Fourier Grain Research Articles

Multiscale Roughness Analysis of Particles: Application to the Classification of Detrital Sediments

The shape of detrital quartz grains, mainly acquired under the effect of mechanical transport agents, has been observed and described for a long time by sedimentologists. The roughness of these grains is recognized as an important parameter for analyzing sediments, but to quantify this parameter with a discriminant measure can be difficult. By using the concept of multiresolution analysis and the wavelet formalism, we develop a roughness descriptor for particles, possessing multiscale analysis capabilities. It allows analyses of wear and erosion phenomena acting on particles by decomposing the information on the shape into different resolution levels, each level corresponding to a different scale. Thus it becomes possible to differentiate coarse roughness from finer roughness of a grain's outline. This descriptor is invariant under affine geometric transformation and can therefore be used to compare sands stemming from a wide range of natural environments. An application to the analysis and the classification of detrital sediments, along with a comparison with Fourier and fractal grain shape analysis, illustrates the performance of the method.

Recognition of seismically induced liquefaction features: application of Fourier grain shape analysis to two sites in the Charleston, South Carolina, area : C. P. Rajendran, R. Ehrlich, P. Talwani & K. Collinsworth, Sedimentary Geology, 87(3–4), 1993, pp 129–138

Recognition of seismically induced liquefaction features: application of Fourier grain shape analysis to two sites in the Charleston, South Carolina, area : C. P. Rajendran, R. Ehrlich, P. Talwani & K. Collinsworth, Sedimentary Geology, 87(3–4), 1993, pp 129–138

Recognition of seismically induced liquefaction features: application of Fourier Grain Shape Analysis to two sites in the Charleston, South Carolina, area

Sediments collected from two sites in Fishburne Creek, Dorchester County, near Charleston, South Carolina, suspected to have been affected by seismically induced liquefaction, were analyzed for shape variation by the Fourier Grain Shape Analysis (FGSA) technique. The results indicate that the shape variation of the samples from these sites can be defined by a four-end-member model. The feature at the first site contains a greater proportion of 5 and 6 end members (rougher grains), and the host has a maxima of 3 and 4 end members (smoother grains). The cumulative probability values obtained for these end members by Fisher's exact test, also indicate the presence of extraneous sand in the feature at the first site, further confirming the FGSA results. No discernible contrast based on shape families can be observed between the feature and the host at the second site, indicating possible absence of injected sand. The discrimination based on the shape of sand grains by the FGSA technique offers an alternative method to differentiate between liquefaction and nonliquefaction features.

How round is round? A new approach to the topic ‘roundness’by Fourier grain shape analysis

ABSTRACTNumerous methods for roundness measurement have been developed. None, however, has been generally accepted, because of conceptual and practical deficiencies. Modern image processing and Fourier grain shape analysis have eliminated the practical shortcomings, but the conceptual ones remained. Single, higher harmonics of the Fourier series, for example, fail to serve as reliable equivalents for roundness evaluation. The concept outlined in this paper recognizes three criteria for the evaluation of roundness. (1) All curvatures, convex as well as concave or plane elements, must be considered. (2) The positions of morphological elements are significant because salient parts of a particle are more easily abraded than protected ones. Consequently, the curvatures have to be weighted by their relative position on the particle. (3) Positions and curvatures of morphological elements have to be compared with the particle's ultimate abraded shape, which is assumed to be an ellipsoid. The ellipsoid reflects the aspect of form or sphericity. The distinction between sphericity and roundness is retained because there is no evidence that sphericity changes significantly during transport. The measurement is based on the outline of a particle's maximum projection plane, which is transformed to a Fourier series. Roundness data are derived from the complete amplitude spectrum. The aspect of sphericity is eliminated by subtracting the amplitude spectrum of the best approximating ellipse from the spectrum of the empirical shape. The residual amplitudes are normalized and summed. In a final step the resulting values are rescaled. This guarantees reasonable boundaries and a normal distribution of roundness values. The procedure is automated and its efficiency permits the calculation of large samples. Tests on fluvial and coastal gravel populations demonstrate that the method is sensitive to abrasional wear during all stages of roundness.

Sources and Distribution of Silt, South Texas Shelf: ABSTRACT

Fourier grain shape and mineralogic analyses were conducted on the coarse silt fraction of the surficial sediments on the south Texas continental shelf to determine the sources and distribution of the silt. The distribution patterns were evaluated in light of the late Pleistocene paleogeography and modern hydrodynamic conditions prevailing on the shelf to determine whether the coarse silt fraction was relict, palimpsest, or modern in origin. Two coarse silt-grain shape types are present in varying proportions in the samples from the south Texas shelf. One is associated with quartzose coarse silt and is considered to represent multicyclic coarse silt-size detritus derived from the Texas coastal plain and high plains. The second type is associated with more feldspathic coarse silt and is considered to represent first-cycle, coarse, silt-size detritus derived from igneous and metamorphic rocks of Texas, New Mexico, and Mexico. Each of the major river systems that supplied sediment to the south Texas shelf during the late Pleistocene and Holocene is characterized by distinctive proportions of first- and multicyclic coarse silt. The Brazos-Colorado and Rio Grande systems, which drain igneous, sedimentary, and metamorphic rock terranes, deposited sediment enriched in first-cycle coarse silt on the shelf during the late Pleistocene low sea level stand. At the same time, the Guadalupe and the Copano-Nueces-Baffin coastal plain river systems, which drain sedimentary rock terranes only, deposited sediment enriched in multicyclic coarse silt on the shelf. In the southern part of the other south Texas shelf, the distribution patterns of first-cycle and multicyclic coarse silt define the late Pleistocene alluvial plains of the Rio Grande and the south Texas coastal plain rivers. The locations of the alluvial valleys, as defined by grain shape analysis, coincide precisely with the locations of these valleys as defined by shallow seismic studies; therefore, the coarse silts in this area are considered to be relict in origin, unmodified by the weak (0-10 cm/sec) semipermanent bottom currents that prevail in the southern part of the outer south Texas shelf. The preservation of paleogeographic features in the surficial sediments of this area of the shelf indicates that no modern coarse silt, which might bury this relict surface, has been depo ited here during modern times. In the northern part of the south Texas outer shelf, first-cycle coarse silt originally deposited on the ancestral Brazos-Colorado delta is found not only in the delta area, but also overlying most of the alluvial valley of the Guadalupe system lying west of the delta. Therefore, the coarse silt on the northern outer shelf in the vicinity of the Brazos-Colorado delta and the ancestral Guadalupe valley is palimpsest in origin and apparently is being reworked by the strong semipermanent bottom currents that prevail in this region. In the southern part of the south Texas inner shelf, the patterns of distribution of first-cycle and multicyclic coarse silt indicate that the inner shelf coarse silt is also relict in origin. The apparent absence of modern coarse silt on this part of the inner shelf is thought to reflect the paucity of this size fraction in the major sediment sources of the southern inner shelf--the Rio Grande and Padre Island. In the northern part of the south Texas inner shelf, evidence indicates that the inner shelf coarse silt is a mixture of palimpsest silt reworked from the late Pleistocene substrate and modern silt provided by the Colorado River. End_of_Article - Last_Page 1215------------

Fourier Grain Shape Analysis as a Tool for Indicating Batch Recoveries of Bitumen from Athabasca Tar Sands: ABSTRACT

Effects of weight percent fines have been considered in the past as important factors in controlling the recoveries of bitumen from tar sands using batch extractors. However, in the marine sands of the Athabasca deposit, fines break down as a predictor of batch recovery; in some places even low fines tar sands do not yield acceptable batch bitumen recoveries. It was predicted that a sand unit high in rough-surfaced, diagenetically altered grains would yield low primary bitumen recovery. Scanning electron microscopy of the solids from batch extraction tests revealed that quartz grains with very rough, pitted, and overgrown surfaces retain bitumen. (These solids appear to be transported preferentially with the bitumen to froth and secondary tailings.) Grains with smooth sur aces were found to be dominant in primary tailings. Fourier grain-shape analysis was employed to identify tar sand shape types since scanning electron microscopy inspections are time-consuming and expensive. Five grain shape families were so identified and verified by SEM. Two types of grains unaltered by diagenesis are very fresh, rounded, sub-aerially abraided grains, and fresh, angular grains with concoidal fractures. Three other grain shape families represent particles whose surfaces were strongly modified by diagenesis. The diagenesis was found to be primarily overgrowth: (1) rough silica plastering with a sponge-like appearance, producing high surface areas; (2) silica plastering with multiple crystals; and (3) complete simple overgrowth. Fourier grain-shape analysis yields the proportion of high surface area grains in 900 grain samples taken from marine sand intervals of 3 cores. That proportion, plotted versus weight percent primary recovery by batch extraction, indicates that when the proportion of high energy grains exceeds 40%, primary recoveries were less than 80 wt. %. (Primary recovery, in contrast, shows no relationship to weight percent fines for these marine sands and cannot be used as a batch recovery indicator.) The results suggest the feasibility of predicting recovery in advance of mining, thus permitting adjustments to mining/extraction strategies. It must be kept in mind, however, that extrapolation of bitumen recovery results from bench-scale batch tests to large-scale continuous units is not straightforward. End_of_Article - Last_Page 549------------

Differentiating Sediments from Different Sources in Gulf Basin by Grain-Shape Analysis: Example from Late Pleistocene-Holocene Sediments of Northwestern Gulf of Mexico Continental Shelf: ABSTRACT

ABSTRACT It has been shown previously that different source rocks produce quartz sand grains with unique gross shape characteristics. These gross shape characteristics cannot be altered by abrasion, and are thus an immutable record of sediment source. Therefore, sand grains in a sedimentary basin should contain in the gross shape a fingerprint of their source unaffected by the amount of reworking to which the sands have been subjected. In order to test this idea, the shapes of late Pleistocene-Holocene sands grains from two sources in the northwest Gulf of Mexico (the Rio Grande and Western Gulf Province) were analyzed with the Fourier grain shape technique. The results indicate that two gross grain shape assemblages are present in the sands of these two provinces. One assemblage is associated with a mineralogical suite typical of relatively mature coastal plain sediments, and thus probably represents the contribution of sediment from such a Coastal Plain Source Terrane. The other assemblage is associated with a relatively immature mineralogical suite more typical of sediments derived from crystalline sources, and thus probably represents the contribution from such a Source Terrane. Both assemblages are found in sands of both provinces, inasmuch as the major rivers in these provinces which act as conduits for these sediments drain both source terrane types. However, the amount of area of these terranes drained by the rivers differs between the provinces, and so the relative proportions of these assemblages in the sands of the two provinces also differ. Rio Grande Province sands contain on the average 59% of the assemblage associated with the Highland Source Terrance, while Western Gulf Province sands contain only 34% of this assemblage. Thus, it is the difference in the relative proportion of these two assemblages in the samples which can be used to identify and distinguish the sands from the two provinces. All in all, the results of this pilot project indicate that the analysis of gross grain shape can indeed differentiate sediments from different sources in the Gulf of Mexico.

Dispersal and Provenance of Terrigenous Sand by Fourier Grain Shape Analysis, Northern Puerto Rico: ABSTRACT

The narrow, steep, north insular shelf of Puerto Rico contains terrigenous sands and silts derived from rivers originating in nearby mountains. This compact system provides an ideal setting for the study of sand sized sediment dispersal and provenance in coastal and nearshore environments using Fourier shape analysis. Quartz sand shape on the north shelf reflects the lateral change in source-rock composition. The shelf can be divided into a western part containing dominantly angular quartz grains and an eastern part containing rounded abraded quartz sand. Rivers feeding the western shelf drain a significant body of granitic rock, whereas rivers to the east drain a quartz-poor, volcanic rock terrane. Rounded grains on the eastern shelf are mostly relict. Quartz sand shapes do not change significantly with changing size either upstream or on the shelf. A size-shape dependence does exist in downstream, river mouth, and slope environments (fine sand is more angular than coarser sand) and on beaches (fine sand is more abraded than coarser sand). It is significant that environments in which size-shape relationship exists are also sites of mixing between sands of different origins and transport histories. For example, samples studied from downstream and river mouth areas indicate mixing between fine-grained, angular fluvial sand, and coarser, smoother residual sand. Mixing occurs because fluvial sand is deposited on the shelf only when storm-induced flooding results in river-mouth bypassing. This study suggests that investigations into the origin of size-shape relationships can aid in understanding climatically controlled, short-term changes in terrigenous output. End_of_Article - Last_Page 573------------

The effect of hydrofluoric acid on quartz shape-Fourier grain shape analysis

Fourier grain shape analysis of quartz grains in sediment has been applied to a wide variety of sedimentological problems. Mineralogically pure samples of quartz are required to eliminate the effects of shape variation due to non-quartz minerals. Hydrofluoric acid treatments of samples, which enables the identification feldspar contaminant grains, has been shown to have no significant effect on the shape of quartz particles, as measured by the first twenty terms of a closed-form Fourier Series.

A Vertical Pattern of Variation in the St. Peter Sandstone--Fourier Grain Shape Analysis

ABSTRACT Fourier grain shape analysis of quartz sand grains from a vertical section of the St. Peter Sandstone at St. Paul, Minn., has detected a vertical pattern of non-random variation in the relative proportions of 2 shape families. The shape families consist of mature, highly abraded sand, and irregularly shaped, immature, sand respectively. Changes in the proportion of mature and irregular sands define large-scale (7, 19 foot) zones characterized by a decrease upwards in irregular sand content, and within each zone smaller scaled units of interbedded mature and irregular sands which form cycles approximately 1 foot thick. In light of studies of Recent shelf environments (Brown and Ehrlich, 1980) the large-scale zones are interpreted as a record of individual transgressive phases with a resultant movement of the littoral energy fence (and concomittantly the shoreline) away from the area. Two and, perhaps, three such zones occur in the uppermost 30 feet studied. If their repetition is due to regressive pulses, this corroborates Sloss' (1963) observations that the middle Ordovician transgression was interrupted by numerous partial regressions. The small-scale cycles within each zone are interpreted to record the breaching of the littoral energy fence; each thin layer of irregular sand is likely storm-generated. Detection of such a detailed record in an otherwise homogeneous, featureless orthoquartzite ind cates that the Fourier grain shape technique, applied on a regional scale to the St. Peter Sandstone, may reveal a clearer record of its accumulation.

Origin of Patterns of Quartz Sand Types on the Southeastern United States Continental Shelf and Implications on Contemporary Shelf Sedimentation--Fourier Grain Shape Analysis

ABSTRACT Quartz sands in the fine sand range were found to form areally discrete zones with different shape characteristics on the continental shelf from Charleston Harbor, South Carolina northward to Cape Fear, North Carolina. The nature and location of these sand zones can be used to gain insights into the past and present hydrodynamic history of the continental margin during the Pleistocene-Holocene. Fourier grain shape analysis of 95 samples indicates that the shelf surface in this area is characterized by coast-perpendicular bands of sand containing alternating high and low percentages of highly abraded (smooth) quartz grains. The bands containing high proportions of smooth grains are interpreted to be of coastal plain origin. The bands containing high proportions of quartz grains of irregular outline represent traces of pre-Holocene alluvial drainages on the exposed shelf during sea level lowstands. This interpretation is greatly strengthened by the fact that all three shelf bands of irregular sand exactly coincide at their landward ends with the coastal positions of Pleistocene courses of the three major Piedmont drainages in the region. The presence and preservation of these coast perpendicular bands emphasize the relict character of the fine sand on the shelf surface as well as the inability of bottom currents to produce significant shore-parallel net transport in this area.

Location of Littoral Energy Fence and Resolution of Relict Features on Atlantic Shelf, United States--Fourier Grain Shape Analysis: ABSTRACT

Even though, in any given area, shelf sands deposited during the Holocene-Pleistocene may have a common provenance, sands deposited during the latest transgression can be distinguished from sands delivered earlier, by using Fourier Grain Shape Analysis. Sands with longer residence times on the Long Island shelf have smooth abraded grain profiles whereas the youngest sand tends to be much more irregularly shaped. In the nearshore zone, the percentage of irregular grains grades rapidly from approximately 100% at the beachface to 70% at the 10 m depth. Seaward of the 10-m isobath, the proportion of irregular sand decreases at a much slower rate. This change in gradient defines a boundary between nearshore sands and more abraded sands of the middle and outer shelves where lit le onshore-offshore mixing of sediments occurs. This boundary, the littoral energy fence, also has been seen on the South Carolina shelf. Sands on the Long Island middle and outer shelf are characterized by relatively high percentages of highly abraded sand. Samples from this zone show areas with slightly higher (80 to 100%) or lower (50 to 80%) proportions of abraded quartz. This pattern appears to be related to morphologic elements on the shelf. In contrast, the South Carolina middle and outer shelf contains broad, coast-perpendicular stripes of abraded sand alternating with stripes from 10 to 30 km wide that are strongly dominated by first-generation irregular sand. Stripes containing high proportions (over 75%) of irregular sands are interpreted to be understories of alluvial valleys of the ancestral Cooper, Santee, and Waccamaw Rivers. These results indicate that shelf sediments preserve a End_Page 773------------------------------ rich record of Pleistocene-Holocene events of both subaerial and subaqueous nature. In addition to clarifying the history of modern shelves, aerial patterns of quartz grain shape variation can be carried into the stratigraphic record, thereby allowing a more detailed paleogeographic-paleoenvironmental reconstruction. End_of_Article - Last_Page 774------------

Determination of Relative Provenance Contributions in Samples of Quartz Sand Using Q-mode Factor Analysis of Fourier Grain Shape Data

ABSTRACT Determination of relative proportions of quartz grains having different provenance-process histories is a major objective of Fourier grain shape analysis. Such unmixing is the key to tracing sediment dispersal pathways and evaluating the relative importance of potential sources. Unmixing is achieved using the Q-mode programs EXTENDED CABFAC-QMODEL on shape frequency distributions. The efficacy of these algorithms was tested using synthetic mixtures as well as an empirical data set. Results indicate that, when used optimally, relative proportions can be estimated with a precision of ± 3 percent.

Sources of shoaling in Charleston Harbor, Fourier grain shape analysis; discussion and reply

Sources of shoaling in Charleston Harbor, Fourier grain shape analysis; discussion and reply

Sources and Nonsources of Beach Sand Along Southern Monterey Bay California--Fourier Shape Analysis

ABSTRACT The shoreline along the southern portion of Monterey Bay California is undergoing severe erosion. Industrial and architectural sand has been dredged from this portion of the bay for the last 70 years. This withdrawal of sand coupled with weak to absent longshore contributions of new sand has been blamed for modern beach erosion. To determine the relative importance of potential sources to the sediment budget, 30 samples of 130-300 grains each were compared using Fourier grain shape analysis. Potential sources (including Flandrian and preFlandrian dunes, Salinas River, and offshore sands) can be discriminated on the basis of grain shape. Comparison of data from the beach samples and samples from the mining operations shows that most beach sand, offshore (shallow water) sands, and the m ned sand are primarily (70%-90%) derived from Flandrian and preFlandrian dunes. North of the Salinas River, the beach is dominated by fluvial sediments. This study does not prove that sand mining is the major cause of erosion along the southern half of the bay. This analysis does demonstrate however, that recharge of sand onto the southern beaches from the Salinas River is not significant and so cannot be invoked to provide a mechanism to support the concept that the mined sand is a renewable resource.

Sources of Shoaling in Charleston Harbor, Fourier Grain Shape Analysis: REPLY

Sources of Shoaling in Charleston Harbor, Fourier Grain Shape Analysis: REPLY

Sources of Shoaling in Charleston Harbor Fourier Grain Shape Analysis

ABSTRACT Shoaling in Charleston Harbor, South Carolina, is a severe economic problem requiring major expenditures for dredging as well as proposals for drastic modifications of the sediment carrying capacities of the rivers discharging into the harbor. Sediment accumulating in dredged channelways consist mostly of sand whereas silts and clays dominate the shallows. Although previous studies agree on the hydrodynamic responses to diversion of the Santee River's 15,000 cfs (425 m3 per sec) flow into Charleston Harbor, no concensus exists concerning the source of sediment accumulating in the dredged channels (i.e. whether or not the source of the shoaling material is from the Cooper River or the proximal continental shelf). The sources of sediment influx into Charleston Harbor and the relative contributions of each source have been determined using the Fourier Series grain shape analysis. Results of the shape analysis on the sand fraction indicate that the major cause of shoaling in the harbor channels is sand derived from a seaward source. Shape analysis of the silt fraction reveals that the silt accumulations are derived primarily from the Cooper River. These results indicate that the deepening of the harbor channels has played a major role in the shoaling of Charleston Harbor as well as the increased freshwater flow from the Santee River.

Detrital Quartz as a Natural Tracer--fourier Grain Shape Analysis

ABSTRACT Quartz grain shape is a highly satisfactory natural tracer of sediment flux and accumulation. Sands from a river-beach-cliff complex near Oceanside, California were analyzed in terms of the variation of the closed-form Fourier amplitude spectra of maximum projection shapes of about 100 grains per sample. The data were analyzed by heirarchical analysis of contingency tables and discriminant functions. River, beach, and cliff samples were clearly defined. Results indicate that, at the end of the dry season, longshore drift had removed most of the sand of the San Luis Rey River from the beach, excepting an area adjacent to a pier where at least 25% of sand grains were river-derived. During the dry season the unconsolidated beach cliff is the dominant source of beach sand.