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Nowadays, the most successful applications of full‐waveform inversion (FWI) involve marine seismic data under acoustic approximations. Elastic FWI of land seismic data is still challenging in theory and practice. Here, we propose a full dispersion spectrum inversion method and apply it to seismic data acquired in West Antarctica. Inspired by the conventional surface wave dispersion curve inversion method, we propose to invert the surface wave dispersion spectrum instead of the complicated waveforms. We compare the frequency‐velocity, frequency‐slowness, and frequency‐wavenumber spectra in terms of their ability to resolve dispersion modes and the feasibility of their adjoint updates and conclude that the frequency‐slowness spectrum is the best for our inversion objectives. We test four objective functions, subtraction, zero‐lag crosscorrelation, optimal transport, and the local‐crosscorrelation to quantify the spectrum mismatch and provide the corresponding adjoint source. We then theoretically analyze the convexity of the proposed objective functions and examine their convergence behavior using numerical examples. We also compare the proposed method with the classic FWI method and the traditional surface wave dispersion curve inversion method and discuss the strengths and weaknesses of each method. This technique is employed to evaluate the shallow velocity structures beneath a seismic array stationed in West Antarctica. Our proposed inversion scheme is also useful for more general applications such as imaging the shallow subsurface of the critical zones, like geothermal reservoirs, and CO2 storage sites. Plain Language Summary: Seismic full‐waveform inversion (FWI) is a cutting‐edge inversion method used for uncovering the Earth's subsurface structure. With the growing interest in clean energy and CO2 sequestration, exploring the subsurface in land is becoming crucial. However, there are only a few success stories of seismic FWI applied to land data mainly because of the complexity of the near‐surface and the increased nonlinearity of the problem. Here, we propose a full dispersion spectrum inversion method that seeks optimal velocity models in the subsurface by matching the seismic dispersion spectra. Dispersion spectra are the skeleton of seismic surface waves, which are simpler to quantify yet retain the key dispersion information of surface waves. It is generally easier for humans, as well as algorithms, to match simplified representations of the observed and simulated data, such as the dispersion spectrum, instead of the seismic waveforms themselves. The proposed method expands conventional 1D dispersion curve inversion to multiple dimensions and is accomplished under the framework of FWI. The proposed inversion method applies to seismic imaging applications in exploration and global seismology. Key Points: We propose a full dispersion spectrum inversion method for imaging the near‐surface and apply it to seismic array data collected in West AntarcticaThe surface wave frequency‐slowness spectrum is preferred over the frequency‐velocity and the frequency‐wavenumber spectra to measure the misfit in the proposed inversionThe optimal transport objective function is immune to cycle skipping but has a lower model resolution [ABSTRACT FROM AUTHOR]