Spatial variability and robust interpolation of seafloor sediment properties using the SEABED data bases
Funded by the Office of Naval Research
University of Texas Institute for Geophysics
Phone: 512-471-0476
Fax: 512-471-0999
E-mail:
goff@ig.utexas.edu
This project is a collaborative effort with C. Jenkins at the Univ.
OBJECTIVES
There are huge amounts of data that describe the character of the seabed
based on samplings and direct inspections made over decades. That data continues
to grow rapidly and are still the richest and most detailed source of seabed
information, an essential adjunct of modern remote sensed data types. One
impediment to the wider use of the sample data is that it is difficult to draw
area-maps (grid or polygon) from it. Other impediments such as word-based data
and 3D-stratigraphic issues have seen much progress recently. This project aims
to solve the remaining problem of reliable map generation. At project end the
marine community will have a toolbox of interpolation tools for surficial seabed
mapping. Researchers and operational groups will then be able to input detailed,
spatially varying values on seafloor properties into models to increase the
accuracy of sediment transport and acoustic propagation predictions.
The issue of seabed variability will also be investigated. Very little is known or published on this
topic, primarily because a large, comprehensive data base has not heretofore
been available. The SEABED data
bases represent a tremendous opportunity.
Our objective here will be to determine seabed variability properties as a
function of environment; i.e., water depth, geology, sediment type,
oceanography, etc. This in itself
will constitute a significant scientific contribution.
Such knowledge could provide a basis for predicting the structure of
seabed variability in undersampled regions.
Variability will also form a primary constraint in the investigation of
robust interpolation techniques, and for optimal survey design decision making.
APPROACH
Goff’s primary contribution to this project will be in statistical analysis of grain size data and developing a tool for correcting noisy data through resampling. Semi-variogram analysis is a robust and flexible tool for investigating spatial variability in data sets, and for assessing noise/uncertainty. It has been used by the PI in published investigations into seabed variability (Goff et al., 2002; 2004). We will apply this tool to the SEABED data bases where sufficient data density exist, investigating the variability structure (primarily rms variability, characteristic horizontal scale, and fractal dimension) as a function of environmental settings. Preliminary results indicate that the word-based estimates of mean grain size are noisier than analytic estimates, but otherwise produce accurate estimates of seabed variability (Figure 1). Through semi-variogram comparisons of word- and analytic-based mean grain size measurements, we can readily estimate and make corrections for the differences between the two measurement types.
Figure 1. Semi-variograms of mean grain size
measurements from the usSEABED data base for the
Correlating seabed variability to environmental parameters will constitute one
of our most significant challenges, and it is in this arena that collaboration
with the USGS promises to be of critical importance.
So little is presently known in this area of
investigation that much of our proposed work will be exploratory. We will, in particular, investigate the
predictability of variability structure.
In other words: what easily measured environmental parameters (e.g.,
bottom wave-climate, water depth, siliciclastic vs. carbonate) or geologic
conditions (e.g., passive margin vs active margin, high sediment input vs. low,
estuarine vs. open marine, etc.) can be used to constrain variability structure
where samples are few or none? The
null hypothesis is that there is no predictability; i.e., that every area we
examine has unique variability structure uncorrelated to any environmental or
geologic parameter. We doubt
strongly that this is the case, however.
For example, a preliminary investigation of variability on the
Figure 2.
Semi-variograms, computed for different water depth ranges, derived from
mean grain size measurements in the usSEABED data base for the
In any geologic application, and particularly word-based mean grain size
values, noisy data are sources of consternation for researchers, inhibiting
interpretability and marring images with unsightly and unrealistic artifacts.
Filtering is the typical solution to dealing with noisy data.
However, filtering commonly suffers from ad hoc (i.e., uncalibrated,
ungoverned) application, which runs the risk of erasing high variability
components of the field in addition to the noise components. For this project we
will establish an alternative to filtering: a methodology for correcting noise
in data by finding the "best" value given the data value, its uncertainty, and
the data values and uncertainties at proximal locations. The motivating rationale is that data
points that are close to each other in space cannot differ by "too much", where
how much is "too much" is governed by the field correlation properties.
Data with large uncertainties will frequently violate this condition, and in
such cases need to be corrected, or "resampled." The best solution for
resampling is determined by the maximum of the likelihood function defined by
the intersection of two probability density functions (pdfs): (1) the sample
pdf, with mean and variance determined by the data value and square uncertainty,
respectively, and (2) the conditional pdf, whose mean and variance are
determined by the kriging algorithm applied to proximal data values. A
WORK COMPLETED
The primary accomplishment of the PI thus far has been to complete the
development of the maximum likelihood resampling algorithm described above. This is the topic of a paper in
preparation. Tests with synthetic
sampling of a known field demonstrate quantitatively and qualitatively the
improvement provided by this algorithm.
Comparison with filtered fields demonstrates that maximum likelihood resampling
does a better job at preserving the spatial statistical character of the field. Here we present two data applications of
resampling: (1) three generations of bathymetric data on the
The region of the US Atlantic margin chosen for analysis contains data from three different sources [Calder, in press]: lead-line data collected in the 1930’s, echo-sounding values collected in the 1970’s (both contained in the National Geophysical Data Center archives), and multibeam data collected in 1996 [Goff et al., 1999]. Regions not constrained by multibeam data are marred by numerous “dimple” artifacts in the bathymetric interpolation (Figure 3). Calder [in press] conducted an error analysis of all three types of data and found that the lead line data were substantially biased toward shallower values; the dimples in Figure 1 are, primarily, caused by these positive errors. While Calder [in press] in his rendering of the bathymetry in this region chose simply to remove the lead line data in order to improve the image, here we retain them in the data set to demonstrate the utility of the maximum likelihood resampling methodology in mitigating such problems without a priori knowledge of their existence. Analysis of the spatial statistics of the bathymetry in this region was conducted by Goff et al. [1999] based on the multibeam bathymetry. The post-resampled image (Figure 4) successfully removes the dimple artifacts while leaving the multibeam data largely unmodified.
Figure 3. Region of
Figure 4. New Jesersey bathymetric data from Figure 3 after application of maximum likelihood resampling algorithm.
Mean grain sizes in the
Figure 5. Mean grain sizes (in f values, where grain size in mm = 2-f) in the northern
Figure 6.
RESULTS
The maximum likelihood resampling algorithm has proven, in both synthetic tests
and disparate data applications, to be a viable method for correcting noisy data
that are spatially correlated. The
essential requirements for applying this method are a quantitative estimate of
the uncertainty of the data and a characterization of the spatial covariance
function for the sampled field.
Potential applications are numerous.
Maximum likelihood resampling is an important alternative to filtering. Primary advantages include: (1) an
objective and optimal method for reducing noise, and (2) better preservation of
the statistical properties of the sampled field.
The primary disadvantage is that maximum likelihood resampling is a
computationally expensive procedure.
Application to large data sets will require cost/benefit considerations.
IMPACT/APPLICATIONS
This project could provide a major advance in marine science, a set of
reliable methods which transform point-site seabed data into griddings that will
be useful across oceanographic disciplines, sediment transport, acoustics,
habitat, wave-energy generation. Our work will result in a set of software tools
that will be open source, and available for inclusion any existing software
packages. These
tools could be of importance to the Navy, particularly in dealing with areas
with sparse data, such as “denied” areas. In particular, an understanding of the
relationship between environmental parameters, geologic setting and spatial
variability could provide an ability to predict the amount and spatial scales of
seabed variability using a parameterized semi-variogram model. This functionality provides a basis upon
which to predict seabed parameters at unsampled locations, and to assess the
uncertainty in that prediction. Such
an understanding will have important implications for assessing acoustic
prediction uncertainty. Furthermore,
the semi-variogram model can be used to investigate optimal survey design,
should it be possible to conduct limited sampling in denied areas via covert
means (e.g., AUV’s).
RELATED PROJECTS
This work is not presently linked to any other programs, but could prove useful
to ONR programs such as the Ripples DRI and the Shallow Water Acoustics ’06
experiment, which will make use of interpolated point data related to seabed
properties.
REFERENCES
Calder, B. (in press),
On the uncertainty of archive hydrographic data sets,
Goff, J. A., D. J. P. Swift, C. S. Duncan, L. A. Mayer, and J. Hughes-Clarke (1999), High resolution swath sonar investigation of sand ridge, dune and ribbon morphology in the offshore environment of the New Jersey Margin, Mar. Geol., 161, 309-339.Goff, J. A.,Wheatcroft, R. A., Lee, H., Drake, D. E., Swift, D. J. P., and Fan, S. (2002), Spatial Variability of Shelf Sediments in the STRATAFORM Natural Laboratory, Northern California, Cont. Shelf Res., 22, 1199-1223.
Goff, J. A., B. J. Kraft, L. A. Mayer, S. G. Schock, C. K. Sommerfield, H. C. Olson, S. P. S. Gulick, and S. Nordfjord (2004), Seabed characterization on the New Jersey middle and outer shelf: Correlability and spatial variability of seafloor sediment properties, Mar. Geol., 209, 147-172.
Smith, W. H. F., and P. Wessel, P. (1990), Gridding with continuous curvature splines in tension: Geophysics, v. 55, no. 3, p. 293-305.
PUBLICATIONS
Jenkins, C. J., and J. A. Goff (submitted), Competent interpolation for seabed substrates, with uncertainty calculations, IEEE J. Ocean Eng.