Determining a high-precision national geoid is a fundamental step in modernizing Kazakhstan’s vertical reference system. However, the country’s vast territory, complex topography, and limited coverage of modern terrestrial and airborne gravimetric surveys present significant challenges. In this context, Soviet-era gravimetric maps at a 1:200,000 scale remain the only consistent nationwide data source, yet their reliability has not previously been rigorously assessed within modern gravity standards. This study presents the first comprehensive validation of Soviet-era gravimetric surveys using two independent approaches. The first approach is about the comparison of gravity anomalies with the global geopotential models EGM2008, EIGEN-6C4 and XGM2019e_2159. The second approach is about the direct evaluation against absolute gravity measurements from the newly established Qazaqstan Gravity Reference Frame (QazGRF). The analysis demonstrates that, after applying systematic corrections, the Soviet-era gravimetric survey retains high information content. The mean discrepancy with QazGRF measurements is 0.7 mGal with a standard deviation of 2.5 mGal, and more than 90% of the evaluated points deviate by less than ±5 mGal. Larger inconsistencies, up to 20 mGal, are confined to mountainous and geophysically complex regions. In addition, several artifacts inherent to the global models were identified, suggesting that the integration of validated regional gravimetric data can also support future improvements of global gravity models. A key finding was the detection of an artifact in the global models on sheet M43. Its presence was confirmed by comparison with terrestrial gravimetric data and inter-model differences. It was established that the anomaly is caused by inaccuracies in the terrestrial “fill-in” component of the EGM2008 model, which subsequently inherited by later global solutions. The results confirm that Soviet gravimetric maps, once critically re-evaluated and tied to absolute observations, can be effectively integrated with global models. This integration delivers reliable, high-resolution inputs for regional gravity-field modeling. It establishes a robust scientific and practical foundation for constructing the first national geoid of Kazakhstan and for implementing a unified state coordinate and height system. It also helps enhance the accuracy of global geopotential models.

Accurate geoid determination is essential for height system unification and for converting Global Navigation Satellite System (GNSS) ellipsoidal heights to orthometric heights. This study demonstrates a national-scale workflow that integrates digitized Soviet-era gravimetric maps at 1:200,000 scale with modern satellite and ancillary datasets to compute a high-resolution gravimetric geoid for Kazakhstan. Legacy gravity maps were systematically digitized, harmonized, and quality-controlled, then integrated with a global geopotential model (XGM2019e_2159) for long-wavelength information and a digital elevation model (FABDEM) for terrain corrections. Geoid computation employed the Least-Squares Modification of Stokes’ Formula, with spectral testing used to select optimal parameters; external control and validation relied on an extensive set of GNSS observations and geometric levelling benchmarks from the national network. The resulting geoid surface captures the country’s full topographic range, from the Caspian Depression to the Tien Shan and Altai. After regression-based removal of residual tilts linked to distortions in the Baltic 1977 height system, we achieved a root-mean-square error of 0.066 m. The integrated use of 1:200,000 gravity maps and modern satellite-derived models yields accuracy improvements over widely used global solutions, establishing a consistent vertical reference for Kazakhstan and supporting datum modernization, GNSS-based heighting, infrastructure development, and environmental monitoring. These results show that digitized Soviet-era gravity maps, when fused with modern satellite datasets, can provide robust, high-accuracy geoid solutions.

The development of a high-precision regional geoid model is an important step in the modernization of Kazakhstan’s vertical reference framework and in improving the efficiency of height determination from GNSS data. This paper proposes a hybrid approach torefining the local geoid model for the Astana area by combining the LSMSA gravimetric base solution with statistical modeling of residual corrections. The base geoid surface is computed using the Least Squares Modification of Stokes’ Formula with additivecorrections and is validated against GNSS/levelling control points. To reduce discrepancies with observations, a correction surface is formed from residuals using a 7-parameter Helmert transformation and machine learning regression models (GPR, SVR, LSBoost). On the independent test subset, SVR reduced RMSE from 0.062 to 0.047 m, corresponding to a 24% decrease in error. The results show that the proposed scheme reduces the spread of residual errors and improves the agreement of the geoid model with GNSS/levelling data.

Accurate geoid determination is essential for height system unification and for converting Global Navigation Satellite System (GNSS) ellipsoidal heights to orthometric heights. This study demonstrates a national-scale workflow that integrates digitized Soviet-era gravimetric maps at 1:200,000 scale with modern satellite and ancillary datasets to compute a high-resolution gravimetric geoid for Kazakhstan. Legacy gravity maps were systematically digitized, harmonized, and quality-controlled, then integrated with a global geopotential model (XGM2019e_2159) for long-wavelength information and a digital elevation model (FABDEM) for terrain corrections. Geoid computation employed the Least-Squares Modification of Stokes’ Formula, with spectral testing used to select optimal parameters; external control and validation relied on an extensive set of GNSS observations and geometric levelling benchmarks from the national network. The resulting geoid surface captures the country’s full topographic range-from the Caspian Depression to the Tien Shan and Altai. After regression-based removal of residual tilts linked to distortions in the Baltic 1977 height system, achieves a root-mean-square error of 0.066 m. The integrated use of 1:200,000 gravity maps and modern satellite-derived models yields accuracy improvements over widely used global solutions, establishing a consistent vertical reference for Kazakhstan and supporting datum modernization, GNSS-based heighting, infrastructure development, and environmental monitoring. These results show that digitized Soviet-era gravity maps, when fused with modern satellite datasets, can provide robust, high-accuracy geoid solutions.

Developing a high–precision regional geoid model is a key element in moderniz-ing Kazakhstan’s vertical reference framework and ensuring consistent GNSS-based height determination. However, the mountainous terrain of southeastern Kazakhstan, characterized by strong topographic gradients and sparse terrestrial gravity coverage, poses significant modelling challenges. This study presents the first AI–enhanced hy-brid geoid model developed for the Almaty region, integrating classical gravimetric modelling with modern machine-learning simulation. The baseline solution was com-puted using the Least-Squares Modification of Stokes’ Formula with Additive correc-tions, combining digitized Soviet-era terrestrial gravity data, the global geopotential model XGM2019e_2159, and the FABDEM 30 m digital elevation model. Validation using GNSS/leveling benchmarks revealed a systematic bias of −0.08 m and an RMS of 0.10 m. To improve the fit between modelled and observed undulations, three ma-chine-learning regressors – Gaussian Process Regression (GPR), Support Vector Re-gression (SVR), and LSBoost—were applied to model the residual correction surface. Among them, the SVR model achieved the optimal balance between accuracy and generalization, reducing the test RMS to 0.032 m without overfitting. The resulting hybrid model, designated NALM2025, achieved centimeter-level consistency with GNSS/leveling data. The results demonstrate that integrating classical geoid computa-tion with AI–based residual modelling provides an efficient computational framework for high-precision geoid determination in complex mountainous environments.

Developing a high-precision regional geoid model is a key element in modernizing Kazakhstan’s vertical reference framework and ensuring consistent GNSS-based height determination. However, the mountainous terrain of southeastern Kazakhstan, characterized by strong topographic gradients and sparse terrestrial gravity coverage, poses significant modelling challenges. This study presents the first AI-enhanced hybrid geoid model developed for the Almaty region, integrating classical gravimetric modelling with modern machine-learning simulation. The baseline solution was computed using the Least-Squares Modification of Stokes’ Formula with Additive Corrections, combining digitized Soviet-era terrestrial gravity data, the global geopotential model XGM2019e_2159, and the FABDEM 30 m digital elevation model. Validation using GNSS/levelling benchmarks revealed a systematic bias of −0.06 m and an RMS of 0.08 m. To improve the fit between modelled and observed undulations, three machine-learning regressors—Gaussian Process Regression (GPR), Support Vector Regression (SVR), and LSBoost—were applied to model the residual correction surface. Among them, SVR provided the best held-out performance (RMSE = 0.04 m), while LOOCV, 10-fold and spatial CV confirmed stable generalization across terrain regimes. The resulting hybrid model, designated N_ALM2025, achieved centimetre-level consistency with GNSS/levelling data. The results demonstrate that integrating classical geoid computation with AI-based residual modelling provides an efficient computational framework for high-precision geoid determination in complex mountainous environments.