IN SEVERAL REGIONS OF THE EARTH UPPER MANTLE VISCOSITY DEPARTS FROM THE GLOBAL AVERAGE VALUES AFFECTING SLAB DEFORMATION LITHOSPHEREMANTLE COUPLING GLACIAL ISOSTATIC ADJUSTMENT MODELS ETC. HERE WE ESTIMATE THE LARGE SCALE LATERAL VARIATIONS OF VISCOSITY IN THE UPPER MANTLE OF THE WESTERN UNITED STATES COMPARED TO THE GLOBAL AVERAGE. WE PERFORM THIS ESTIMATE BY EXAMINING THE RELATIONSHIP BETWEEN MANTLE DENSITY ANOMALIES MANTLE RHEOLOGY AND THE GEOID. EARTH'S LONG-WAVELENGTH STATIC GRAVITY FIELD IS A FUNCTION OF BOTH THE MASS DENSITY DISTRIBUTION WITHIN THE EARTH AND THE DEFORMATION DUE TO THE DYNAMIC FLOW IN THE MANTLE DRIVEN BY THIS DENSITY DISTRIBUTION. BEGINNING IN THE LATE 1980S AND CONTINUING SINCE STUDIES HAVE RELATED THE DENSITY STRUCTURE OF THE MANTLE ESTIMATED BY SEISMIC TOMOGRAPHY AND ITS FLOW TO THE GRAVITY FIELD OBSERVED AT THE SURFACE TO INFER THE RHEOLOGY OF THE MANTLE. THIS WORK WAS ACCOMPLISHED MAINLY BY TWO METHODS. IN THE FIRST METHOD ONE-DIMENSIONAL 'GEOID KERNELS' WERE DEVELOPED WHICH ARE SEMI-ANALYTIC GREEN'S FUNCTIONS RELATING DENSITY ANOMALIES IN THE MANTLE TO GRAVITY OBSERVATIONS AT THE SURFACE. IN THE SECOND METHOD FULLY NUMERICAL (E.G. FINITE-ELEMENT) 3D CALCULATIONS ALSO SOLVE THE FORWARD PROBLEM BUT AT GREATER COMPUTATIONAL COST. IF WE WISH TO CONSIDER LATERAL VARIATIONS IN MANTLE VISCOSITY WE HAVE UNTIL NOW BEEN LIMITED TO USING FULLY NUMERICAL CALCULATIONS. IN THIS PROPOSAL WE UPDATE THE CLASSICAL SEMI-ANALYTIC METHOD TO STUDY LATERAL VARIATIONS IN MANTLE RHEOLOGY BY ALTERING THE OBSERVABLES USED (I.E. THE GRAVITY FIELD) SO THAT THE RELATION BETWEEN DENSITY ANOMALIES AND GRAVITY REMAINS 1D IN A LOCAL REGION. BY REPRESENTING THE GRAVITY FIELD IN AN ALTERNATE BASIS SET TO SPHERICAL HARMONICS SLEPIAN FUNCTIONS WE LOCALIZE NASA'S DATA TO SPECIFIC REGIONS OF THE GLOBE AND FOCUS ON THE MANTLE RHEOLOGY OF THE WESTERN UNITED STATES COMPARING THIS REGION WITH THE RHEOLOGY THAT CAN BE DETERMINED GLOBALLY. WE WILL USE OBSERVATIONS OF THE STATIC GRAVITY FIELD WHICH HAVE SIGNIFICANTLY IMPROVED SINCE THE LAUNCH OF THE GRACE (GRAVITY RECOVERY AND CLIMATE EXPERIMENT) SATELLITE MISSION IN 2002. ALSO IN THIS REGION RECENT IMPROVEMENTS IN SEISMIC MODELS WILL IMPROVE THE RESULTING RESOLUTION COMPARED TO USING GLOBAL SEISMIC MODELS. WITH THE SPECIFIC OBJECTIVE OF DETERMINING LARGE SCALE LATERAL VARIATIONS IN MANTLE RHEOLOGY WE 1) DEVELOP FULLY 3D SLEPIAN GEOID KERNELS WHICH NOW RELATE DENSITY ANOMALIES IN SPECIFIC VOLUMES OF MANTLE TO GRAVITY AT THE SURFACE. WE PAIR THESE SEMI-ANALYTIC KERNELS WITH 3D NUMERICAL RESULTS USING THE OPEN SOURCE GEODYNAMIC CODE ASPECT TO VERIFY THE ADEQUACY OF THIS METHOD AT REGIONAL SCALES IN THE FORWARD PROBLEM. WE THEN USE OUR SLEPIAN GEOID KERNELS TO CAST THE STUDY AS A REGIONAL INVERSE PROBLEM USING MARKOV-CHAIN MONTE-CARLO METHODS. USING THIS METHOD WE 2) EXAMINE LARGE AND RELATIVELY SIMPLE AREAS OF THE EARTH INCLUDING THE PACIFIC OCEAN BASIN TO ESTIMATE THE RADIAL MANTLE VISCOSITY PROFILE WHICH BEST EXPLAINS THE GEOID IN THE LOCAL REGION OF INTEREST. ADDITIONALLY WE 3) EXAMINE THE VISCOSITY OF AN AREA WITH MORE COMPLEXITY NOTABLY NORTH AMERICA. HERE WE CAN MAKE USE OF IMPROVED SEISMOLOGICAL MODELS OF THE UPPER MANTLE AS WELL AS SEMI-ANALYTICAL SPECTRAL SOLUTIONS OF GLACIAL ISOSTATIC ADJUSTMENT TO INCLUDE GEOID RATES OF CHANGE IN OUR LOCALIZED ANALYSIS. FINALLY WE 4) USE THE INFORMATION LEARNED IN PREVIOUS OBJECTIVES TO UPDATE THE LONG-TERM SECULAR RATES OF CHANGE OF ICE MASS BALANCE OF EARTH'S LARGE ICE SHEETS USING TIME-VARIABLE GRAVIMETRY FROM THE GRACE MISSION. GIVEN THAT CORRECTIONS FOR SOLID EARTH DEFORMATION ARE AMONG THE LARGEST SOURCE OF UNCERTAINTY IN ICE SHEET MASS BALANCE IMPROVEMENT IN THESE DEFORMATION MODELS AND THE MANTLE RHEOLOGY ON WHICH THEY ARE BASED WILL REDUCE UNCERTAINTY IN ICE SHEET MASS BALANCE RATES.