An important application of spectral decomposition (SD) is to identify subsurface geological anomalies such as channels and karst caves, which may be buried in full-band seismic data. However, the classical SD methods including the wavelet transform (WT) are often limited by relatively low time–frequency resolution, which is responsible for false high horizon-associated space resolution probably indicating more geological structures, especially when close geological anomalies exist. To address this issue, we impose a constraint of minimizing an lp (0 < p < 1) norm of time–frequency spectral coefficients on the misfit derived by using the inverse WT and apply the generalized iterated shrinkage algorithm to invert for the optimal coefficients. Compared with the WT and inverse SD (ISD) using a typical l1-norm constraint, the modified ISD (MISD) using an lp-norm constraint can yield a more compact spectrum contributing to detect the distributions of close geological features. We design a 3D synthetic dataset involving frequency-close thin geological anomalies and the other 3D non-stationary dataset involving time-close anomalies to demonstrate the effectiveness of MISD. The application of 4D spectrum on a 3D real dataset with an area of approximately 230 km2 illustrates its potential for detecting deep channels and the karst slope fracture zone.