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Fig. 3.48 Sketch illustrating receiver functions that correspond to three simplified velocity structures. Positive arrivals
correspond to positive velocity contrast (conventionally shown in red); negative arrivals indicate the top of the low
velocity zone (conventionally shown in blue).
104 Seismic structure of the lithosphere
Moho and intracrustal discontinuities
Since the amplitudes of the arrivals in a RF depend on the velocity contrast at the seismic
converter, a boundary with the largest velocity contrast will produce the strongest converted
waves. Therefore, in crustal studies the largest contrast need not necessarily be at the base of
the crust but may be at an intracrustal boundary. For example, in the case of a high-velocity
lowermost crust with Vp~ 7.5 km/s, the velocity contrast at theMohomay be only c. 0.5 km/s,
while the velocity contrast between the middle and the lowermost crust may be as large as
1.0 km/s. In such a case, the RF method will likely image the depth to the sharp intracrustal
interface but not to the Moho. This may be the case in Greenland where conflicting depths
to the Moho have been derived by RF, while refraction results agree with the deepest
determination of the crust–mantle transition (Dahl-Jensen et al., 2003; Kumar et al.,
2007). A similar example comes from Iceland, where the seismic signal from the Moho
boundary varies from undetectable, to gradient zones and discrete discontinuities
(Schlindwein, 2006). The complicated character of the signal is caused by the velocity
structure of the crust, with the layer of rapid velocity increase at 8–14 km depth overlying the
layer with almost constant velocities, which is masking seismic phases from the Moho.
Mantle discontinuities and the S-receiver functions
The RF method based on P-to-S converted waves has a disadvantage in studies of mantle
seismic interfaces located at a depth of c. 70–200 km since in P receiver functions (PRF),
the converted P phases from discontinuities in the mantle arrive in the time interval
dominated by multiple reflections and scattering from crustal discontinuities (not neces-
sarily from the Moho, but from the strongest crustal reflectors) (Fig. 3.50). To overcome
this problem, the RF technique based on the S-to-P conversions has been proposed,
Fig. 3.49 Stacked receiver functions in the Vp/Vs – H domain used to determine the crustal thickness, H, beneath the PAS
station in Southern California. The best estimate is 28 km with a Vp/Vs = 1.73; the ellipse shows the 1σ uncertainty
(Zhu and Kanamori, 2000).
105 3.4 Receiver function (converted waves) studies
in particular to study the depth to the lithosphere base (Farra and Vinnik, 2000). The
S-receiver function technique (SRF) is based on the analysis of S-to-P converted phases
(Sp) at seismic discontinuities in the upper mantle beneath stations. P-waves converted
from a mantle velocity contrast arrive at the station much earlier than the direct S-waves,
while all the multiple crustal reverberations arrive later than the S arrival (Fig. 3.50). Since
high-amplitude direct S-waves can usually be easily identified even when they arrive
within the crustal multiples, the S-receiver function analysis has advantages in studies of
mantle discontinuities. Moreover, gradational boundaries in the mantle with a thickness
of c. 30 km may be transparent at short periods (2–5 s) in PRF, but may be detectable at
longer periods (10–15 s) in SRF.
A detailed discussion of the advantages and limitations of the S-receiver function
technique is presented by Farra and Vinnik (2000) and is summarized here in brief:
* the time advance of the converted phase Sp relative to the direct S-wave depends on the
depth of the discontinuity;
* the amplitude of Sp phase is nearly proportional to the Vs velocity contrast at the
discontinuity;
* the approximate position of the region sampled by the converted phase is at a roughly
similar distance from the seismic station as the depth of the discontinuity;
* the greatest depth sampled by the SRF depends on epicentral distance;
* the method allows for detection of converted phases from the 410 km discontinuity
implying that the SRF method is sensitive to detection of a Vs velocity contrast of
c. 0.2 km/s at a depth of about 400 km.
The apparent velocity of the Sp phase converted from a deep discontinuity may differ from
the apparent velocity of the parent phase. For example, for the Sp phase from the 410 km
discontinuity, the difference between the slowness of the Sp phase and its parent seismic
phase (differential slowness) is around 0.6 s/deg for a standard Earth model. Because of
noise or lateral heterogeneity of the Earth’s structure, the observed slowness (the slowness of
Fig. 3.50 A schematic diagram of P- and S-receiver functions for a seismic converter at 70–200 km depth in the mantle. In
P-receiver functions phases from the mantle converter arrive within the crustal multiples and may not easily be
identified. In contrast, in S-receiver functions it is the direct S-wave that arrives within the crustal multiples (due to
high amplitude it can always be identified), while phases from the mantle converter arrive earlier and can also be
easily identified.
106 Seismic structure of the lithosphere
the trace with maximum amplitude of signal) may deviate from the theoretical predictions
and for the phase converted at a dipping interface differential slowness may diverge from the
standard value by about 0.2 s/deg for a tilt of 1 deg.
3.4.2 Examples of PRF and SRF studies of the crust and the upper mantle
Thickness of Precambrian crust in Greenland
Over the past two decades, receiver function analysis has become a routine technique for
estimating the depth to the Moho. The method has been successfully used, in particular, in
imaging the crust–mantle transition in complex tectonic settings such as subduction zones
(e.g. Bostock et al., 2002; Li et al., 2003b).
One of the most spectacular examples is the RF application to the GLATIS (Greenland
Lithosphere Analysed Teleseismically on the Ice Sheet) seismic data acquired in the interior
parts of Greenland where the crustal thickness was previously completely unknown
(Fig. 3.51) (Kumar et al., 2007; Dahl-Jensen et al., 2003). In spite of the excellent data
quality, RF interpretations for four out of 16 temporally deployed broadband stations were
complicated by strong converted phases generated at the base of the ice sheet (more than
3 km thick in some places). Since RF analysis is based on the assumption that the observed
Fig. 3.51 Individual receiver functions (RFs) from all events used at the permanent seismic station DAG on the coast of
northern East Greenland (a), the sum of the normal move-out-corrected individual RFs (a positive Ps has a peak
to the right) (b), the distance in degrees (black symbols) and azimuth in degrees (gray symbols) for each
event (c), and a plot of stack energy for various VP/VS ratios and the depth to Moho. VP is assumed to be 6.5 km/s
(from Dahl-Jensen et al., 2003).
107 3.4 Receiver function (converted waves) studies
wavefield is acquired at the free surface of an elastic half-space, seismic data collected on
ice and on the ocean bottom have an added complication for RF interpretations as the time
series constrained by standard methods may contain scattered energy from the ice or water
column.
Receiver function studies in Greenland revealed significant lateral variations in the
depth to the Moho. While the extended crust along the coast of East Greenland is less than
30 km thick, the Proterozoic part of central Greenland (north of the Archean core) has
the largest values with an average depth to Moho close to 48 km (Fig. 3.52). Further to the
north the Proterozoic crust is thinner, 37–42 km; similar values (around 40 km) were
determined for the Archean crust in southern Greenland. Variations of 6–8 km in