Inversion with exponentially encoded seismic data can include exponentially encoding acquired seismic data and associated synthetic seismic data, storing the exponentially encoded acquired seismic data and the exponentially encoded associated synthetic seismic data, determining a one-dimensional (1D) Wasserstein distance between the exponentially encoded acquired seismic data and the exponentially encoded associated synthetic seismic data, and generating an adjoint source based on the 1D Wasserstein distance. The example method also includes adapting a dynamic weight implementation of a sensitivity kernel to the adjoint source to build a gradient associated with the acquired seismic data and the associated synthetic seismic data, and iteratively inverting a waveform associated with the exponentially encoded acquired seismic data and the exponentially encoded associated synthetic seismic data based on the gradient. An image of a subsurface location can be generated based on results of the iterative inversions.