Introduction

In Chapter 6 we introduced the important concept of tapering a time series as a way of obtaining a spectral estimator with acceptable bias properties. While tapering does reduce bias due to leakage, there is a price to pay in that the sample size is effectively reduced. When we also smooth across frequencies, this reduction translates into a loss of information in the form of an increase in variance (recall the Ch factor in Equation (248b) and Table 248). This inflated variance is acceptable in some practical applications, but in other cases it is not. The loss of information inherent in tapering can often be avoided either by prewhitening (see Sections 6.5 and 9.10) or by using Welch's overlapped segment averaging (WOSA – see Section 6.17).

In this chapter we discuss another approach to recovering information lost due to tapering. This approach was introduced in a seminal paper by Thomson (1982) and involves the use of multiple orthogonal tapers. As we shall see, multitaper spectral estimation has a number of interesting points in its favor:

1. In contrast to either prewhitening which typically requires the careful design of a prewhitening filter or the conventional use of WOSA (i.e., a Hanning data taper with 50% overlap of blocks) which can still suffer from leakage for spectra with very high dynamic ranges, the multitaper scheme can be used in a fairly ‘automatic’ fashion. Hence it is useful in situations where thousands – or millions – of individual time series must be processed so that the pure volume of data precludes a careful analysis of individual series (this occurs routinely in exploration geophysics).

2. […]