Errors in travel times measured on paper seismograms

Summary. The investigation of temporal variations in seismic velocities sometimes requires the use of paper seismograms. For this reason, an investigation of all of the sources of random error in measuring travel times on seismograms has been undertaken using a mathematical model devised by Jeffreys and some additional results derived using elementary statistics. The most important contribution to the total error is often the error due to linear interpolation between minute markers or other time marks on the seismogram, which can be as high as 0.13 s on smoked paper seismograms recorded at 120 mm min⁻¹, and as high as 0.076 s on short-period seismograms of the Canadian network recorded at 60 mm min⁻¹. For 32 explosions at short distances (< 50 km) recorded on smoked paper, however, the median value of the total error in the travel times was 0.016 s. Interpolation errors are generally insignificant for travel-time studies of teleseisms, but may be important in some special studies of local earthquakes and explosions. The theoretical results are useful, not only in seismology, but wherever the accurate timing of an event relative to two reference time markers on a chart recorder is required.     

End-point contributions to synthetic seismograms

Summary . Synthetic seismograms represented by integrals generally display signals associated with the limits of integration. Sometimes these 'end-point' contributions are spurious (e.g. in the WKBJ seismogram) and sometimes they are the main physical interest (e.g. the Kirchhoff integral for an edge). The end-point contributions may be asymptotically approximated using integration by parts or Laplace's method and it may then be possible to reduce them if desired. We describe examples in the WKBJ seism ogram for reflected or transmitted waves in homogeneous layers and for turning waves. We also study signals due to discontinuities in reflection coefficients, by partitioning the real slowness integral so that the discontinuities lie at end points. Examples are the head wave, which is a physically correct signal, and spurious diffractions caused by using plane-wave coefficients for grazing rays in the WKBJ seismogram.     

Generation of complete theoretical seismograms for SH-III

Summary. Earlier efforts to generate the entire theoretical seismograms, including both body and surface waves for realistic sources buried in a radially heterogeneous anelastic, spherical earth, are extended to include the summation of 16 modes. The comparison between a real seismogram and theoretical time series, relative to different attenuation models in the upper mantle, yields information concerning the anelasticity under the Pacific Ocean.     

Generation of complete theoretical seismograms for SH—

Summary. We report the initial results of our attempts to obtain theoretical seismograms for direct comparison with the experimental time series obtained with the long-period instruments of the WWSSN. The entire theoretical seismogram, including both body waves and surface waves, can be generated for a spherical, anelastic earth by simple inverse Fourier transformation of the sum of the propagating fundamental and higher-mode surface waves. The key to success in reproducing the WWSSN records involves the number of modes, and the minimum period used in these computations; here we use eight modes and a minimum period of 2 s. Efficient computational algorithms make it possible to handle up to 2000 frequency points for each mode; approximately 200 layers are used to model the radial heterogeneity of the earth; attenuation is treated exactly. Examples are given of the SH theoretical seismograms resulting from dislocation sources buried at various depths in the Earth.