A Scattered-Wave Image of Subduction Beneath the Transverse Ranges


Justin Revenaugh
Institute of Tectonics,
Earth Sciences,
University of California,
Santa Cruz, CA 95064

SECTIONS
Abstract Introduction Methods Results Discussion Summary References Figure Captions
ABSTRACT
Over 5600 short-peiord recordings of teleseismic events are used to create deterministic maps of P-wave scatterers in the upper mantle beneath southern California. Between depths of 50 and 200 km, the southern flank of the slab subducting beneath the Transverse Ranges is marked by strong scattering. The marked scattering indicates that the edge of the slab is a sharp thermal boundary. Such a boundary could be produced by slab shearing or small-scale convection in the surrounding mantle. The northern limb of the slab is not a strong scatterer, consistent with thicker lithosphere north of the Transverse Ranges.

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INTRODUCTION
The Transverse Ranges comprise a distinct physiographic province the cuts across the dominant, north by northwest, tectonic fabric of Southern California and showcases some of the most spectacular topography in North America. The mantle beneath the ranges, home of a 60-km-wide tabular velocity anomaly to depths in excess of 200 km(1, 2), is no less spectacular. This curtain of high P-wave velocity draped from the Transverse Ranges is commonly agreed to be subducted subcrustal lithosphere resulting from >5 Ma of oblique convergence across the San Andreas fault zone (3, 4), but the details of the anomaly are unclear. For instance, is subduction one-sided or two (5)? Does the anomaly extend from the base of the crust or does it only appear at greater depths (6)? And where does the slab detach from the crust? The subhorizontal crustal detachments beneath Los Angeles and the Ventura Basin-poorly understood but capable of great earthquakes (7)-are tied to deeper detachments of the Transverse Ranges.

In this study, I present a mode of imaging crust and upper mantle structure that uses singly scattered energy within the coda of teleseismic P. The method, known as Kirchhoff coda migration (8), allows imaging of short length scale (~2 km) velocity and density heterogeneity and structures transparent to travel-time tomography. The scattered-wave images are not as intuitive as tomography's, but the combination of the two methods is powerful. I applied Kirchhoff coda migration to 13 years of teleseismic seismicity recorded by the Southern California Seismograph Network (SCSN) to map loci of significant scatterers between depths of 50 and 200 km. The results confirm intracontinental subduction and point out asymmetry in lithospheric structure across the Transverse Ranges.

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METHODS
In Kirchhoff coda migration (KCM), the subsurface is treated as a collection of closely spaced isotropic point scatterers, and travel times of scattered energy are computed such that each subsurface point is mapped to time in the coda (8). The sum, correctly normalized, of data along the arrival-time surface of a scatterer measures the scatterer's strength (Fig. 1).

S(x). The size of S(x) required to be significantly above background levels is obtained by replacing S(x) with its cumulative probability of occurrence in noise-only data, obtained from repeated migration of trace sets with randomized station associations resulting in bootstrap approximation of S(x) probability density in the absence of coherent, singly scattered energy (12). Assigning seismograms to stations at random destroys the correlation structure of data without affecting amplitude-distance ratios or geographic variation in station density and source-station geometry, thus site and geometrical effects are accounted for that would otherwise severely bias estimation (13).

The data set consists of short-period, vertical component recordings of 120 teleseismic events of intermediate and deep circum-Pacific earthquakes between 1981 and 1993. Records were obtained from 232 stations with an average of 47 stations per event. In total, 5606 seismograms were input to migration. A minimum of 500 contributing seismograms at each grid point was imposed, and migration was not performed for regions outside the SCSN with poor azimuthal station coverage. Variations in detector efficiency across the SCSN raise and lower the detection threshold such that some strong scatterers may be missed in regions of poor detection whereas globally weaker, but locally strong, scatterers in other areas are detected (Fig. 2). For the most part, variations of S(x) about the bootstrap mean closely mimic scatterer significance such that high significance usually implies high scattering strength. To avoid confusion, however, I refer to scatterer significance as potential, such that high potential implies highly probable detection of scattered energy. Synthetic tests are used to help distinguish detector efficiency from scatterer strength and to identify experimental artifacts.

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RESULTS
The images show that from 75 km depth to at least 150 km (Figures 2b, c and d), a single feature dominates the scattering field: a nearly east-west trending ridge of high potential centered on 34N and strongest between 119W to 116W (14). The ridge correlates well with the southern limb of the tabular velocity anomaly imaged beneath the central and eastern Transverse Ranges by a number of tomographic studies (1, 2). Although I performed migration to depths of 400 km, resolution is poor below 200 km, and it is difficult to assign a maximum depth to the ridge, although there is some evidence of a signature to 250 km. Between 75 and 200 km, where resolution is best, prominent along-strike variations in potential appear to be relatively consistent with depth. I attribute some of this consistency to vertical leakage of energy during KCM, but synthetic tests suggest that significant leakage does not exceed 25 km at these depths, and I regard the vertical continuity of potential highs and lows as genuine. The ridge also appears to shift slightly to the north as depth increases, suggesting a nearly vertical northward dip, although this interpretation is debatable given the diffuse quality of the image. I refer to feature as the 34N High.

An equivalent northern limb to the Transverse Ranges anomaly is not seen although there are hints of coherent patterns in the 50 to 100 km images near 35.25N on the western edge of the study area. Synthetic tests (Fig. 3) show that a second ridge displaced 0.5 to 1.5 degrees N, but otherwise similar to the 34N High, would be imaged. Clearly any northern parallel to the 34N High is weak in comparison.

The diffuse zone of potential highs north of 35.5N in the southern Sierra Nevada (~118.5W) at a depth of 50 to 100 km (Figure 2a, b, and c) may be related to the Lake Isabella anomaly, a 3 to 5% high velocity patch in the uppermost mantle (15). Above 100 km there is intriguing visual correlation between potential highs and high gradient zones in independently obtained velocity tomograms, but potential fades rapidly below 100 km while the tomographic anomaly extends to ~200 km. This discrepancy has implications for the 34N High.

The basic structural elements in the uppermost mantle beneath southern California are well defined by tomographic maps of P wave velocity; the scattered-wave images add detail to this structural picture and raise two related questions: (i) How does the near- vertical, slab-like Transverse Ranges velocity anomaly scatter teleseismic P waves? (ii) Why is the scattering asymmetric, that is, why isn't the northern limb of the anomaly seen?

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DISCUSSION
Humphreys and Hager (4) modeled the Transverse Ranges velocity anomaly as the paired subcrustal lithospheres of North America and the Pacific subducting vertically to 250 km beneath the eastern Transverse Ranges, shallowing to 100 km on the western margin. The 3.5% velocity perturbation associated with the anomaly implies a slab ~60 km wide having temperatures 4000-550 degrees C colder than the surrounding mantle. Scattering along the southern limb of the anomaly requires that the length scale of velocity variation, a, is much less than the seismic wavelength, l = 2PI/k (16). The wavelength of incoming teleseismic P ranges from about 3 to 15 km with peak energy near 8 km, implying scatterer length scales certainly less than 10 km and likely less than 5 km. A 60-km wide slab initially 750 degrees cooler than the surrounding mantle, allowed to cool for 2 Ma (17), would have horizontal temperature gradients about 10 to 20 degrees C/km, resulting in velocity gradients of 0.1 to 0.2% per km. Thus the most favorable combination of scattering sampling length and velocity gradient results in a velocity perturbation of 2%, but 0.5% is more realistic. 2% is sufficient if the geometry of heterogeneity favors scattering and energy is scattered more or less isotropically over the 70 degree range of scattering angles sampled, but neither of these conditions is easily reconciled with a near-vertical, tabular thermal anomaly-a poor scatterer of near-vertical P waves whose smooth horizontal velocity gradients favor coherent reflection (directionally dependent radiation) over aziumthally isotropic scattering.

Additional insight into the scattering strength of downwelling mantle can be gleaned from vanishing of the Lake Isabella scattering signature below 100 km. Jones et al. (15) attribute the tomographic anomaly to downwelling in the mantle. Above 100 km where the thermal contrasts have had little time to diffuse and remain sharp, the anomaly is apparent in the scattering image, but at greater depths the increasingly broad diffusive boundaries lose their scattering signature despite having greater overall velocity contrast. The Transverse Ranges anomaly ought to behave similarly.

The inadequacy of simple slab geometry and the vertical continuity of high potential sites along the 34N High suggest an alternative: scattering from slab corners produced by simple shear during oblique subduction. I favor a shearing mechanism, as depicted in Fig. 4: it not only produces corners which radiate energy out in all directions, but also enhances the contrast in temperatures by exposing cooler (core) lithosphere to the surrounding mantle. Corners produced by shear may correspond to the high potential patches at 75 to 150 km in the P to P migration images (18). The block-like character of the Transverse Ranges anomaly in the tomographic studies is consistent with the notion of pervasive shear planes, and there is some correspondence between the block edges and the loci of high scattering potential along the southern limb of the anomaly. The prominent breaks in along-strike geometry of the Transverse Ranges at the junctures of the western San Emigdio/Pine Mountain, central San Gabriel, and eastern San Bernardino segments might be mirrored in breaks in the down going slab. Diffusive erosion of thermal anomalies at shear corners ultimately destroys the scattering signal (19). Slow clockwise rotation of the San Andreas in the Big Bend region (3), if it is occurring, might maintain scattering at depth by increasing slab shear during subduction.

Scattering from shear corners, as part of deformation mandated by oblique subduction (4), appears capable of explaining the 34N High. It does not, however, explain the absence of scattering from the northern limb of the Transverse Ranges anomaly, which I propose is due to subduction of less active (i.e., more thermally mature) lithosphere north of the Transverse Ranges, reducing the temperature contrast along shear planes and slab corners. There are alternatives to this scenario. (i) Subduction is itself asymmetric (one- sided), producing high temperature gradients where cool lithosphere recently at the base of the crust comes into direct contact with the mantle. A south-over-north geometry correctly locates scattering along the southern edge of the tomographic anomaly, but conflicts with the slight northward dip of the 34N High and the symmetry of the tomographic anomaly viewed perpendicular to the Transverse Ranges (2). One-sided subduction also requires Pacific lithosphere to move around, rather than through, the Big Bend region, which seems implausible. (ii) If the proposed mechanism for the 34N High is correct, asymmetric scattering would result if North American lithosphere is converging perpendicular to the Transverse Ranges and no shear during subduction is required. I do not favor this case because, north of the Garlock fault, the San Andreas fault system trends at roughly a 45 degree angle to the Transverse Ranges, suggesting oblique convergence north of the Transverse Ranges as well. (iii) The large lateral temperature contrasts associated with pervasive shear as illustrated in Fig. 4 would superpose small- scale structure upon regional convective flow. While this would hasten dispersal of the thermal anomaly (and hence the scatterer), it could augment scattering strength along portions of the slab's southern limb, with absence of a northern high potential ridge attributed to lower temperatures (and higher viscosity) resulting in laminar flow. Whether small-scale convective flow is a strong source of scattering and/or responsible for the marked north-south asymmetry is difficult to say, but it is a potential contributor to the 34N High.

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SUMMARY
Subduction of subcrustal lithosphere beneath the Transverse Ranges is apparent in the scattering signature of the mantle and broadly agrees with tomographic estimates of size, shape and location. That it scatters efficiently requires something more than broad, diffusive temperature gradients between the slab and mantle and I propose scattering from through-going shear planes in the slab that result from oblique convergence. The north-south symmetry of the velocity anomaly is not mirrored in the scattering response which is much weaker along the northern limb, suggesting that the cooler, thicker lithosphere north of the Big Bend region of the San Andreas does not have sufficiently sharp thermal gradients to scatter short-period P waves.

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REFERENCES AND NOTES
  1. S. A. Raikes, Geophys J. R. Astron. Soc. 63, 187 (1980); G. Hu, W. Menke, C. Powell, J. Geophys. Res. 99, 15,245 (1994).
  2. E. D. Humphreys and R. W. Clayton, J. Geophys. Res. 95, 19,725 (1990).
  3. P Bird and R. W. Rosenstock, Geol. Soc. Am. Bull. 95, 946 (1984).
  4. E. D. Humphreys and B. H. Hager, J. Geophys. Res. 95, 19,747 (1990).
  5. B. Sheffels and M. McNutt, J. Geophys. Res. 91, 6419 (1986). See also (3) and (4).
  6. D. Hadley and H. Kanamori, Geol. Soc. Am. Bull. 88, 1469 (1977). See also (2).
  7. R. S. Yeats, J. Geophys. Res. 88, 569 (1983); E. Hauksson and L. M. Hones, J. Geophys Res. 94, 9569 (1989); T. L. Davis, J. Namson, R. F. Yerkes, J. Geophys. Res. 94, 9644 (1989).
  8. J. Revenaugh, Geophys. Res. Lett. 22, 543 (1995).
  9. First arrivals (teleseismic P) of all records are aligned upon t0. This eliminates delays accrued before entry into the study area and from shallow structure beneath stations.
  10. Travel times are based on the IASP91 model of B. L. N. Kennett in IASPEI 1991 Seismological Tables, B. L. N. Kennett, Ed. (Research School of Earth Sciences, Australian National University, Canberra, 1991), 165 pp. Velocity heterogeneity dephases scattered energy, resulting in lowered stack amplitudes; the use of unsigned data and running means partially alleviates phase incoherence, but reduces resolution.
  11. Nth-root stacking is discussed in P. L. McFadden, B. J. Drummond, S. Kravis, Geophysics 51, 1879 (1986). Linear stacking has n = 1; higher values of n result in better suppression of incoherent energy. We use sixth-root stacking (i.e., n = 6), but results are stable for 1 <= n <= 8.
  12. This is not a true bootstrap, which would approximate the distribution of observed S(x); while that is not without interest, I am most concerned with the significance of scatterer detection which necessitates estimation of the distribution of S(x) in the absence of scattered energy. 1000 bootstrap iterations were performed at each migration point.
  13. Finite source duration and source-side scattering are treated by deconvolution of a generalized source-time function obtained from a linear stack of all stations recorded the event. The bootstrap includes station-side reverberations due to coherent crustal reflections and basin resonances, minimizing their effects on scattering potential.
  14. Synthetic tests of linear arrays of point scatterers at these depths reveal a tendency of KCM to extend scattering beyond its true spatial terminus and to warp the ends down or up depending on location within the SCSN, explaining the "frowns" outside the range 119W to 116W. See Fig. 3.
  15. C. H. Jones, H. Kanamori , S. W. Roecker, J. Geophys. Res. 99, 4567 (1994); see also (2).
  16. This conclusion is reached on the combined basis of: (i) success of the isotropic scattering model (highly directional or very low-angle scattering would be strongly damped); (ii) consistency of results over a range of scattering angles; and (iii) temporal localization of energy on the seismogram (Eq. 2 sums less than 1s of data per seismogram per scatterer), all of which are consistent with ka << 1; K. Aki and P. G. Richards, Quantitative Seismology (Freeman, San Francisco, 1980), 932 pp.
  17. 2 Ma is less than half the duration of subduction (4), thus the predicted boundary layer width is a lower bound favoring scattering.
  18. Scattering from planar contacts within the slab also occurs, but is minor since the radiation pattern is highly directional.
  19. Although it is not possible to directly estimate absolute scattering strength from non- linear stacks, forward modeling suggests that slab-induced P to P single scattering explains only a very small fraction of coda energy, probably less than 5%. Shallow P to P and P to S scattering, P to Rg scattering near the free surface, and multiple scattering comprise most of the P wave coda.
  20. The author thanks Eugene Humphreys and an anonymous reviewer for helpful comments and suggestions. Research supported by the US National Science Foundation. Lunchtime Software Guild contribution number 13.

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FIGURE CAPTIONS
Fig. 1. Schematic illustration of the wave field due to a point scatterer at depth. With seismograms aligned on P, secondary arrivals from the scatterer move out across the array asymmetrically due to finite ray parameter of direct P. Scatterer strength is estimated by summing data along the P to P (or P to S) scattered-wave travel time curve with corrections for propagation effects and wavefront obliquity at the free surface. Modified bootstrap estimation is used to assign significance levels to scatterer detection.

Fig. 2. (a) 50 km depth slice of the Kirchhoff coda migration for southern California. Shown are contours of P to P scattering significance resolved upon a rectangular grid with 0.1 degree node spacing. Values near unity imply highly significant detection of scattered energy. Solid triangles mark stations of the SCSN (additional stations outside the plot bounds were employed). Because of insufficient data or poor azimuthal station coverage, no estimates were made in non-shaded regions. The Transverse Ranges are composed of the San Emigdio/Pine Mountain (SE/PM), San Gabriel (SGM) and San Bernardino (SBM) segments. ISA marks the Lake Isabella mantle anomaly; ST marks the Salton Trough. (b) Depth slice at 75 km. Note the distinct high potential ridge along 34¡N. (c) Depth slice at 100 km. (d) Depth slice at 150 km. (e) Depth slice at 200 km. Because of decreased resolving power, only grid points sampled by more than 2500 seismograms are shown in (d).

Fig. 3. Depth slice at 100 km of a synthetic experiment with two planes of isotropic scatterers aligned along 34N and 35N between 119W and 116W (the northern plane is shifted 0.5 degrees W). Scatterers are placed at 0.5 degrees along strike and every 25 km down dip (80 degrees between 50 and 150 km depth. The synthetic data replicate experimental geometry and include high noise levels, strong signal attenuation and ~1 s travel time variations. The northern plane is well imaged demonstrating that the experimental geometry is favorable for detection of a northern limb to the Transverse Ranges anomaly.

Fig. 4. Schematic depth slice of the Transverse Ranges slab illustrating the relation of slab shear and strong scattering sites. Shear is mandated by oblique subduction (4), although the prominent corners may derive from along-strike breaks in the deformation front along the Transverse Ranges. Shading refers to velocity with dark areas being fast; also shown is a velocity contour spatially averaged as in tomography. Thicker lithosphere and lower thermal gradients north of the slab axis reduce scattering strength at shear corners, explaining the absence of a northern scattering high.

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