Global geoidal undulations as inferred from the Bruns formula and from inversion of the geopotential series

Резюме

Меmо¶rt;ом лuнеaрuзaцuu выве¶rt;ены aнaлumuческuе формулu ¶rt;ля рaсчеma рa¶rt;uусa — некmорa, в коmорыцх uсnользовaны коэффuцuенmы рaзложенuя внешне

о

рaвumaцuонно

о nоля Землu u naрaмеmры земно

о эллunсоu¶rt;a. Прu вuво¶rt;е формулы uсnолвзовaна блuзосmь коэффuцuенmов розложенuя nоmенцuaлa u коэффuцuенmов рaзложенuя рa¶rt;uусa — векmорa. Сре¶rt;неквa¶rt;рamuческaя ошuбкa, вызвaннaя лuнеaрuзaцuеŭ, nоря¶rt;кa 1 мм. Прuве¶rt;ены чuсленные рaсчеmы ¶rt;ля мо¶rt;елu

рaвumaцuонно

о nоля GEM-L2. Нaмu nолученнaя nоверхносmв оmклоняеmся оm чaсmо nрuменяемоŭ annроксuмaцuu

еоu¶rt;a, основaнноŭ нa mеореме Брунсa, в nре¶rt;елaх ± 90 см.

Summary

The problem of inverting the geopotential series with respect to the geoid radius has been solved. A linearization of the radius powers, making use of a reference surface, has been applied. The body given by the Bruns' formula has been chosen as the reference surface. Corrections to the Bruns' formula in an analytical explicit form have been derived. An internal linearization accuracy of the order of 1 mm has been achieved. The geoid radius coefficients for the GEM-L2 model have been evaluated numerically. The corrections have been found to range from −90 to 90 cm.