Effective mass (solid-state physics) from both sides gives where is the th element of , is the th element of , and are the th and th elements of , respectively, and is the total energy of the particle according to the Planck–Einstein relation. The index is contracted by the use of Einstein notation (there is an implicit summation over ). Since Newton's second law uses the inertial mass (not the gravitational mass), we can identify the inverse of this mass in the equation above as the tensor This tensor expresses the change in group velocity due to a change in crystal momentum. Its
Ekman velocity used here, interpolated to 1°X1°grid, spanning the domain of 25°N-25°S,90°E-290°E, during Oct1992-Sep1998). Geostrophic and Ekman velocity are assumed to satisfy the lowest-order dynamics of the surface velocity, and they can be obtained independently from surface height and wind stress data. Standard "f" plan satisfies geostrophic balance, the lowest-order balance for quasi-steady circulation at higher latitudes. However, coriolis parameter "f" is close to zero near the equator, the geostropic balance is not satisfied as the velocity is proportional to the height gradient divided by the coriolis parameter "f". It has been shown in many studies that beta plane geostrophic approximation involving