The precise shape of the Sun is sensitive to the influence of gravity, differential rotation, local turbulence and magnetic fields. It has been previously shown that the solar shape exhibits asphericity that evolves with the 11-year cycle. Thanks to the capability of the SoHO/MDI and SDO/HMI instruments to observe with an unprecedented accuracy the surface gravity oscillation (f) modes, it is possible to extract information concerning the coefficients of rotational frequency splitting, a1, a3 and a5, that measure the differential rotation, together with the a2, a4 and a6 asphericity coefficients. Analysis of these helioseismology data for almost two solar cycles, from 1996 to 2017, reveals a close correlation of the a1 and a5 coefficients with the solar activity, whilst a3 exhibits a long-term trend and a weak correlation in the current cycle indicating a substantial change of the global rotation, potentially associated with a long-term evolution of the solar cycles. Looking in more details, the asphericity coefficients, a2, a4 and a6 are more strongly associated with the solar cycle when applying a time lag of respectively 0.1, 1.6 and -1.6 years. The magnitude of a6-coefficient varies in phase with the sunspot number (SN), but its amplitude is ahead of the SN variation. The last measurements made in mid 2017 indicate that the magnitude of a6-coefficient has probably reached its minimum; therefore, the next solar minimum can be expected by the end of 2018 or in the beginning of 2019. The so-called seismic radius in the range of f-mode angular degree: l=137-299 exhibits a temporal variability in anti-phase with the solar activity; its relative value decreased by 2.3E-05 in Solar Cycle 23 and 1.7E-05 in Cycle 24. Such results will be useful for better understanding the physical mechanisms which act inside the Sun, and so, better constrain dynamo models for forecasting the solar cycles.
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