Principal Investigator: John A. Goff
Funded by: Office of Naval Research
Recent Field Results:
Abstracts for current and submitted papers
Detailed investigation of
continental shelf morphology using a high resolution swath sonar survey: The Eel margin,
northern California
1996 Planning Letter
Introduction
The application of statistical methods of characterization to the bathymetry and
stratigraphy of continental margins is a substantially new scientific effort. Much of the
work will necessarily be exploratory, both applying established methods and developing new
ones. The primary motivation for this work is to construct a basis for quantifying a
morphology produced by a physical system with many chaotic (i.e., deterministically
unpredictable) components (e.g., floods, storms, slumps, drainage). In addition to several
scientific interests detailed below, a major goal of the proposed work is to develop a
capability for conditional simulation in the stratigraphic environment. The intent
of conditional simulation is to generate a morphology (in this case a stratigraphic
sequence) which satisfies prior deterministic and statistical information (i.e., seismic
records, bathymetry, core logs, statistical characterization, etc.). In this way we can
realistically interpolate or extrapolate stratigraphic morphology in regions of incomplete
data coverage. The work proposed here will lay the necessary ground work for generating
conditional simulations.
Below are highlighted scientific issues in statistical characterization of bathymetry
and stratigraphy and methods to be employed.
Shelf Bathymetry
The STRATAFORM swath mapping field program conducted off northern California and the
planned field program for the New Jersey margin will constitute the most comprehensive and
detailed bathymetric coverage to date on a continental shelf. Such data will allow us to
address for the first time basic questions regarding the statistical characteristics of
shelf morphology, including: what are the roughness characteristics from the ~10 meter to
10's of kilometer scale? what are the principal scales of horizontal variability in the
down-slope and cross-slope directions? what is the pattern of drainage? Various
statistical analysis techniques will be brought to bear, including covariance and spectral
analysis, providing quantitative estimation of basic roughness characteristics, including
rms variation, characteristic scales, fractal dimension, and, in two or three dimensions,
structural anisotropy. This information will be used in the STRATAFORM program as input
into dynamic models of shelf sedimentation processes. Other statistical measures which
apply to quantitative analysis of drainage patterns will also be investigated. The
statistical analysis of shelf bathymetry will be an important component in a study of
horizontal variability in the stratigraphic sequence (see below).
Slope Bathymetry
Continental slope bathymetry data on the New Jersey margin have been collected in many
areas (including the New Jersey margin) using hull-mounted 12 kHz multibeam systems (i.e.,
Sea Beam). Dr. L. Pratson (LDEO), a STRATAFORM participant, is currently working with
these data in studies of slope failure and canyon development. The STRATAFORM
swath-mapping field program will, using a 95 kHz system, provide unprecedented bathymetric
resolution and detail of the mid- to upper-slope region. The combination of the 12 and 95
kHz data sets will constitute a "nested" bathymetric survey, providing
information over a large range in scales (meters to 100's of kilometers). Preliminary work
by Pratson suggests that a systematic, multi-scale statistical analysis of continental
slope bathymetry will yield significant results. In particular, Pratson finds evidence
suggesting significant differences in fractal properties down-slope and cross-slope.
Furthermore, in the cross slope direction he finds evidence for the existence of a
characteristic scale which is indicative of a characteristic spacing of slope canyons. We
can also anticipate that cross-slope statistical properties will change with depth. These
statements can be made quantitative and robust through application of covariance and
spectral analysis techniques. Such information will provide critical constraints on
process models of slope failure and canyon development.
Vertical Stratigraphic Sequence
Statistical characterization of the vertical structure within the stratigraphic
sequence should provide essential information on scales of temporal variability and the
self-similarity (or not) of the process of generating sequences. Stratigraphic data can
take on a number of forms, typically derived from either well-log or seismic data. The
simplest and most prevalent stratigraphic sections consist of images of impedance
contrasts detected by seismic reflection. This type of data is highly limited in that
information is provided only at a discrete number of points within the continuum of the
stratigraphic sequence. It can be represented by a binary field, with 1's and 0's
identifying alternating strata. The spatial statistics of a binary field are largely
specified by (1) the relative distribution of 1's and 0's and (2) the second-order spatial
statistics (i.e., the covariance or the power spectrum). These characteristics are easily
and robustly estimated. Similar statistical estimation techniques will also be applied to
continuous data provided by well-logs. This data is much richer in content, and several
different variables (i.e., density, grain size, compressional velocity, etc.) are
provided. Though such data will likely be sparse and only 1-dimensional, they provide the
most direct and comprehensive opportunity for quantitatively comparing stratigraphic
models with data (see below).
Horizontal Variability in the Stratigraphic Sequenc
Methods of statistical characterization of horizontal variability in stratal
boundaries should be essentially identical to those developed for seafloor bathymetry. It
is important that the bathymetric surface and stratal boundaries be quantified in the same
context. For example, stratigraphic modelers will need to compare bathymetry to underlying
stratal boundaries to ascertain to what extent modern bathymetry acts as, or ultimately
influences, a stratal boundary. The following questions, readily addressed with the
bathymetric and seismic data to be collected, should have important implications for that
work: over what scales are the bathymetric surface and underlying stratal boundaries
deterministically similar or dissimilar (i.e., coherent)? over what scales are the
bathymetric surface and underlying stratal boundaries statistically similar or dissimilar?
Deterministic similarity among stratal boundaries might imply spatial coincidence of such
factors as the 3-D pattern of sediment input and erosion from one stratum to the next.
Statistical similarity might imply that stratigraphic processes, though quite variable on
shorter time scales, might be similar on longer time scales.
Quantitative Comparison Between Stratigraphic Models and Data
A principal scientific goal of the STRATAFORM program is to advance our understanding
of the process of strata construction through the systematic comparison of stratigraphic
models and data. For this to be successful, such comparisons must be made quantitative, so
as to establish an objective and rigorous basis for assessing the quality of the
comparison. Standard correlation techniques can be used to quantitatively assess
deterministic similarity between a model run and a data set. However, many of the
processes associated with stratigraphic formation (e.g., storms, floods, slope failure,
drainage patterns) are chaotic, leading to inherent unpredictability of deterministic
structure, but possible predictability of statistical structure. In this case, statistical
characterization such as proposed here represents the best hope for meaningful
quantitative comparison. In practice, it is anticipated that some combination of
deterministic and stochastic methods of quantitative comparison will be required, and that
use of one or the other will depend on spatial and temporal scale.
Interpolation of Data
One of the principal concerns of the U.S. Navy, and a driving force behind the
STRATAFORM program, is to attain a capability to interpolate bathymetric and stratigraphic
information from sparsely collected data such that the "essential
characteristics" of the morphology are well-predicted. Such an interpolation is
called a "conditional simulation", and differs from all other interpolation
techniques which tend toward smoothness through minimum error criteria. The latter
typically fail to predict the "essential characteristics" of the morphology, in
particular small-scale variability. A vital ingredient of a conditional simulation is a
well-resolved statistical model - the principal goal of the work described here. Standard
techniques for conditional simulation exist in the oil industry literature. However, these
techniques are typically designed for simulating porosity structure, which is typically
Gaussian or near-Gaussian distributed in 3-D, and are not going to be obviously relevant
to simulating stratigraphic information, which largely consists of sets of surfaces
associated with acoustic impedance contrasts. It is anticipated that new techniques will
need to be developed, and will require significant effort which will likely require more
than two years time to fully develop. The form that these techniques take will depend
strongly on the results of the research described above.
California swath mapping data:
Figure: Gridded sidescan and bathymetry data from the Eel River Basin swath mapping survey. Colors are derived from side scan backscatter data, with warmer colors (red and yellow) indicating high backscatter, and cooler colors (blue and purple) indicating low backscatter. Shading is derived from artificial sun illumination of bathymetry (azimuth N25degE). Contours are in meters. Principal features discussed in the text are identified.