We use accelerograms, seismograms, and data from sparse continuous Global Positioning System (GPS) and campaign‐mode GPS stations, deployed along the Pacific coast of Mexico, to study scaling of horizontal peak ground displacement (PGD) with seismic moment (M0) in the epicentral zone above the Mexican subduction thrust. The thrust interface is located at a depth of 25  km below the coast. We select recordings with (SP) time 5.9  s (R46  km) and reduce the amplitudes to (SP) time of 3.2 s (R  =  25  km). The dataset consists of 58 events and covers a M0 range of 10131021  N·m. We find that the double integration of accelerograms, using piecewise linear detrending schemes, leads to sufficiently accurate estimation of PGD to study the scaling relation. The sparse data for great earthquakes are complemented with theoretical static displacement computed using the model of Okada (1992). For earthquakes with M01.26×1018  N·m (Mw6.0) the point‐source, far‐field approximation holds, and the PGD data follows theoretically expected M02/3 scaling. For great earthquakes (M0>1.26×1021  N·m; Mw>8.0), static offset (which is approximately equivalent to PGD) scales as M01/3. About two‐thirds of the observed PGD data fall within a factor of 0.67 and 1.5 of the relation given above. The relationship may be useful in earthquake engineering as well as for rapid estimation of magnitude for early tsunami alert.

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