It has been known for decades that the present-day shortening rates across the Western Transverse Ranges (WTR) in southern California are rapid, reaching 10-15 mm/yr near the heavily populated Los Angeles area. However, only recently have geodetic measurements of vertical motion in the WTR been sufficiently dense to resolve a tectonic vertical signal. In this study, we show that much of the geodetically-derived vertical velocity field in the WTR can be attributed to the interseismic signal of strain accumulation on reverse faults. We invert geodetic and geologic data for slip rate and interseismic coupling on faults using a kinematic model consisting of faults embedded in an elastic crust over an inviscid mantle. This method allows us to infer the permanent, long-term component of vertical motions from recoverable, short term motions. We infer that much of the geodetically observed 3-4 mm/yr of differential vertical motion across the WTR, involving subsidence along the Santa Barbara coastline and uplift of the Santa Ynez Range, can be attributed to recoverable elastic deformation associated with interseismic locking on faults dipping under the WTR. The sum of dip-slip rates across the WTR decreases from 10.5-14.6 mm/yr on the east side near Ventura, California to 5-6.2 mm/yr across the western side of the Santa Barbara Channel. The total moment accumulation rate in both the Santa Barbara Channel and the combined San Fernando Valley-LA Basin regions is equivalent to about two M=7 earthquakes every 100 years.