Teleseismic P-wave residuals, cleared of the effects of various source
regions and deep mantle paths, reflect the composition and structure
of the lithosphere and asthenosphere beneath seismological stations. W
e use a method with which we compute two components of the relative re
siduals for each station, namely a directionally independent average a
nd azimuth-incidence angle dependent terms, and also the ACH 3-D inver
sion method. The representative averages show consistent variations ov
er the Iberian Peninsula with a relatively steep gradient in some area
s-the Iberian Massif and the Betic Cordillera. These changes attain va
lues around 1 s over a distance of about 200 km. The lateral variation
s of these residual averages are transformed into a tentative model of
the lithosphere thickness. A thick lithosphere is observed beneath th
e Iberian Massif, the Pyrenees, and beneath part of the Betic Cordille
ra. Waves from events at different teleseismic distances and various a
zimuths provide consistent residual patterns and a systematic directio
nal dependence of the relative residuals especially at stations in the
Betic Cordillera.