a rough estimation, the resolution as 4° for shorter periods and 6° for longer periods within Chinese territory and neighboring seas.