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.

Ultrasonic measurement of anisotropic reflectivity from Water-Phenolic CE Interface

In this contribution, we experimentally test the effects of azimuth and tilt angle on the acoustic reflectivity of a liquid- anisotropic solid interface. For this study, we are using a large source transducer, and acquired data for samples with different tilt angles. We use Phenolic CE material, which is known to have orthorhombic symmetry. Our results show that changes of the tilt angle produce important variations on the reflectivity that are larger as the tilt increases. The most remarkable feature is the change of the critical angle with the azimuth, which shows a larger spread for larger tilts. The spectral components of the acquired waveforms also show characteristic features linked to the location of the critical angle, we particularly observed a drop in the peak frequency. These observations suggest that care must be taken about the interpretation and inversion of observed incidence and azimuth dependent seismic reflectivities and critical angles in obtaining information on a formation's anisotropy. Zip archive contains four segy files: - LAB_TI00, is not tilted sample in contact with water, - LAB_TI30, is 30degrees tilted sample in contact with water, - LAB_TI45, is 45 degrees tilted sample in contact with water, - LAB_TI90, is 90 degrees tilted sample in contact with water.