The generalized spherical harmonics, which arise as representations of the rotation group, provide a natural basis for the expansion of tensors of any order in spherical co-ordinates. By using the covariant differentiation rules of Burridge, it is possible to obtain economically the separated differential equations of elastic vibration in a radially symmetric sphere. Derivation of the excitation of an Earth model by a point force or point dislocation is also carried out with the aid of these functions. While all the results obtained are known, the methods used have a substantially greater simplicity than conventional methods.

Active and passive seismic experiments show that the southern Sierra, despite standing 1.8 to 2.8 kilometers above its surroundings, is underlain by crust of similar seismic thickness, about 30 to 40 kilometers. Thermobarometry of xenolith suites and magnetotelluric profiles indicate that the upper mantle is eclogitic to depths of 60 kilometers beneath the western and central parts of the range, but little subcrustal lithosphere is present beneath the eastern High Sierra and adjacent Basin and Range. These and other data imply the crust of both the High Sierra and Basin and Range thinned by a factor of 2 since 20 million years ago, at odds with purported late Cenozoic regional uplift of some 2 kilometers.

Abstract. 21 well-distributed teleseisms (30 ø to 100 ø distance) were recorded by mixed broadband (BB) and short-period (SP) seismic arrays at Mineral King (MK) and Horseshoe Meadow (HM) in the southern Sierra Nevada and at Darwin Plateau (DP) between the Inyo and Argus ranges. These arrays permit identification and separation of direct P and S arrivals, reflections from topography, scattered energy, and arrivals from different back azimuths (multipath arrivals). P-to-S conversions can be identified from beamed BB or SP seismograms. Least squares time domain processing recovered single-event receiver functions from these beamed seismograms. Converted phases attributable to the Moho are clear and uncomplicated at DP; Ps-P times of 3.9-4.2 s correspond to crustal thicknesses of 31-33 km, assuming a mean P crustal velocity of 6.2 km/s and a Poisson's ratio (v) of 0.255. Ps-P times at HM (eastern Sierra) are 3.9-4.6 s (32-37 km) excepting some unusual seismograms from events at back azimuths of 2250-239 ø. MK (western Sierra) times for Ps-P show a strong E-W asymmetry: 3.9-4.1 s (31-33 kin) from the east, and 4.8-5.3 s (39-42 km) from the west. The MK arrivals from the east are multiple and substantially weaker by comparison with HM and DP. These results confirm the absence of a thick crust under the southern High Sierra inferred from both a refraction experiment coincident with this experiment and some earlier studies. At DP the Moho event follows an intracrustal negative polarity event defining the top of an S wave low-velocity zone. This feature dips west under the Sierran crest at HM but is absent farther west at MK. This feature appears to be a manifestation of extensional strain and thus indicates that the surficially undeformed Sierra overlies a tectonized lower crust. Sub-Moho energy is absent under the Basin and Range (DP) but is conspicuous under the High Sierra at positive arrivals -7.3 s (MK) and -9 s (HM) after the P. These arrivals might be from the base of a low-velocity, low-density upper mantle body supporting the Sierra.

Long‐period P waves from distant earthquakes have been analyzed from seismograms recorded at Albuquerque and Bermuda in the light of Haskel's theory of the spectral response of a layered crust. By using the ratio of the vertical spectrum to the horizontal component spectrum, we obtain a function which depends on structure beneath the station. Because of the poorly understood nature of the signal which follows the first P wave motion, the methods of power spectrum analysis are applied and a lag window selected to discriminate against long time correlations within the signal. Corrections for the differing responses of the three components are made by using the power spectral matrix of calibration signals. A range of crustal models has been found which agrees with the data. We are restricted primarily in choosing models for the lower half of the crust; variations of structure in the upper half do not noticeably affect the theoretical curves in the period range considered (0.02 to 0.20 cps). At Albuquerque the crust is about 40 km thick and the lower crust has velocities in the range 6.6 to 7.0 km/sec. The Mohorovicic (M) discontinuity under Bermuda is 12 km below sea level, and the structure appears to be a normal oceanic crust depressed elastically by the weight of the volcanics which compose the island.

COCORP seismic reflection profiling in the western and northern Mojave Desert of southern California has revealed the presence of numerous major low‐angle reflecting horizons within the crust. These complex, though laterally continuous, horizons are interpreted to represent major southwesterly dipping crustal fault zones, and as such they place important constraints on the tectonic evolution of the region. The upper‐most horizon is interpreted to be the Rand thrust, which, where exposed, places Precambrian and Late Cretaceous crystalline rocks over possibly younger Pelona‐Rand‐Orocopia Schist. This reflecting horizon extends for 25 km southwest of the Rand Mountains where it appears to be truncated at a depth of about 7.4 km by another horizon, which may be a later low‐angle normal fault. The other reflecting horizons are not traceable to the surface, and so greater ambiguity remains in their interpretation. The most prominent of these horizons occurs at midcrustal depths (15±6 km), exhibits a “ramp and flat” geometry, and extends over the northern area of the Mojave survey into the Basin and Range Province. A lower horizon, at depths of 20–30 km in the northern part of the survey area, is antiformal and appears to terminate above a flat and relatively continuous Moho‐depth horizon. The crustmantle transition appears to be represented by a continuous series of reflections which occur at about 10 s (33 km) in the north of the survey and at about 8–9 s (26–29 km) in the south. These reflections are offset in the vicinity of the town of Mojave. The deep intracrustal fault zones inferred from the COCORP survey may represent (1) the deep crustal continuation of the system of Mesozoic thrusts which crops out in southern Nevada and southeastern California, (2) Late Cretaceous to Early Cenozoic, northeast‐vergent thrusts related to the uplift of the Pelona‐Orocopia‐Rand Schist, or (3) low‐angle normal faults related to Early Miocene, northeast‐southwest directed crustal extension. The COCORP survey also traversed the major strike‐slip faults that bound the Mojave block. The San Andreas fault zone appears to truncate reflectors at depths of 6, 8 and 20 km within the Mojave basement, suggesting that it is a major vertical feature which extends to at least 20 km depth. Conversely, the Garlock fault does not offset an underlying reflecting horizon which occurs at 9 km depth and therefore appears to be a relatively shallow crustal feature.