Topological pumping provides a robust way to transport waves against disorders and defects. Surface wave is a key object studied in seismology and is widely used in electronic devices such as filters, oscillators, and transformers. Here, we extend the topological pumping to the surface wave with synthetic dimension by attaching topologically modulated elastic pillars. To guarantee the eigenmodes are a surface mode, we design the system whose eigenmodes locate below the sound cone. Then, we use the tight-binding model to simplify the problem to discrete matrix equations. After that, we solve the equations by using WKB approximation and obtain the adiabatic theorem. By setting the instantaneous eigenmode from right edge mode to bulk mode to left edge mode, we demonstrate the topological pumping numerically and experimentally. Finally, we discuss the immunization of the topological pumping from disorders and defects.
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