Code and readme of a MATLAB-based graphical user interface program for computing functionals of the geopotential

We present a novel graphical user interface program GrafLab (GRAvity Field LABoratory) for spherical harmonic synthesis (SHS) created in MATLAB®. This program allows to comfortably compute 38 various functionals of the geopotential up to ultra-high degrees and orders of spherical harmonic expansion. For the most difficult part of the SHS, namely the evaluation of the fully normalized associated Legendre functions (fnALFs), we used three different approaches according to required maximum degree: (i) the standard forward column method (up to maximum degree 1800, in some cases up to degree 2190); (ii) the modified forward column method combined with Horner's scheme (up to maximum degree 2700); (iii) the extended-range arithmetic (up to an arbitrary maximum degree). For the maximum degree 2190, the SHS with fnALFs evaluated using the extended-range arithmetic approach takes only approximately 2-3 times longer than its standard arithmetic counterpart, i.e. the standard forward column method. In the GrafLab, the functionals of the geopotential can be evaluated on a regular grid or point-wise, while the input coordinates can either be read from a data file or entered manually. For the computation on a regular grid we decided to apply the lumped coefficients approach due to significant time-efficiency of this method. Furthermore, if a full variance-covariance matrix of spherical harmonic coefficients is available, it is possible to compute the commission errors of the functionals. When computing on a regular grid, the output functionals or their commission errors may be depicted on a map using automatically selected cartographic projection.

(Table 2) Grain composition of sediments from ODP Hole 161-974B and from beach samples

Miocene to Pleistocene sand and sandstone were recovered at Ocean Drilling Program Site 974 in the Tyrrhenian Basin and Sites 976 and 977 in the Alboran Basin. Sand detrital modes were determined for 45 samples from these sites, as well as 10 samples of Spanish beach sand. At Site 974, the Pleistocene section includes a number of volcaniclastic (vitric ash) and terrigenous sand layers; the latter are heterogeneous and contain sedimentary and metamorphic lithic fragments. Submarine canyon and onshore drainage patterns suggest that the most likely source of this sediment is the Tiber River drainage basin in central Italy, where a Pleistocene volcanic field is superimposed on Apennine orogenic rocks. In contrast, the Miocene sand in Unit III at Site 974 may have been derived from local basement highs. The quartzolithic composition and preponderance of metamorphic and sedimentary lithic debris in sand samples from Unit II at Site 976, Unit I at Sites 977 and 978, and Unit I at Site 979 are consistent with derivation from metamorphic rocks and sedimentary cover sequences that crop out in the Betic Cordillera of southern Spain (976-978) and in the Rif of Northern Africa (979). The sedimentary to metamorphic lithic fragment ratios in these samples reflect the relative proportion of metamorphic and sedimentary rocks exposed in onshore source terranes. In contrast, the source of the few quartzose Pleistocene sands at Site 976 was likely the Flysch Trough Units that crop out near Gibraltar. The significant volcanic component in certain intervals at Sites 976 (upper Miocene) and 977 (lower Pliocene to Miocene) is consistent with widespread volcanic activity during basin inception and development. Mean sand detrital modes for sand subgroups from both the Alboran and Tyrrhenian Basin sites plot in the Recycled Orogenic and Magmatic Arc compositional fields of Dickinson et al. (1983, doi:10.1130/0016-7606(1983)94<222:PONAPS>2.0.CO;2), reflecting the hybrid tectonic histories of these basins.