At scale lengths less than 100 km or so, statistical descriptions of seafloor morphology can be usefully employed to characterize ridge crest processes, off‐ridge tectonics and vulcanism, sedimentation, and postdepositional transport. We seek to develop methods for the estimation of seafloor statistics that take into account the finite precision, resolution, and sampling obtained by actual echo sounding systems. In this initial paper we restrict our attention to the problem of recovering second‐order statistics from data sets collected by multibeam devices such as Sea Beam. The seafloor is modeled as a stationary, zero‐mean, Gaussian random field completely specified by its two‐point covariance function. We introduce an anisotropic two‐point covariance function that has five free parameters describing the amplitude, orientation, characteristic wave numbers, and Hausdorff (fractal) dimension of seafloor topography. We formulate the general forward problem relating this model to the statistics of an ideal multibeam echo sounder, in particular the along‐track autocovariance functions of individual beams and the cross‐covariance functions between beams of arbitrary separation. Using these second moments as data functionals, we then pose the inverse problem of estimating the seafloor parameters from realistic, noisy data sets with finite sampling and beamwidth, and we solve this inverse problem by an iterative, linearized, least squares method. The inversion method is applied to Sea Beam transit data from both the Pacific and Atlantic oceans. Sea Beam system noise stands out as a sharp spike on the along‐track autocovariance function and can be modeled as a white noise process whose amplitude generally increases with beam angle. The five parameters in our second‐order model can be estimated from the inversion of data sets comprising ∼100–200 km of track length. In general, the cross‐track wave number is the most poorly determined, although uncertainties in the assumed Sea Beam response may bias the values of the fractal dimension. Using the assumed beamwidth, the measured noise values, and the seafloor parameters recovered from the inversion, we generate Sea Beam “synthetics” whose statistical character can be directly compared with raw Sea Beam data. For most of the track segments we have processed thus far the synthetics are similar to the data. In the case of one Atlantic profile, however, the comparison clearly indicates the necessity of incorporating higher‐order statistics. The space domain procedures described in this paper can be extended for this purpose.

We present a new synthesis of oceanic crustal structure from two‐dimensional seismic profiles to explore differences related to spreading rate and age. Primary results are as follows: (1) Layer 2 has an average thickness of 1.84 km but is thicker for young slow‐spreading crust and thinner for young superfast‐spreading crust. At faster‐spreading rates the layer 2/3 boundary likely corresponds to the lithologic boundary between dikes and gabbros. At slow‐spreading centers, the layer 2/3 boundary is interpreted to mark a change in porosity with depth within the dikes. (2) Total crustal thickness averages 6.15 km and is similar across all spreading rates. (3) Velocities at the top of layer 2 increase rapidly from 3.0 km/s at 0 Ma to 4.6 km/s at 10.5 Ma, with a slower increase to 5.0 km/s at 170 Ma. The rapid increase in velocity at young ages is attributed to crack closure by precipitation of hydrothermal alteration products; the increase at older ages suggests that this process persists as the oceanic crust evolves. (4) There is a correlation between velocities at the top of layer 2 and sediment thickness, with velocities of 5.8–5.9 km/s associated with a sediment thickness of 4.0–4.3 km. The thick sediment may collapse large‐scale features such as lava tubes and fractures. (5) Average velocities at the top of layer 3 are lower for young slow‐spreading and intermediate‐spreading oceanic crust (6.1–6.2 km/s) than for older or faster‐spreading oceanic crust (6.5–6.7 km/s). These low velocities are likely associated with faults penetrating into the sheeted dikes.

[1] The rate of generation of internal gravity waves in the lee of small length scale topography by geostrophic flow in the World Ocean was estimated using linear theory with corrections for finite amplitude topography. Several global data sets were combined for the calculation including an ocean circulation model for the near-bottom geostrophic flow statistics, over 500 abyssal current meter records, historical climatological data for the buoyancy frequency, and two independent estimates of the small scale topographic statistical properties. The first topography estimate was based on an empirically-derived relationship between paleo-spreading rates and abyssal hill roughness, with corrections for sedimentation. The second estimate was based on small-scale (<100 km) roughness of satellite altimetry-derived gravity field, using upward continuation relationships to derive estimates of abyssal hill roughness at the seafloor at scales less than approximately 20 km. The lee wave generation rate was found to be between 0.34 to 0.49 TW. The Southern Hemisphere produced 92% of the lee wave energy, with the Southern Ocean dominating. Strength of the bottom flow was the most important factor in producing the global pattern of generation rate, except in the Indian Ocean where extremely rough topography produced strong lee wave generation despite only moderate bottom flows. The results imply about one half of the mechanical power input to the ocean general circulation from the extra-equatorial wind stress of the World Ocean results from abyssal lee wave generation. Topographic length scales between 176 m and 2.5 km (horizontal wavelengths between 1 and 16 km) accounted for 90% of the globally integrated generation.Citation: Scott, R. B., J. A. Goff, A. C. Naveira Garabato, and A. J. G. Nurser (2011), Global rate and spectral characteristics of internal gravity wave generation by geostrophic flow over topography,

This paper presents the results of a global and regional stochastic analysis of near‐ridge abyssal hill morphology. The analysis includes the use of Sea Beam data for the estimation of stochastic parameters up to order 4. These parameters provide important quantitative physical information regarding abyssal hills, including their rms height, azimuthal orientation, characteristic width, aspect ratio, Hausdorff dimension, skewness, tilt, and peakiness. The global data set consists of 64 Sea Beam swaths near the Rivera, Cocos, and Nazca spreading sections of the East Pacific Rise, the Mid‐Atlantic Ridge, and the Central Indian Ridge. In one form of analysis, the parameters are averaged among spreading rate bins. Each of the spreading rate subsets can be identified as unique from the others in at least one aspect The slowest spreading rate subset (Mid‐Atlantic data) exhibit the largest scales (rms height and characteristic width and length) of abyssal hills. These parameters generally decrease as spreading rate increases up to the fast spreading rate data (Pacific‐Cocos) but increase going from fast to very fast (Pacific‐Nazca) spreading rate data. This indicates some complexity in the relationship between spreading rate and abyssal hill morphology. The plan view aspect ratio is nearly twice as large for the fast spreading rate data than for any of the other subsets and is smallest for the very fast spreading rate data. The fractal dimension is nearly identical for all spreading rate subsets. The vertical skewness is positive for the slow and medium spreading rate data, indicating larger peaks than troughs, and negative for the fast spreading rate data, indicating larger troughs than peaks. The kurtosis, or peakiness is everywhere larger than the Gaussian value of 3 and tends to be larger in the Atlantic than the Pacific. The tilting parameter provides substantial evidence indicating steeper inward facing slopes in the medium and fast spreading rate data, but only marginal evidence for it in the slow spreading rate data. From an analysis of correlations among parameters it is found that subsets sometimes behave differently from the entire data set. In particular, while over the global data set the characteristic width exhibits a well‐resolved positive trend when plotted versus rms height, these parameters exhibit a more gradual positive trend in the Mid‐Atlantic data and a negative trend in the Pacific‐Cocos data. In addition, the plan view aspect ratio, while generally uncorrelated with rms height for the global data set, is positively correlated with rms height for the Pacific‐Cocos data set. These results emphasize a strong uniqueness of the Pacific‐Cocos data relative to the rest of the data global set The Pacific‐Cocos data consist of 27 swaths concentrated between the Siquieros and Orozco fracture zones. These data provide very good abyssal hill coverage of this well‐mapped and well‐studied region and form the basis of a regional analysis of the correlation between ridge morphology and stochastic abyssal hill p...

that the position and longevity of segments are controlled primarily by the subaxial position of buoyant mantle diapirs or focused zones of rising melt. Within segments, there are distinct differences in seafloor depth, morphology, residual mantle Bouguer gravity anomaly, and apparent crustal thickness between inside-corner and outside-corner crust. This demands fundamentally asymmetric crustal accretion and extension across the ridge axis, which we attribute to low-angle, detachment faulting near segment ends. Cyclic variations in residual gravity over the crossisochron run of segments also suggest crustal-thickness changes of at least 1-2 km every 2-3 m.y. These are interpreted to be caused by episodes of magmatic versus relatively amagmatic extension, controlled by retention and quasiperiodic release of melt from the upwelling mantle. Detachment faulting appears to be especially effective in exhuming lower crust to upper mantle at inside corners during relatively amagmatic episodes, creating crustal domes analogous to "turtleback" metamorphic core complexes that are formed by low-angle, detachment faulting in subaerial extensional environments.

No abstract

Rise. We find that abyssal hills generated along axial high mid-ocean ridges are very different from those generated along axial valley mid-ocean ridges, not only with respect to size and shape, but also in their response to such factors as spreading rate and segmentation.

[1] Abyssal hills, which are pervasive landforms on the seafloor of the Earth's oceans, represent a potential tectonic record of the history of mid-ocean ridge spreading. However, the most detailed global maps of the seafloor, derived from the satellite altimetry-based gravity field, cannot be used to deterministically characterize such small-scale (<10 km) morphology. Nevertheless, the small-scale variability of the gravity field can be related to the statistical properties of abyssal hill morphology using the upward continuation formulation. In this paper, I construct a global prediction of abyssal hill root-mean-square (rms) heights from the small-scale variability of the altimetric gravity field. The abyssal hill-related component of the gravity field is derived by first masking distinct features, such as seamounts, mid-ocean ridges, and continental margins, and then applying a newly designed adaptive directional filter algorithm to remove fracture zone/discontinuity fabric. A noise field is derived empirically by correlating the rms variability of the small-scale gravity field to the altimetric noise field in regions of very low relief, and the noise variance is subtracted from the small-scale gravity variance. Suites of synthetically derived, abyssal hill formed gravity fields are generated as a function of water depth, basement rms heights, and sediment thickness and used to predict abyssal hill seafloor rms heights from corrected small-scale gravity rms height. The resulting global prediction of abyssal hill rms heights is validated qualitatively by comparing against expected variations in abyssal hill morphology and quantitatively by comparing against actual measurements of rms heights. Although there is scatter, the prediction appears unbiased.Citation: Goff, J. A. (2010), Global prediction of abyssal hill root-mean-square heights from small-scale altimetric gravity variability,