NOVELTY - The method involves rotating a drill tubular to drill a borehole. A set of surface parameter measurements is performed in a time window of parameters of the drill tubular at or above a surface of the earth during rotation by using a sensor. The downhole lateral vibrations are estimated using a signal processor that receives the set of measurements corresponding to series of time windows and without an input from a downhole sensor, where the time windows exceed a time period of a fundamental torsional vibration mode.    USE - Method for estimating downhole lateral vibrations/accelerations of a drill tubular placed in a borehole penetrating earth or a component e.g. bottom hole assembly, logging tool, or drill bit (all claimed), coupled to the drill tubular for applications e.g. carbon sequestration, geothermal production and hydrocarbon exploration and production, in a drilling industry.    ADVANTAGE - The method enables obtaining surface measurements of drill string parameters versus a cost and effort to obtain downhole data in a low cost. The method enables diagnosing the drill bit in a forward and backward in real time. The method enables analyzing downhole component failures or drill bit failures where downhole vibration data is not available so as to determine a beginning point of damage.    DETAILED DESCRIPTION - The parameters comprise minimum torque of drill tubular measured in the time window, torque variation of the drill tubular measured in the time window, average torque of the drill tubular measured in the time window and a rate of penetration (ROF) of the drill tubular into the earth measured in the time window. INDEPENDENT CLAIMS are also included for the following:    (1) an apparatus for estimating downhole lateral vibrations of a drill tubular placed in a borehole penetrating earth or a component coupled to the drill tubular    (2) a non-transitory computer-readable medium comprising a set of instructions for estimating downhole lateral vibrations of a drill tubular placed in a borehole penetrating earth or a component coupled to the drill tubular.    DESCRIPTION OF DRAWING(S) - The drawing shows a graph representing a comparison of downhole lateral vibration data obtained from a downhole sensor with lateral vibration data estimated from measurements of surface parameters of a drill string.    Lateral vibration estimate plot (20)    Lateral vibration estimate plot (21)