Global geophysical networks provide powerful databases to infer globally coherent signals, and array processing techniques are useful for inferring them. In this study, we comprehensively analyze seven spherical harmonic-based array processing techniques: spherical harmonic stacking (SHS) as well as its gridded form (SHS_GT) and grid-interval weighted forms (SHS_GK1, SHS_GK2); matrix SHS (MSHS); multi-station experiment (MSE); and optimal sequence estimation (OSE). We first use more specific synthetic tests to evaluate the pros and cons of these techniques, and estimate bias in solutions caused by the station distributions. These methods are applied to four global observation networks, the Global Geodynamics Project (GGP) Network, the Global Seismographic Network (GSN), the Global Geomagnetic (GGM) Network and the Global GNSS Network. For the first time, we restored a much cleaner sequence for one singlet of the 0S2 mode based on the GGP network, and restored similar result for one singlet of the 3S1 mode based on the GSN network. We further isolate different Ylm-related tidal signals from the GGM network for the first time. Moreover, based on global GNSS observations, we estimate the Love number h21 = 0.6243(±7e−4) − 0.01(±6e−3)i at the Chandler Wobble (CW) frequency with OSE/MSHS (The accuracy of the estimate is an order of magnitude higher than the previous results), and further obtain the corresponding lower-mantle anelasticity (fr(ω) = −29.5 ± 0.9, fi(ω) = 12.0 ± 7.2). Our findings confirm that OSE and MSHS methods can more accurately obtain the complex amplitude of any Ylm-related signal, which is not possible with other methods (and we do obtain more precise results than previous studies upon using them); besides, we also confirm that OSE and MSHS methods can greatly reduce the interference of other signals to the target signals. Hence, we believe the results obtained from the OSE/MSHS will helpful for obtaining reasonable geophysical explanations.