@article{fdi:010055989,
  title = {{S}pherical harmonic modelling to ultra-high degree of {B}ouguer and isostatic anomalies},
  author = {{B}almino, {G}. and {V}ales, {N}. and {B}onvalot, {S}ylvain and {B}riais, {A}.},
  editor = {},
  language = {{ENG}},
  abstract = {{T}he availability of high-resolution global digital elevation data sets has raised a growing interest in the feasibility of obtaining their spherical harmonic representation at matching resolution, and from there in the modelling of induced gravity perturbations. {W}e have therefore estimated spherical {B}ouguer and {A}iry isostatic anomalies whose spherical harmonic models are derived from the {E}arth's topography harmonic expansion. {T}hese spherical anomalies differ from the classical planar ones and may be used in the context of new applications. {W}e succeeded in meeting a number of challenges to build spherical harmonic models with no theoretical limitation on the resolution. {A} specific algorithm was developed to enable the computation of associated {L}egendre functions to any degree and order. {I}t was successfully tested up to degree 32,400. {A}ll analyses and syntheses were performed, in 64 bits arithmetic and with semi-empirical control of the significant terms to prevent from calculus underflows and overflows, according to {IEEE} limitations, also in preserving the speed of a specific regular grid processing scheme. {F}inally, the continuation from the reference ellipsoid's surface to the {E}arth's surface was performed by high-order {T}aylor expansion with all grids of required partial derivatives being computed in parallel. {T}he main application was the production of a 1' x 1' equiangular global {B}ouguer anomaly grid which was computed by spherical harmonic analysis of the {E}arth's topography-bathymetry {ETOPO}1 data set up to degree and order 10,800, taking into account the precise boundaries and densities of major lakes and inner seas, with their own altitude, polar caps with bedrock information, and land areas below sea level. {T}he harmonic coefficients for each entity were derived by analyzing the corresponding {ETOPO}1 part, and free surface data when required, at one arc minute resolution. {T}he following approximations were made: the land, ocean and ice cap gravity spherical harmonic coefficients were computed up to the third degree of the altitude, and the harmonics of the other, smaller parts up to the second degree. {T}heir sum constitutes what we call {ETOPG}1, the {E}arth's {TOP}ography derived {G}ravity model at 1' resolution (half-wavelength). {T}he {EGM}2008 gravity field model and {ETOPG}1 were then used to rigorously compute 1' x 1' point values of surface gravity anomalies and disturbances, respectively, worldwide, at the real {E}arth's surface, i.e. at the lower limit of the atmosphere. {T}he disturbance grid is the most interesting product of this study and can be used in various contexts. {T}he surface gravity anomaly grid is an accurate product associated with {EGM}2008 and {ETOPO}1, but its gravity information contents are those of {EGM}2008. {O}ur method was validated by comparison with a direct numerical integration approach applied to a test area in {M}orocco-{S}outh of {S}pain ({K}uhn, private communication 2011) and the agreement was satisfactory. {F}inally isostatic corrections according to the {A}iry model, but in spherical geometry, with harmonic coefficients derived from the sets of the {ETOPO}1 different parts, were computed with a uniform depth of compensation of 30 km. {T}he new world {B}ouguer and isostatic gravity maps and grids here produced will be made available through the {C}ommission for the {G}eological {M}ap of the {W}orld. {S}ince gravity values are those of the {EGM}2008 model, geophysical interpretation from these products should not be done for spatial scales below 5 arc minutes (half-wavelength).},
  keywords = {{B}ouguer gravity anomalies ; {I}sostatic gravity anomalies ; {E}arth's topography ; {S}pherical harmonics ; {S}urface gravity anomalies ; {S}urface gravity perturbations},
  booktitle = {},
  journal = {{J}ournal of {G}eodesy},
  volume = {86},
  numero = {7},
  pages = {499--520},
  ISSN = {0949-7714},
  year = {2012},
  DOI = {10.1007/s00190-011-0533-4},
  URL = {https://www.documentation.ird.fr/hor/fdi:010055989},
}