A 1918-m-deep bore holes in a late Miocene shield basalt/central volcano mixed contains 58 stratigraphically distinct volcanistic interbands, constituting 8.8% of the extrusive part of the section. Textural, mineral chemical and bulk chemical criteria are applied to identify the original nature, composition, and origin of these rocks which have been metamorphosed by hydrothermal alteration betwen 100¿C (top) to ca. 300¿C (base of the section). Units range from a few centimeters to 18 m, excluding a 30-m-thick ignimbrite, with 75% of the units being less than 1 m thick. Formely vitric to tachylitic shards and lapilli, lithic fragments, and crystals are the main components. Most thin volcaniclastic units are basaltic vitric to tachylitic tuffs. Thin felsic air fall tuffs, a few millimeters to a few centimeters thick, occur as separate layers and interbedded with basaltic tuffs. Nearly all thicker units are made up dominantly of felsic vitric to lithic clasts and crystals. Phenocrysts, common only in felsic air fall tuffs, are clinopyroxene, ranging from augite to ferrohedenbergite, and plagioclase, ranging from An80-20, both of which span the entire range of compositions previously known from Iceland. Bulk chemical analyses of major and 11 trace elements of 65 samples allow texturally indistinct rocks to be compositionally identified, even though chemical changes due to mixing and alteration are pronounced in many rocks. The rhyolitic ignimbrite unit is composed of four flow units, the upper most being slightly more mafic in composition because of admixture of a basaltic component. The two central flow units show extensive, high-temperature devitrification with lensoid, tridymite-rimmed cavities (now laumontite-filled), representing collapsed pumice lapilli. The composition of the clastic units corresponds in a general way to that of the interbedded lava flows. These data and evidence for weathering and reworking in some units are used to reconstruct the volcanic history of the area: phase A (1918--1306 m), dominantly mafic shield basalts, contains only few and mostly basaltic tuffs except for sparce rhyolotic air fall tuff from distant central volcanos; Phase B (1306--653 m), composed dominatly of evolved basalts and icelandites, culminating with the rhyolitic ignimbrite (920--950 m), probably represents the eastern flank of a nearby central volcanic complex, whose center may be situated less than 10 km westward downdip. The upper extrusive 500 m of the section (phase C) are basalt lavas of average tholeiitic composition, containing abundant chiefly felsic and reworked clastic units in the interval between 286 and 410 m. These are tentatively interpreted to reflect a phase of structural basin-forming not compensated by extrusive volcanic activity. Allanite phenocrysts were found for the first time in Icelandic rocks, and the host pumice tuffs may constitute an important stratigraphic marker horizon that may help to tie the drilled section to the subaerial volcanic series in this part of eastern Iceland. The alteration of the elastic layers is discussed in a companion paper.