Pn tomography

Pn tomography beneath the Pannonian basin


The Pannonian depression is an extensional back-arc basin in central Europe and is an integral part of the Alpine-Carpathian orogenic mountain belts. It is completely encircled by the Carpathian Mountains to the north and east, the Dinarides to the south, and the Southern and Eastern Alps to the west. The Pannonian basin is not a single basin, but a system of small deep subbasins separated by relatively shallow basement highs and low hills.

Topography and index map of the Pannonian basin.

Recent studies have shown that the present structural layout of the Pannonian basin can be considered as a result of complex kinematic and dynamic processes that took place since the Neogene, triggered by the continental collision between Europe and several continental fragments to the south, including Africa. Geophysical features such as an updoming of the mantle, a thinned lower crust, and a strong geothermal anomaly are all characteristic to the basin. The crust is rather thick in the mountain ranges around the Pannonian basin, while the basin itself is characterized by thin crust, ranging from 22.5 to 30 km. The lithosphere also has smaller thickness than the average: several research results suggest that the lithosphere is thinner than 80 km.

Moho depth beneath the Pannonian basin.

Basically, there are three portions to a Pn raypath: the raypath from the source to the mantle, the raypath in the upper mantle, and the raypath from the mantle to the receiver. The ray mainly travels below the Moho discontinuity with wave velocity characteristic of the uppermost mantle. As a consequence, tomographic imaging of Pn traveltimes can yield the lateral distribution of wave velocity in the uppermost mantle. Lateral variations in Pn velocity have been associated with variations in upper mantle temperature, compositional differences, and pressure effects. Thus, mapping Pn velocity can yield valuable constraints on the styles of tectonic deformation that are responsible for the evolution of the continental crust.

To better understand the structure and formation of the Pannonian basin, I used Pn traveltimes from regional and local earthquakes to tomographically image the lateral velocity variations in the uppermost mantle beneath the region (Wéber 2002).


The data used in this study are traveltimes from regional events that are listed in the bulletins of the International Seismological Centre (ISC) and local earthquakes published in the Hungarian Earthquake Bulletin. An iterative data selection procedure was used to help ensure a quality solution. As a result 4481 Pn traveltimes have been collected from 417 earthquakes that occurred in or around the Pannonian basin from 1964 to 1999, recorded at 57 stations.

The figure below shows the selected 4481 Pn raypaths (open circles: epicenters; solid triangles: stations). Unfortunately, their spatial distribution is very heterogeneous leading to heterogeneous resolution and reliability of the tomographic solution as well. Ray coverage is smallest in the northeastern part of the investigated area, whereas it is highest in the western half of Hungary (Transdanubia) and the Croatian part of the Pannonian basin.

Pn raypaths in the Pannonian basin.

The selected traveltimes are depicted in the next figure as a function of the epicentral distance. The straight line fit to these data points gives an estimate of the mean Pn velocity (from the inverse slope) of 7.9±0.01 km/s and the mean crustal delay (from the intercept time) of 6.23±0.06 s. These initial estimates are used as the starting model for the subsequent tomographic inversion. The estimated data variance after the straight line fit is 3.24 s2. This is a large amount of error, although perhaps not too surprising, considering the nature of the data base.

Pn traveltime curve for the Pannonian basin.

Inversion method

Detailed description of the tomographic method used in this experiment can be found in Hearn (1984) and Hearn et al. (1991). It is briefly reviewed here.

The regional traveltimes are modelled as refracted Pn raypaths. A refracted raypath can be described as the sum of three portions: the source-to-mantle raypath, the raypath in the uppermost mantle, and the raypath from the mantle to the receiver. For estimating lateral velocity variations within the uppermost mantle, it is divided into rectangular cells with constant velocities. Therefore, Pn traveltimes can be described by the time term equation as

tij = ei + rj + ∑kdijksk

where tij is the traveltime between source i and receiver j, ei the static delay time for event i, rj the static delay time for receiver j, while dijk denotes the horizontal distance the ray travels in cell k with slowness (inverse velocity) sk. The sum is over all cells through which the ray travels between the source and the receiver.

If the vector t contains the observed traveltime residuals (i.e. the differences between the observed Pn traveltimes and the traveltimes predicted by the linear fit) and x is the vector of the unknown delay times and slowness perturbations (relative to the mean upper mantle velocity of 7.9 km/s), then for a set of many source-receiver pairs the tomographic equations can be written as

Ax = t,

where A is the tomographic matrix. In order to obtain the solution of this system of linear equations, I used a truncated singular value decomposition (TSVD) algorithm. The explicit computation of the generalized inverse of the tomographic matrix allows us to deduce both the resolution matrix and the covariance matrix of the final solution.

Resulting upper mantle velocity structure

The overall low average Pn velocity of 7.9 km/s found beneath the Pannonian basin can be attributed to the high temperature of the uppermost mantle in that region. The surface heat flow in the basin has values in general between 70 and 110mW/m2 and in some particular areas it even reaches 130-135mW/m2. In the surroundings, however, the mean surface heat flow values do not exceed 50-60mW/m2. According to some model calculations, the temperature on the Moho surface below this hyperthermal zone has values on average 400-500 °C more than those in the surrounding areas.

Pn velocities beneath the Pannonian basin.

The Pn velocity image presented in the above figure shows several small-scale heterogeneities with regional importance. The thin white contour line denotes zero velocity anomaly. The resolution can be regarded as satisfactory only inside the region surrounded by the white closed curve corresponding to the 0.6 resolution contour. The tomographically imaged uppermost mantle velocities range from about 7.6 to 8.2 km/s. Due to high Moho temperature, below the North Hungarian Range low (7.6-7.7 km/s) velocities can be found. High-velocity anomalies of around 8.1 km/s can be detected along the W-SW boundaries of Hungary showing remarkable correlation with the deepest subbasins, as well as at the junction of the Pannonian basin and the Southern Carpathians. The Great Hungarian Plain shows average (7.9 km/s) Pn velocities.

Std deviation of Pn velocities beneath the Pannonian basin.

The standard deviation for the velocity cells of the tomographic model ranges from 0.08 to 0.12 km/s. The highest errors appear at those parts of the image where the angular coverage of raypaths is inadequate. In well resolved parts of the investigated area, the characteristic velocity anomalies have magnitudes at least two times greater than the corresponding standard deviations.


The reported investigation was financially supported by the Hungarian Scientific Research Fund (Nos. F019277 and T029076).


    • Hearn, T.M., 1984: Pn travel times in southern California, J. Geophys. Res. 89, 1843-1855.
    • Hearn, T., Beghoul, N., Barazangi, M., 1991: Tomography of the western United States from regional arrival times, J. Geophys. Res. 96, 16369-16381.