A summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented in this tutorial. An examination of the underlying time series model assumed by each technique serves as the common basis for understanding the differences among the various spectrum analysis approaches. Techniques discussed include the classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods. A summary table in the text provides a concise overview for all methods, including key references and appropriate equations for computation of each spectral estimate.

Spectrum analysis&#8212;A modern perspective

Fifteen andesite-dacite stratovolcanoes on the volcanic front of a single segment of the Andean arc show along-arc changes in isotopic and elemental ratios that demonstrate large crustal contributions to magma genesis. All 15 centers lie 90 km above the Benioff zone and 280±20 km from the trench axis. Rate and geometry of subduction and composition and age of subducted sediments and seafloor are nearly constant along the segment. Nonetheless, from S to N along the volcanic front (at 57.5% SiO2) K2O rises from 1.1 to 2.4 wt %, Ba from 300 to 600 ppm, and Ce from 25 to 50 ppm, whereas FeO*/MgO declines from >2.5 to 1.4. Ce/Yb and Hf/Lu triple northward, in part reflecting suppression of HREE enrichment by deep-crustal garnet. Rb, Cs, Th, and U contents all rise markedly from S to N, but Rb/Cs values double northward — opposite to prediction were the regional alkali enrichment controlled by sediment subduction. K/Rb drops steeply and scatters greatly within many (biotite-free) andesitic suites. Wide diversity in Zr/Hf, Zr/Rb, Ba/Ta, and Ba/La within and among neighboring suites (which lack zircon and alkali feldspar) largely reflects local variability of intracrustal (not slab or mantle) contributions. Pb-isotope data define a limited range that straddles the Stacey-Kramers line, is bracketed by values of local basement rocks, in part plots above the field of Nazca plate sediment, and shows no indication of a steep (mantle+sedimentary) Pb mixing trend. 87Sr/86Sr values rise northward from 0.7036 to 0.7057, and 143Nd/144Nd values drop from 0.5129 to 0.5125. A northward climb in basal elevation of volcanic-front edifices from 1350 m to 4500 m elevation coincides with a Bougueranomaly gradient from −95 to −295 mgal, interpreted to indicate thickening of the crust from 30–35 km to 50–60 km. Complementary to the thickening crust, the mantle wedge beneath the front thins northward from about 60 km to 30–40 km (as slab depth is constant). The thick northern crust contains an abundance of Paleozoic and Triassic rocks, whereas the proportion of younger arc-intrusive basement increases southward. Primitive basalts are unknown anywhere along the arc. Base-level isotopic and chemical values for each volcano are established by blending of subcrustal and deep-crustal magmas in zones of melting, assimilation, storage and homogenization (MASH) at the mantle-crust transition. Scavenging of mid-to upper-crustal silicic-alkalic melts and intracrustal AFC (prominent at the largest center) can subsequently modify ascending magmas, but the base-level geochemical signature at each center reflects the depth of its MASH zone and the age, composition, and proportional contribution of the lowermost crust.

Crustal contributions to arc magmatism in the Andes of Central Chile

Analysis of the sedimentary, volcanic, structural, and metamorphic chronology in mountain belts, and consideration of the implications of the new global tectonics (plate tectonics), strongly indicate that mountain belts are a consequence of plate evolution. It is proposed that mountain belts develop by the deformation and metamorphism of the sedimentary and volcanic assemblages of Atlantic-type continental margins. These assemblages result from the events associated with the rupture of continents and the expansion of oceans by lithosphere plate generation at oceanic ridges. The earliest assemblages thus developed are volcanic rocks and coarse clastic sediments deposited in fault-bounded troughs on a distending and segmenting continental crust, subsequently split apart and carried away from the ridge on essentially aseismic continental margins. As the continental margins move away from the ridge, nonvolcanic continental shelf and rise assemblages of orthoquartzite-carbonate, and lutite (shelf), and lutite, slump deposits, and turbidites (rise) accumulate. This kind of continental margin is transformed into an orogenic belt in one of two ways. If a trench develops near, or at, the continenal margin to consume lithosphere from the oceanic side, a mountain belt (cordilleran type) grows by dominantly thermal mechanisms related to the rise of calc-alkaline and basaltic magmas. Cordilleran-type mountain belts are characterized by paired metamorphic belts (blueschist on the oceanic side and high temperature on the continental side) and divergent thrusting and synorogenic sediment transport from the high-temperature volcanic axis. If the continental margin collides with an island arc, or with another continent, a collision-type mountain belt develops by dominantly mechanical processes. Where a continent/island arc collision occurs, the resulting mountains will be small (e.g., the Tertiary fold belt of northern New Guinea), and a new trench will develop on the oceanic side of the arc. Where a continent/continent collision occurs, the mountains will be large (e.g., the Himalayas), and the single trench zone of plate consumption is replaced by a wide zone of deformation. Collision-type mountain belts do not have paired metamorphic belts; they are characterized by a single dominant direction of thrusting and synorogenic sediment transport, away from the site of the trench over the underthrust plate. Stratigraphic sequences of mountain belts (geosynclinal sequences) match those asciated with present-day oceans, island arcs, and continental margins.

Mountain belts and the new global tectonics

A comprehensive study of the observations of seismology provides widely based strong support for the new global tectonics which is founded on the hypotheses of continental drift, sea-floor spreading, transform faults, and underthrusting of the lithosphere at island arcs. Although further developments will be required to explain certain part of the seismological data, at present within the entire field of seismology there appear to be no serious obstacles to the new tectonics. Seismic phenomena are generally explained as the result of interactions and other processes at or near the edges of a few large mobile plates of lithosphere that spread apart at the ocean ridges where new surficial materials arise, slide past one another along the large strike-slip faults, and converge at the island arcs and arc-like structures where surficial materials descend. Study of world seismicity shows that most earthquakes are confined to narrow continuous belts that bound large stable areas. In the zones of divergence and strike-slip motion, the activity is moderate and shallow and consistent with the transform fault hypothesis; in the zones of convergence, activity is normally at shallow depths and includes intermediate and deep shocks that grossly define the present configuration of the down-going slabs of lithosphere. Seismic data on focal mechanisms give the relative direction of motion of adjoining plates of lithosphere throughout the active belts. The focal mechanisms of about a hundred widely distributed shocks give relative motions that agree remarkably well with Le Pichon's simplified model in which relative motions of six large, rigid blocks of lithosphere covering the entire earth were determined from magnetic and topographic data associated with the zones of divergence. In the zones of convergence the seismic data provide the only geophysical information on such movements.

Two principal types of mechanisms are found for shallow earthquakes in island arcs: The extremely active zone of seismicity under the inner margin of the ocean trench is characterized by a predominance of thrust faulting, which is interpreted as the relative motion of two converging plates of lithosphere; a less active zone in the trench and on the outer wall of the trench is characterized by normal faulting and is thought to be a surficial manifestation of the abrupt bending of the down-going slab of lithosphere. Graben-like structures along the outer walls of trenches may provide a mechanism for including and transporting sediments to depth in quantities that may be very significant petrologically. Large volumes of sediments beneath the inner slopes of many trenches may correspond, at least in part, to sediments scraped from the crust and deformed in the thrusting.

Simple underthrusting typical of the main zone of shallow earthquakes in island arcs does not, in general, persist at great depth. The most striking regularity in the mechanisms of intermediate and deep earthquakes in several arcs is the tendency of the compressional axis to parallel the local dip of the seismic zone. These events appear to reflect stresses in the relatively strong slab of down-going lithosphere, whereas shearing deformations parallel to the motion of the slab are presumably accommodated by flow or creep in the adjoining ductile parts of the mantle. Several different methods yield average rates of underthrusting as high as 5 to 15 cm/yr for some of the more active arcs. These rates suggest that temperatures low enough to permit dehydration of hydrous minerals and hence shear fracture may persist even to depths of 700 km. The thickness of the seismic zone in a part of the Tonga arc where very precise hypocentral locations are available is less than about 20 km for a wide range of depths. Lateral variations in thickness of the lithosphere seem to occur, and in some areas the lithosphere may not include a significant thickness of the uppermost mantle.

The lengths of the deep seismic zones appear to be a measure of the amount of under thrusting during about the last 10 m.y. Hence, these lengths constitute another ‘yardstick’ for investigations of global tectonics. The presence of volcanism, the generation of many tsunamis (seismic sea waves), and the frequency of occurrence of large earthquakes also seem to be related to underthrusting or rates of underthrusting in island arcs. Many island arcs exhibit a secondary maximum in activity which varies considerably in depth among the various arcs. These depths appear, however, to correlate with the rate of underthrusting, and the deep maxima appear to be located near the leading (bottom) part of the down-going slab. In some cases the down-going plates appear to be contorted, possibly because they are encountering a more resistant layer in the mantle. The interaction of plates of lithosphere appears to be more complex when all the plates involved are continents or pieces of continents than when at least one plate is an oceanic plate. The new global tectonics suggests new approaches to a variety of topics in seismology including earthquake prediction, the detection and accurate location of seismic events, and the general problem of earth structure.

Seismology and the new global tectonics

At ocean margins where two plates converge, the oceanic plate sinks or is subducted beneath an upper one topped by a layer of terrestrial crust. This crust is constructed of continental or island arc material. The subduction process either builds juvenile masses of terrestrial crust through arc volcanism or new areas of crust through the piling up of accretionary masses (prisms) of sedimentary deposits and fragments of thicker crustal bodies scraped off the subducting lower plate. At convergent margins, terrestrial material can also bypass the accretionary prism as a result of sediment subduction, and terrestrial matter can be removed from the upper plate by processes of subduction erosion. Sediment subduction occurs where sediment remains attached to the subducting oceanic plate and underthrusts the seaward position of the upper plate's resistive buttress (backstop) of consolidated sediment and rock. Sediment subduction occurs at two types of convergent margins: type 1 margins where accretionary prisms form and type 2 margins where little net accretion takes place. At type 2 margins (∼19,000 km in global length), effectively all incoming sediment is subducted beneath the massif of basement or framework rocks forming the landward trench slope. At accreting or type 1 margins, sediment subduction begins at the seaward position of an active buttress of consolidated accretionary material that accumulated in front of a starting or core buttress of framework rocks. Where small-to-medium-sized prisms have formed (∼16,300 km), approximately 20% of the incoming sediment is skimmed off a detachment surface or decollement and frontally accreted to the active buttress. The remaining 80% subducts beneath the buttress and may either underplate older parts of the frontal body or bypass the prism entirely and underthrust the leading edge of the margin's rock framework. At margins bordered by large prisms (∼8,200 km), roughly 70% of the incoming trench floor section is subducted beneath the frontal accretionary body and its active buttress. In rounded figures the contemporary rate of solid-volume sediment subduction at convergent ocean margins (∼43,500 km) is calculated to be 1.5 km³/yr. Correcting type 1 margins for high rates of terrigenous seafloor sedimentation during the past 30 m.y. or so sets the long-term rate of sediment subduction at 1.0 km³/yr. The bulk of the subducted material is derived directly or indirectly from continental denudation. Interstitial water currently expulsed from accreted and deeply subducted sediment and recycled to the ocean basins is estimated at 0.9 km³/yr. The thinning and truncation caused by subduction erosion of the margin's framework rock and overlying sedimentary deposits have been demonstrated at many convergent margins but only off northern Japan, central Peru, and northern Chile has sufficient information been collected to determine average or long-term rates, which range from 25 to 50 km³/m.y. per kilometer of margin. A conservative long-term rate applicable to many sectors of convergent margins is 30 km³/km/m.y. If applied to the length of type 2 margins, subduction erosion removes and transports approximately 0.6 km³/yr of upper plate material to greater depths. At various places, subduction erosion also affects sectors of type 1 margins bordered by small- to medium-sized accretionary prisms (for example, Japan and Peru), thus increasing the global rate by possibly 0.5 km³/yr to a total of 1.1 km³/yr. Little information is available to assess subduction erosion at margins bordered by large accretionary prisms. Mass balance calculations allow assessments to be made of the amount of subducted sediment that bypasses the prism and underthrusts the margin's rock framework. This subcrustally subducted sediment is estimated at 0.7 km³/yr. Combined with the range of terrestrial matter removed from the margin's rock framework by subduction erosion, the global volume of subcrustally subducted material is estimated to range from 1.3 to 1.8 km³/yr. Subcrustally subducted material is either returned to the terrestrial crust by arc-related igneous processes or crustal underplating or is lost from the crust by mantle absorption. Geochemical and isotopic data support the notion that upper mantle melting returns only a small percent of the subducted material to the terrestrial crust as arc igneous rocks. Limited areal exposures of terrestrial rocks metamorphosed at deep (>20–30 km) subcrustal pressures and temperatures imply that only a small fraction of subducted material is reattached via deep crustal underplating. Possibly, therefore much of the subducted terrestrial material is recycled to the mantle at a rate near 1.6 km³/yr, which is effectively equivalent to the commonly estimated rate at which the mantle adds juvenile igneous material to the Earth's layer of terrestrial rock.

/pdf/observations-at-convergent-margins-concerning-sediment-3eqc86cp0u.pdf

Observations at convergent margins concerning sediment subduction, subduction erosion, and the growth of continental crust

A crustal section across the Puerto Rico Trench, from 450 km north to 250 km south of San Juan, was deduced from seismic refraction and gravity data. The result, a refinement of previous work, was made possible through more complete seismic refraction coverage and a program for high-speed electronic computation of two-dimensional gravity problems. On the basis of refraction data, the crust was divided into five layers having compressional wave velocities of 1.54, 2.1, 3.8, 5.6, and 7.0 km/sec. Densities taken from a density-velocity curve compiled by Nafe and Drake are 1.03, 2.0, 2.4, 2.7, and 3.0 gm/cc, respectively. Depths to the Mohorovicic discontinuity were computed from the gravity data using sub-crustal density of 3.4 gm/cc, which corresponds to 8.2 km/sec on the density-velocity curve. (A similar calculation was made using a sub-crustal density of 3.3 gm/cc). Depth to M under the trench is about 20 km decreasing sharply on both sides. Northwards, it reaches a minimum of about 10 km under the Outer Ridge and then deepens gradually to about 13 km beneath the southern margin of the Nares Basin. South of the trench M rises under the Puerto Rico Shelf to about 17 km and then deepens sharply to about 30 km beneath Puerto Rico. South of Puerto Rico the depth decreases again to about 14 km under the Venezuelan Basin.

Depths to M were also obtained by using Airy isostatic anomalies and assuming constant crustal density of 2.67 gm/cc over a mantle of density 3.27 gm/cc. The crustal section thus deduced differs significantly from that obtained when the density structure within the crust was considered.

A crustal section across the Puerto Rico trench

Many geophysical measurements, including seismic refraction, gravity, magnetics, and echo soundings, have been made along the continental margin of eastern North America north of Cape Hatteras in the last twenty years. These have revealed the presence of two sedimentary troughs, one under the shelf, the other in deeper water under the continental slope and rise which are separated by a ridge in the basement near the edge of the shelf. The sediments in the shelf trough have been drilled to a depth of 10,000 ft and are of shallow water character. Cores of the upper part of the sediments of the outer trough have revealed features attributed to slumping, sliding, and turbidity current action, and, in part, sediments similar to the graywackes of Pettijohn's (1949) classification. This sedimentary system is quite comparable to the Appalachian system as restored for early Paleozoic time. The sediments of the inner and outer troughs are similar to those of the Appalachian miogeosyncline and eugeosyncline ( Kay , 1951), respectively, and the basement ridge resembles the Pre-Cambrian axis which separates these two troughs in the Appalachians. While there is no active volcanism in the outer (eugeosynclinal) trough at the present time, evidence of past volcanism is present in the form of partially buried seamounts with large magnetic anomalies. Conditions in the Appalachian eugeosyncline appear to have been similar with but limited volcanism prior to the beginnings of Taconic activity. The gravity calculations reveal an abrupt change in depth of the Mohorovicic discontinuity near the edge of the shelf. There is some indication that the boundary between the crust and the mantle in this area is gradational rather than a sharp discontinuity. The major process necessary to convert the present continental margin into a mountain system is the one which thickens the crust under the outer, or eugeosynclinal trough. Since the miogeosyncline is already based on a crust of continental proportions, its deformation requires only a means of folding and thrusting the surficial sediments. This is but a minor part of the overall tectonic activity.

Continental margins and geosynclines: The east coast of North America north of Cape Hatteras

Seismometer operation for 21 days at Tranquillity Base revealed, among strong signals produced by the Apollo 11 lunar module descent stage, a small proportion of probable natural seismic signals. The latter are long-duration, emergent oscillations which lack the discrete phases and coherence of earthquake signals. From similarity with the impact signal of the Apollo 12 ascent stage, they are thought to be produced by meteoroid impacts or shallow moonquakes. This signal character may imply transmission with high Q and intense wave scattering, conditions which are mutually exclusive on earth. Natural background noise is very much smaller than on earth, and lunar tectonism may be very low.

https://science.sciencemag.org/content/sci/167/3918/455.full.pdf

Passive Seismic Experiment

Unusually long reverberations were recorded from two lunar impacts by a seismic station installed on the lunar surface by the Apollo 12 astronauts. Seismic data from these impacts suggest that the lunar mare in the region of the Apollo 12 landing site consists of material with very low seismic velocities near the surface, with velocity increasing with depth to 5 to 6 kilometers per second (for compressional waves) at a depth of 20 kilometers. Absorption of seismic waves in this structure is extremely low relative to typical continental crustal materials on earth. It is unlikely that a major boundary similar to the crustmantle interface on earth exists in the outer 20 kilometers of the moon. A combination of dispersion and scattering of surface waves probably explains the lunar seismic reverberation. Scattering of these waves implies the presence of heterogeneity within the outer zone of the mare on a scale of from several hundred meters (or less) to several kilometers. Seismic signals from 160 events of natural origin have been recorded during the first 7 months of operation of the Apollo 12 seismic station. At least 26 of the natural events are small moonquakes. Many of the natural events are thought to be meteoroid impacts.

Seismic Data from Man-Made Impacts on the Moon

Spectral analyses of seismograms of the great Chilean earthquake of May 22, 1960, from a newly installed strain seismograph at Ogdensburg, New Jersey, and from pendulum seismographs at Palisades, New York, have revealed spectral peaks corresponding to fundamental spheroidal modes 2 to 34, fundamental torsional modes 2 to 9, and the first overtone of the second spheroidal mode. Other peaks, some of which may be overtones, occur in the spectra but are not yet identified. Amplitudes of some observed spectral peaks vary radically between two time intervals on the same record. The peaks do not decrease in amplitude according to any simple law, and, rarely, an increase in amplitude with time is observed, indicating the apparent acquisition of energy in the mode between the time intervals. The periods of the graver modes of oscillation, both spheroidal and torsional, are in agreement with the theoretical values of Alterman, Jarosch, and Pekeris. The periods of the fundamental spheroidal oscillations between 250 and 500 seconds have been determined very accurately. These periods show excellent agreement with theoretical values calculated by Bolt and Dorman for a mantle with velocities according to the Gutenberg model and densities according to the Bullen model A. Also, phase velocities obtained from these periods are in agreement with Rayleigh wave phase velocities observed directly from the same earthquake by Brune, Nafe, and Alsop. Good agreement is also observed between torsional periods and theoretical values of Sato, Landisman, and Ewing, based on velocities of Jeffreys and densities of Bullen model A.

George H. Sutton

Papers

A crustal section across the Puerto Rico trench

Continental margins and geosynclines: The east coast of North America north of Cape Hatteras

Passive Seismic Experiment

Seismic Data from Man-Made Impacts on the Moon

Free oscillations of the Earth observed on strain and pendulum seismographs