Optimised spectral merge of the background model in seismic inversion

Abstract The inversion of seismic reflection data to absolute impedance generates low-frequency deviations around the true impedance if the frequency content of the background impedance model does not merge seamlessly into the spectrum of the inverted seismic data. We present a systematic method of selecting a background model that minimises the mismatch between the background model and the relative impedance obtained by inverting the seismic data at wells. At each well a set of well-log relative impedances is formed by passing the impedance log through a set of zero-phase high-pass filters. The corresponding background models are constructed by passing the impedance log through the complementary zero-phase low-pass filters and a set of seismic relative impedances is computed by inverting the seismic data using these background models. If the inverted seismic data is to merge perfectly with the background model, it should correspond at the well to the well-log relative impedance. This correspondence is the basis of a procedure for finding the optimum combination of background model and inverted seismic data. It is difficult to predict the low-frequency content of inverted seismic data. These low frequencies are affected by the uncertainties in (1) measuring the low-frequency response of the seismic wavelet and (2) knowing how inversion protects the signal-to-noise ratio at low frequencies. Uncertainty (1) becomes acute for broadband seismic data; the low-frequency phase is especially difficult to estimate. Moreover we show that a mismatch of low-frequency phase is a serious source of inversion artefacts. We also show that relative impedance can estimate the low-frequency phase where a well tie cannot. Consequently we include a low-frequency phase shift, applied to the seismic relative impedances, in the search for the best spectral merge. The background models are specified by a low-cut corner frequency and the phase shifts by a phase intercept at zero frequency. A scan of the misfit between the well-log and seismic relative impedances as a function of corner frequency and phase intercept then reveals the most consistent combination of the background and relative impedances. The method is illustrated by application to a synthetic example and a broad-band data set.