Determination of the three-dimensional seismic structure of the lithosphere

A new three-dimensional earth modeling is proposed as a framework to obtain more detailed and accurate information about the earth's interior. We start with a layered medium of classic seismology but divide each layer into many blocks and assign a parameter to each block which describes the velocity fluctuation from the average for the layer. Our data are the teleseismic P travel time residuals observed at an array of seismographs distributed on the surface above the earth's volume we are modeling. By isolating various sources of errors and biases we arrive at a system of equations to determine the model parameters. The solution was obtained by the use of generalized inverse and stochastic inverse methods. Our method also gives a lower limit of the true rms slowness fluctuation in the earth under the assumption of ray theory. Using P wave residual data from the Norwegian Seismic Array (Norsar), we have obtained the map of velocity anomalies at various depths up to a depth of 126 km. The rms slowness fluctuation was found to be at least 3.1%. This is in agreement with estimates obtained from statistical analysis of P time fluctuations based on the Chernov theory. The three-dimensional velocity anomalies are presented both by the generalized inverse and by the stochastic inverse solutions. We prefer the dual presentation because it gives the reader greater freedom in judging the results than a single `optimal' solution. Both methods gave essentially the same results. The discrepancies, when they existed, were always explainable in terms of differences in the smoothing procedure which is explicitly given in the resolution matrix. The dominant features in the obtained three-dimensional velocity image of the lithosphere beneath the Norsar array are low velocities to the west and high velocities to the east. The latter feature may be attributed to rocks of the Baltic shield which are undisturbed by the Caledonian orogeny or by Permian volcanism. Our result conclusively demonstrates the existence of strong small-scale inhomogeneities to the bottom of the lithosphere. More theoretical and experimental works are needed to relate these velocity anomalies with the magma ascent mechanism which caused the Oslo graben.