Application of a method for detecting lamina characteristics in ...

31 堆積学研究第 74 巻第 1 号 31-43（2015） Journal of the Sedimentological Society of Japan Vol. 74, No. 1, p. 31-43 (2015)

Application of a method for detecting lamina characteristics in sediments for time series analysis: an example using a soft X-ray image of varves from the Hiruzenbara Formation Hana Sasaki1＊, Megumi Saito-Kato2, Junko Komatsubara3 and Yoshiro Ishihara4 Varved sediments are very useful for studies attempting to clarify the high-resolution record of paleoenvironments, because they are expected to contain annual or sub-annual records of depositional environments. In order to obtain annual records such as annual thicknesses, color tones, and chemical compositions, at the very least, it is necessary to detect the boundaries of annual bands. Additionally, such detection and thickness measurements should be reproducible. The detection of boundaries and the measurement of thicknesses in varved sediments are commonly carried out by megascopic or image analyses. However, human error and difficulties in assessment of reproducibility often accompany megascopic measurements. On the other hand, photographs, soft X-ray images (X-ray radiographs), and the results of XRF mapping can be used for image analysis. Image analysis methods such as the peak detection method and wavelet analysis attempt to detect varve boundaries and measure varve number and sedimentation rate; however, some difficulties remain in these analyses, especially for recognizing varve boundaries. In addition, wavelet analysis has low resolution for detecting individual lamina boundaries, and waveform analyses such as the peak detection method are not suited for data containing high-frequency physical noise. In this study, we applied a novel method for detecting lamina boundaries, especially in varved sediments, which is described by the following procedure: (1) smooth pixel values (gray value) of the lamina image, (2) map a maximum slope point of gray value in a square-shaped moving window (W1) on the image, (3) obtain a median gray value in a linear moving window (W2) along a stratigraphical section, and (4) detect lamina boundaries using a combination of the maximum slope point and the median value. An application of the lamina identification method of this study to a soft X-ray image of varved diatomite yielded a well-defined tricolored varve image and averaged transmittance value of soft X-rays in each lamina of the varve image. The thicknesses of varved sediments obtained using the tricolored image and the transmittance value of lamina can be easily converted into time series, and applied to spectral analyses. Key words : Hiruzenbara Formation, image analysis, soft-X ray image, time series, varved sediments ㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇㍇

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Received: June 12, 2014; Accepted: January 14, 2015 Graduate School of Fukuoka University 8-19-1 Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan National Museum of Nature and Science 4-1-1 Amakubo, Tsukuba 305-0005, Japan Geological Survey of Japan/AIST Department of Earth System Science, Fukuoka University 8-19-1 Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan C-7, 1-1-1 Higashi, Tsukuba 305-8567, Japan Corresponding author: [email protected]

Annually laminated varved sediments (Fig. 1) include high-resolution paleoenvironmental records; therefore, many studies have been carried out on such deposits of various ages and at various sites (Ripepe et al., 1991; Anderson, 1993; Vos et al., 1997; Berger and von Rad, 2002; Nakagawa et al., 2005; Nakagawa et al., 2012). Primary and extremely important procedures in these studies include the identification of boundaries of varves and their laminae (sub-annual layers), varve counting, and measure-

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H. Sasaki, M. Saito-Kato, J. Komatsubara and Y. Ishihara

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Fig. 1 Soft X-ray image of varved diatomite of the Hiruzenbara Formation and profiles of its transmittance value shown as gray values. (A) Unprocessed “raw” soft X-ray image. (B) Processed soft X-ray image (gamma correction was applied). (C) Three profiles of gray values of the raw soft X-ray image in (A). The line widths of the profiles are 1, 10, and 50 pixels from the top. High-frequency noise in the profiles is reduced from the top, and some peaks suggesting lamina of a varve are unclear.

ment of the thickness of varves (Lotter and Lemcke, 1999; Petterson et al., 1999; Böoes and Fagel, 2005; Marshall et al., 2012; Sirocko et al., 2013; Staff et al., 2013). Some methods for identifying and measuring varves, such as megascopic measurements by microscope and image analyses (Fig. 2), have been proposed. In some of these methods, however, problems associated with objectivity and reproducibility exist, and confirmation by the researcher through visual examination is required. In recent years, more objective identification and measurement of varves utilizing digital-image analyses have been applied (Cooper, 1997; Petterson et al., 1999; Prokoph and Patterson, 2004; Ojala and Saarinen, 2002; Ojala, 2004; Ojala and Alenius, 2005; Haltia-Hovi et al., 2007; Petterson et al., 2010). For example, Cooper (1997) summarized techniques of image analysis for laminated sediments. Haltia-Hovi et al.(2007) used digital images of X-ray radiographs of lake sediments in Finland, and clarified the last 2000 years of climatic variability associated with solar activity. Thus, developing a high-resolution and objective age model based on varve counting by image analysis is becoming more and more important. In the present study, we summarize methods for iden-

tifying and measuring the thickness of varves and develop a novel and simple method using a digital image of laminae. The method of the present study facilitates identification of laminae, measurement of laminae, and the acquisition of information from images of laminae (e.g., the average gray value of a lamina), which can be converted to time-series data. We applied the method to varved sediment in the middle Pleistocene Hiruzenbara Formation, Okayama Prefecture, Japan, and verified its effectiveness. Lamina identification and measurement In the analysis of varved sediments, counting varves to estimate an age model (e.g., Marshall et al., 2012) and measuring the thickness of varves to evaluate paleoenvironmental change (e.g., Ripepe et al., 1991) have been performed commonly. Because varves are composed of the cyclic deposits of a lamina set consisting of different components, it is necessary to identify a varve and its components (laminae) first, whether the aim is varve counting or measuring varve thickness. Photographs, soft X-ray images (X-ray radiographs; Marshall et al., 2012), and elemental composition maps (Ojala and Saarinen, 2002) expressed as

Application of a method for detecting lamina characteristics in sediments for time series analysis

Fig. 2 Synthetic lamina and methods for lamina identification. (A) Synthetic lamina sediments. (B) “Megascopic method.” (C) “Peak method” using peaks of gray value to define a lamina. (D) “Slope method” using the rate of change in a gray-value profile. (E) “Wavelet method” for calculating sedimentation rates. Most studies have used the peak method for lamina counting. Image processing is required in many cases. The slope method has the advantage of detecting lamina boundaries; however, high-frequency noise should be avoided as much as possible. The wavelet method can be used to estimate sedimentation rates at sub-lamina resolution; however, it may, in fact, have low resolution depending on the attributes of the method.

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images are available to establish boundary definitions for varves or laminae by image analyses. Methods for recognizing varves or laminae and for measuring the thicknesses of varves include (1) manual microscopic analysis (Fig. 2B), (2) peak detection from image profiles (Fig. 2C), (3) inflection point detection in image profiles (Fig. 2D), and (4) dominant-wavelength (annual cycle) detection in image profiles using wavelet analysis (Fig. 2E). Some advantages and disadvantages are associated with each of these methods; however, the method used to analyze images is selected after considering of the objective of the study. In the following, we briefly summarize these methods. Manual microscopic analysis (e.g., Zolitschka, 1996; Walker, 2005), performed by using fresh sediment surfaces, thin sections, and photomicrographs, allows the detection of varve boundaries and measurement of varve thicknesses. Detection by megascopic analysis is relatively easy because decisions about varves and their boundaries rely on an integration of relative differences in varve color, components, and so forth. Although sub-annual laminae in varves can be detected by the method, objectivity and reproducibility are difficult to maintain. Additionally, the measurement of varve thickness suffers from the difficulty of objective boundary identification. The method based on peak detection (peak method) of a gray-value profile of a varve image has been used mostly to count and measure varves (e.g., Marshall et al., 2012). As fluctuations in the gray value of varve images, such as freshsurface photographs and X-ray radiographs, are clearly shown in the profiles, the method is thought to be the most effective one. However, image processing such as enhancement and filtering are required before peak detection (e.g., Cooper, 1997), when gray-value profiles of lowquality images are used in this method. For this reason, the peak method is frequently carried out manually; lamina boundaries are, for example, identified macroscopically in the gray value profile on a PC screen (Marshall et al., 2012). Additionally, profile peaks do not necessarily correspond to varve boundaries, so varve thickness measured by the method does not represent exact annual thickness (Fig. 2C). The method of detecting varve boundaries based on inflection points in gray-value profiles (slope method) can possibly detect the lamina boundaries composing a varve (Fig. 2D). On the other hand, high-frequency noises in the varve image derived from the condition of samples can be a very severe problem in this method. That is, definition of some threshold values removing noises is required so that inflection points in the profiles of varve images can indicate lamina boundaries because fine and low amplitude noise commonly tends to have large inflection values. Although

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image processing before applying this method is also required in these cases, measurements of varve thickness will be easy to carry out when the lamina boundaries of the varve are recognized. The wavelet analysis method (Prokoph and Patterson, 2004) has a substantial difference in results from the other methods. On the gray-value profiles in varve images, the most dominant wavelength is the one-year cycle in which the varve is composed of two different types of laminae. Spectral analyses, such as wavelet analysis, allow the detection of the dominant wavelength in the section analyzed as a series of sedimentation rates (varve thickness / year) (Fig. 2E). Using this method, we can obtain the varve thickness as a sedimentation rate at each point of the analyzed varved sediment, but the resolution of the wavelet transform is insufficient because the peaks of dominant wavelength obtained from an actual “noisy” varved sediment having vague waveforms of gray value are broad, discontinuous and sometimes unclear (Fig. 2E). Of the methods described above, methods (2) to (4) have another problem relating to the analyzed line and analyzed width (Fig. 1C to E). Varves and laminae do not necessarily have flat boundaries that continue horizontally, so the orientation of the analyzed line will affect the results, especially in a series of varve thicknesses. Therefore, it is better to use a horizontally averaged profile line with a width of several pixels (Fig. 1E) because high-frequency noise on the thick lines is reduced and the averaged profile is likely to have sufficient accuracy (Zolitschka, 1996). On an actual analysis, on the other hand, the excess width of the analyzed line will produce a profile with broad peaks, which makes it difficult to detect and measure varves. Identification and measurement of varves should be treated and solved as separate issues. A method for analyzing lamina images In the present study, we devised a procedure composed of a varve identification method and a time-series conversion. In the present study, a varve is defined as a couplet of two different types of lamina, thus varve boundaries correspond to upper and lower boundaries of laminae. Because the procedure of the present study can apply to laminae in sediments of similar nature, such as a deposit consisting of bicolored laminae in an image, each verve is then identified based on the results of lamina identification. For lamina identification, not only for varves, the recognition of laminae and the boundaries of the lamina are directly processed on digital images. The time-series conversion is performed based on the result of the lamina

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identification. We here test the procedure using an example of synthetic laminae (Fig. 3A). A gray-value series of the synthetic laminae (sg) was formed from a composition of three types of sinusoidal waves and quasi-random numbers (ε) that range from 0 to 1 at an interval of t as follows. sgt=sin 0.1 tπ180 +2sin 0.2 tπ180+sin 0.5 tπ180+ε In the synthetic laminae, horizontal fluctuations in gray value along the boundaries are not included (completely horizontal lamina). (1) Identification of lamina type and boundaries

The identification of lamina boundaries is carried out by the following procedure: (1) a square-shaped sampling window W1 is set in a gray-value image of the synthetic laminae to evaluate the change rates of gray value (Fig. 3A), (2) a linear sampling window W2 is set in an image profile from the gray-value image to calculate median values of gray value in the window, and (3) laminae boundaries are identified at the points that have the maximum change rate at the median value (Fig. 3C, D, E). The details follow. On a gray-value image of the synthetic laminae (Fig. 3A), we set a square-shaped data sampling window (W1: window 1) at each pixel except for margins of the image. The window size is 3 m×3 m pixels, and each window can be subdivided to 3×3 sub-windows (Fig. 3B). Thus, each subwindow has m×m pixels, with integer. Here, when each pixel in W1 has a gray value P (Fig. 3B), the average gray value h i j of each sub-window is then calculated by the following equation. h i j=

1 m m ∑ ∑ P mm m2

In each W1, the intensity of slope (change rate) (S ij) at the center of each W1 (Fig. 3B) is calculated as follows (Kamiya et al., 1999). S ij= S x 2+S y 2 where, S x= h i1 j1+h i1 j+h i1 j1−h i1 j1+h i1 j+h i1 j1 6D x S y= h i1 j1+h i j1+h i1 j1−h i1 j1+h i j1+h i1 j1 6D y


Fig. 3 The procedure for identifying lamina in this study and examples of lamina counting by the “peak method.” (A) Synthetic laminae. The laminae are composed of an integration of sinusoidal waves. No horizontal change in lamina boundaries is included. Details are described in the text. (B) Schematic illustration of calculations of W1 (window 1). In W1, data smoothing and slope calculations are processed in a 3×3 grid (a portion of the result is shown in (D)). Details are in the text. (C) Stratigraphic series of values (in this case, gray values) and their median values in W2 (window 2). (D) Change rate obtained from the slope analysis in (B). (E) Lamina identified map estimated from synthetic varve (A) through the procedure. Lamina boundaries and laminae are defined by the integration of the slope analysis and median values. (F) Lamina counting at white laminae detected by the “peak method” using moving windows. The boundaries are at the lowest value of change rate of gray value in a moving window. The window sizes were 10 pixels (upper) and 15 pixels (lower).

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Fig. 4 Procedure for obtaining time series of the synthetic laminae. (A) The synthetic laminae, same as Figure 3A. (B) Identified lamina map, same as Figure 3F. (C, D) Stratigraphic changes in frequency of pixel number along lamina planes. The thickness of a lamina is measured as the distance between the upper boundary suggested by a transit point in the two frequency series and the lower boundary suggested in same manner as the upper boundary (C: light-colored, D: dark-colored). (E) Schematic view of average values of pixels in the synthetic varve in (A) corresponding to each defined lamina in (B). These values can also be used in time-series analyses.

The values D x and D y, indicating distances between neighboring grids, can be ignored when the analyzed image is a regular grid because relative change rates are required for this analysis. To obtain a smoothed dataset, the preferred size of W1 is half of a “varve” thickness, suggesting the thicknesses of light and dark lamina, because the size of W1 should not largely exceed a thickness of light or dark lamina for the classification of them, and large noises on a waveform of gray value affecting lamina identification should be removed. Data smoothing and calculation of change rate in W1 yield a smoothed change-rate map (an example of a profile is shown in Fig. 3D). To calculate the median values along gray-value profiles, we set another window (W2) in the image along a stratigraphic section with one pixel wide and l pixels long (Fig. 3C). In W2, gray values of pixels are sorted and a median value suggesting a lamina boundary value is calculated. Thus, the length l of the W2 along the section should contain one or two sets of “varve” (a couplet of lamina) thickness. A median value is first calculated in a W2. Then, we move to a neighboring pixel along the stratigraphic section, set a subsequent W2, and repeat this procedure on all areas of the image except for intervals within l/2 pixels from the top and base. A lamina boundary is identified at the point having the largest value of change rate in W1 corresponding to a median value calculated in W2, which is used for identification of the lamina types (Fig. 3C, D, E). In fact,

when the gray value of a pixel in a W2 is larger than the median value (Fig. 3C) and the pixel is between two peaks in the change rate of slope (Fig. 3D), the pixel is determined as one of pixels in a “light-colored” lamina. On the other hand, when the gray value of a pixel in a W2 is smaller than the median value (Fig. 3C) and the pixel is between two peaks in the change rate of slope (Fig. 3D), the pixel is determined as one of pixels in a “dark-colored” lamina. If a pixel does not match either of the two definitions, the pixel is classified as neutral. In this manner, the laminae image is converted into a lamina identified map (Fig. 3E). Pixel sizes of the W1 and W2 mentioned above can be decided arbitrarily and be adjusted later, but the decision to use a spectral analysis is preferable for objectivity. When a spectral analysis, such as a wavelet analysis (e.g., Prokoph and Patterson, 2004), is applied to a gray-value profile of a varved sediment image (e.g., Figure 1C), we can obtain the most dominant wavelength of the profile suggesting an annual lamina thickness as an index of W2. Because W1 acts as a smoothing window, it should be smaller than half of the dominant wavelength. (2) Measurement of lamina thickness

Measurement of lamina thickness or the conversion of varve data to time-series data is processed by using the lamina-identified map as follows (Fig. 4). First, pixel numbers are counted along the horizontal direction to make histograms of “light-colored” and “dark-colored” pixels (Fig. 4C and D) for each horizon perpendicular to the


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Fig. 5 Distribution of the middle Pleistocene Hiruzenbara Formation and site of the sampling point. (A, B) Locality of Hiruzenbara Highland. (C) Distribution of the Hiruzenbara Formation (Research Group for Hiruzenbara, 1975a). The sampling site in the mining pit of the Showa Chemical Industry Co., Ltd is shown as a filled circle.

stratigraphic direction of the lamina-identified map (Fig. 4B). Because the pixel values in the synthetic laminae are emplaced to continue in the horizontal directions for simplicity, fluctuations of the lamina-identified map in that direction are not observed and pixel frequencies are changed completely at the boundaries (Fig. 4C, D). In actual varves or laminae, lamina boundaries commonly fluctuate and many “neutral” pixels are included, so the histograms have tails at both sides and are overlapped together. In this case,

a point at which the most frequent pixel type changes is defined as a varve boundary. The thickness of a lamina is calculated from the pixel number between two boundaries. “Averaged raw” pixel values of each lamina can be used as an index gray-value of the lamina (Fig. 4D). The values obtained from the “raw” pixel data can also be used in a time-series analysis.

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Application to varved sediments of the middle Pleistocene Hiruzenbara Formation (1) Lacustrine varves of the Hiruzenbara Formation

The middle Pleistocene Hiruzenbara Formation, including lacustrine diatomites, is distributed in the Hiruzenbara Highland, Maniwa City, Okayama Prefecture, southwest Japan (Fig. 5; Research Group for Hiruzenbara, 1975a, b). The Hiruzenbara Formation consists of dammed lake deposits of the Paleo-Hiruzenbara Lake, which formed in the Hiruzenbara Highland around Marine Isotope Stage 13 (Research Group for Hiruzenbara, 1975a, b; Ishihara and Miyata, 1999). The formation consists of a lower lake deposit of varved diatomites and an upper fluvial deposit of conglomerates. The diatomites, composed of 95% or more of fossil diatoms, contain varved sediments in most parts of the lower Hiruzenbara Formation. Light-green laminae consist of a large Stephanodiscus sp., which bloomed during the winter season, whereas darkgreen laminae are composed mainly of small Cyclotella comta, which bloomed from spring to autumn. Thus, a couplet of light- and dark-green laminae indicates an annual sediment layer (Research Group for Hiruzenbara, 1975a, b; Ishihara and Miyata, 1999). Cyclicities corresponding to solar activity are found in the time series of varve thickness (Ishihara and Miyata, 1999). A varve of the Hiruzenbara Formation, annual sediment with a thickness of 2 to 3 mm, consists of a couplet of light- and dark-green laminae (Fig. 1). A block sample of the varved sediment, 250×15×15 mm, was obtained from the lowest part of the formation at a mining pit of the Showa Chemical Industry Co., Ltd. in the Hiruzenbara Highland. A soft X-ray image of the sample (Fig. 1A, B), which was thinned to a thickness of 7 mm, was obtained as a negative film and converted to a digital image with a resolution of 1200 dpi. The exposure time for the image was 3.5 min, and the acceleration voltage and tube current were 40 kV and 3 mA, respectively. In the soft Xray image, the light-green laminae exhibit as dark layers because they are porous and have low density, whereas the dark-green laminae exhibit as light layers. The image shows some clearly laminated parts and some unclearly laminated parts (Fig. 1A, B). High-density laminae, such as those at ca. 165 mm from the top, suggest dark-green laminae containing much silt derived from river inflow. (2) Identification of a varve

The identified varves are shown in Figure 6 as tricolored lamina-identified maps with varied smoothing window sizes. The smoothing windows are changed from 30 to 60 pixels in W1 and from 1.5 to 2.5 mm (71 to 118 pixels) in

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W2. In Figure 6, black pixels suggest the high-transmittance light-green laminae, and white pixels suggest the low-transmittance dark-green laminae. Gray pixels represent an unidentified pixel type or the margin of the analyzed image. The unidentified type, which cannot be identified as a white or black pixel, includes irregular pixels such as points having the same gray values in adjacent pixels at the median value in the W2. The margin of the maps (Fig. 6) depends on the smoothing window sizes, i.e., when the size of W1 is 60 pixels, about 30 pixels are colored gray at both sides of the map, and the top and base are also colored gray with half the size of W2. In Figure 6, the map with W1 of 40 pixels and W2 of 1.5 mm (71 pixels) shows the smallest number of gray-colored pixels, so the map is an example of a mostly identified map. The best window sizes correspond to lamina thickness such that W1 is about half of a lamina thickness and W2 is the average thickness of a lamina as described above. (3) Measurements of the varve data

The identified laminae in the map do not necessarily align horizontally and some laminae pinch out, so the thickness measurement depends on the analyzed width. In this case, however, we used the maximum width (336 pixels＝ca. 7 mm) of the map in the trial to test difficulties of the measurement. Time-series graphs of varve thickness, laminae thickness, and the average and variance of gray values in a lamina, an indicator of the transmittance of soft X-rays, are shown in Figure 7. The time-series graph of varve thickness fluctuates from 1 to 3 mm, especially in the upper part. Thickness fluctuations of “white-” and “black-colored” laminae are broadly concordant with the time-series graph of varve thickness, as the “black-colored” laminae tend to vary in the upper part. The time-series graph of average gray value shows higher values in the lower parts of both colored lamina. In the time-series graph, a high-density lamina, illustrated in Figure 1A, is clearly confirmed in the 94th “white-colored” lamina from top (Fig. 7). The time-series graph of variance normalized by average gray value suggests heterogeneity in laminae, but no clear trend can be observed in Figure 7. Discussion In the present study, we summarized varve analysis methods and devised a newly automated method for identifying and measuring laminae of varves. As a result, we obtained time series of lamina properties, such as average gray value in addition to varve thickness, when we applied the present method. Because the method uses a


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Fig. 6 Tricolored identified-lamina maps of varves from the Hiruzenbara Formation. The unprocessed original image is from Figure 1. Analyzed window sizes are shown as values of W1 and W2. In these maps, low-density laminae have a high transmittance value for soft X-rays and are thus defined as “dark-colored” laminae, whereas high-density laminae are defined as “light-colored” laminae. Gray-colored pixels indicate parts in which a varve was not identified at the margins of the image. The lamina map using windows of 40 pixels (W1) and 1.5 mm (W2) is suitable for translating to a time series.

“raw” digital image despite processed image data, we could obtain additional varve information in the image, such as averaged gray-value in each lamina. Most of the methods for varve counting and measurement of their thickness in previous studies have been carried out on a thin line in an image to be analyzed (e.g., Tiljander et al., 2002). Furthermore, many automated methods using a digital image of varves use the peak method because the main subject of these studies is obtaining a precise age model for paleoenvironmental analyses (e.g., Marshall et al.,

2012). In the present study, we proposed a procedure in which boundary identification is first obtained. Then, thickness of lamina is measured based on the result of the lamina identification. When varve identification and measurement was carried out under a single operation in some previous studies, the accuracy of the operation remained unclear. However, because we separated the operations, some complications could be realized and solved, i.e., problems related to the width and location of the scan line for analyzing the image, which probably affect varve

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Fig. 7 Time-series graph of the varves translated from the lamina map (W1: 40 pixels and W2: 1.5 mm). (A) Time series graph of varve thickness. (B) Time series graph of thickness of sub-annual laminae (light- and darkcolored laminae). (C) Time series graph of transmittance value to soft X-rays suggested from gray values of the image (Fig. 1A). (D) Time series graph of variance of the gray value in each lamina. Values of variance are standardized using the average value. Arrow indicates the low-transmittance 94th lamina from the top. The highly variant value of variance at the 18th varve from the top suggests a varve containing a very thin portion of light- and dark-colored lamina in from opposite lamina, respectively.

identification, could be avoided in the present study. We can also measure the thickness of varves in a given location and the width on a varve-identified map for any purpose. Examples of the peak method applied to the synthetic image (Fig. 3F) suggest that identified lamina numbers are strongly influenced by window sizes. In the peak method, each lamina was detected at the lowest value of change rate of gray value in a moving window. The window sizes of the examples in Figure 3 are 10 pixels (upper) and 15 pixels (lower). Although the detected laminae clearly correspond to peaks of the gray-value profile, noises on the profile are also detected in the example of the narrow window (Fig. 3F upper). The example of the wide window (Fig. 3F lower)

shows the same lamina number in the result of the present method (Fig. 3E), but lamina boundaries could not be detected. One advantage of the present method is the ability to measure thickness of each lamina based on the identification of lamina boundaries. We set two smoothing windows, W1 and W2. These window sizes were assumed arbitrarily; however, a more objective procedure for window determination based on the dominant wavelength can be implemented by using spectral analysis (e.g., Prokoph and Patterson, 2004), as described above. A changeable moving window size based on the dominant period (annual lamina thickness) allows more precise varve identification because the window sizes


strictly affect the identification map (Fig. 6). Finally, in the present study, we used a soft X-ray image for analysis, but digital images such as a picture of a fresh surface and element mapping data can be applied to the method. The present method will be a helpful tool for analyzing paleoenvironmental records. Conclusion Identification of laminae boundaries in varved sediments and measurement of their thickness are the most basic and important procedures for obtaining high-resolution paleoenvironmental information. In the present study, we proposed a novel imge-analysis method and applied to identify lamiae in varved sediments of the Hiruzenbara Formation and to automatically measure the thickness of and information contained in the laminae. The method of the present study allows us to identify lamina boundaries well and measure lamina thickness, averaged gray value, and variance of the gray value in each lamina. The time series of varve thickness data and gray value of laminae evaluated by the method have the potential to provide more objective paleoenvironmental data for analyses. Additionally, the method is quite simple and robust, so application of the method to other cyclic deposits is not difficult. Acknowledgements We thank the staff of the Showa Chemical Industry Co., Ltd., for permission to sample in the mining pit. The authors would like to appreciate Dr. Tetsuya Sakai and the referee’s comments which helped improve this paper. This study was partly supported by funds (No. 127102) from the Central Research Institute of Fukuoka University. References Anderson, R.Y., 1993, The varve chronometer in Elk Lake: Record of climatic variability and evidence for solar/ geomagnetic 14C-climate connection. In Bradbury, J.P. and Dean W.E. eds., Elk Lake, Minnesota: Evidence for Rapid Climate Change in the North-Central United States (Geological Society of America Special Paper, 276), 45-68, Geological Society of America. Berger, W.H. and von Rad, U., 2002, Decadal to millennial cyclicity in varves and turbidites from the Arabian Sea: hypothesis of tidal origin. Global and Planetary Change, 34, 313-325. Böoes, X. and Fagel, N., 2005, Impregnation method for detecting annual laminations in sediment cores: An overview. Sedimentary Geology, 179, 185-194.

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Cooper, M.C., 1997, The use of digital image analysis in the study of laminated sediments. Journal of Paleolimnology, 19, 33-49. Haltia-Hovi, E., Saarinen, T. and Kukkonen, M., 2007, A 2000year record of solar forcing on varved lake sediment in eastern Finland. Quaternary Science Reviews, 26, 678689. Ishihara, Y. and Miyata, Y., 1999, Periodic variation extracted from lacustrine laminated diatomite of the middle Pleistocene Hiruzen-bara Formation, Okayama Prefecture. Journal of Geological Society of Japan, 105, 461-472. Kamiya, I., Tanaka, K., Hasegawa, H., Kuroki, T., Hayata, Y., Odagiri, S. and Masaharu, H., 1999, Production of slope map and its application. Geoinformatics, 10, 76-79. (in Japanese) Lotter, A. F. and Lemcke, G., 1999, Methods for preparing and counting biochemical varves. Boreas, 28, 243-252. Marshall, M., Schlolaut, G., Nakagawa, T., Lamb, T., Brauer, A., Staff, R., Ramsey, C.B., Tarasov, P., Gotanda, K., Haraguchi, T., Yokoyamai, Y., Yonenobu, H. and Tada, R., 2012, A novel approach to varve counting using μXRF and X-radiography in combination with thin-section microscopy, applied to the Late Glacial chronology from Lake Suigetsu, Japan. Quaternary Geochronology, 13, 7080. Nakagawa, T., Kitagawa, H., Yasuda, Y., Tarasov, P., Gotanda, K. and Sawai, Y., 2005, Pollen/event stratigraphy of the varved sediment of Lake Suigetsu, central Japan from 15, 701 to 10,217 SG vyrBP (Suigetsu varve years before present): Description, interpretation, and correlation with other regions. Quaternay Science Reviews, 24, 1691-1701. Nakagawa, T., Gotanda, K., Haraguchi, T., Danhara, T., Yonenobu, H., Brauer, A., Yokoyama, Y., Tada, R., Takemura, K., Staff, R. A., Payne, R., Ramsey, C.B., Bryant, C., Brock, F., Schlolaut, G., Marshall, M., Tarasov, P., Lamb. H. and Suigetsu 2006 Project Members, 2012, SG06, a fully continuous and varved sediment core from Lake Suigetsu, Japan: stratigraphy and potential for improving the radiocarbon calibration model and understanding of late Quaternary climate changes. Quaternary Science Reviews, 31, 57-64. Ojala, A.E.K., 2004, Application of X-ray radiography and densitometry in varve analysis. In Francus, P., ed., Image Analysis Sediments and Paleoenvironments, 187-202, Springer. Ojala, A.E.K. and Alenius, T., 2005, 10000 years of interannual sedimentation recorded in the Lake Nautajarvi (Finland) clastic-organic varves. Palaeogeography Palaeoclimatology Palaeoecology, 219, 285-302. Ojala, A.E.K. and Saarinen, T., 2002, Palaeosecular variation of the Earth’s magnetic field during the last 10000 years based on the annually laminated sediment of Lake Nautajarvi, central Finland. Holocene, 12, 391-400. Petterson, G., Odgaard, B.V. and Renberg, I., 1999, Image analysis as a method to quantify sediment components. Journal of Paleolimnology, 22, 443-455.

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時系列解析のための年縞堆積物の特徴を検出する手法の適用：蒜山原層の年縞堆積物の軟 X 線画像を用いた例佐々木

華・齋藤めぐみ・小松原純子・石原与四郎，2015，堆積学研究，Vol. 74，No. 1，31−43

Sasaki, H., Saito-Kato, M., Komatsubara, J. and Ishihara, Y.: Application of a method for detecting lamina characteristics in sediments for time series analysis: an example using a soft X-ray image of varves from the Hiruzenbara Formation Jour. Sed. Soc. Japan, Vol. 74, No. 1, 31−43 年縞堆積物は，年単位，場合によってはそれ以下の分解能をもち，高解像度の環境記録が得られることから，古くから多くの解析が行われてきた．このような解像度で情報を得るためには，一年ごとの年縞境界を認定し，年縞層厚やその中に含まれる物質の化学組成，微化石などを解析する必要がある．このような年縞境界の認定や層厚の計測は可能な限り客観的な方法が望ましい．年縞境界の認定・計測は，一般に目視や画像を利用した方法が行われる．目視による認定や測定は，人為的な誤差や境界の判定の難しさがある．一方，画像を用いた手法では，写真画像，軟 X 線画像，元素組成画像等を用いることができ，認定においては画像濃淡のピークをカウントする方法，しきい値を用いる方法，Wavelet 解析を用いる手法等がある．しかしながら，画像を利用した方法でも特に境界の認定に関わる様々な問題が指摘されている．たとえば，しきい値を用いる方法ではどの層準でも一定の基準を用いることができないこと，Wavelet 解析では分解能が十分で無いこと，ピーク等，波形処理ではノイズに弱いこと，等である．本研究では，年縞を始めとする縞状堆積物の葉理境界を認定する手法として，以下のような手順を試みた．すなわち，（1）画像濃淡の平滑化，（2）画像濃淡（たとえば明度）の最大傾斜面の認定，（3）画像濃淡の振幅の中間値の取得，（4）（2），（3）の組み合わせで境界の認定を行う，である．その結果，目視で認定した葉理境界と近い認定がなされた上，葉理内部の情報（たとえばある葉理内の軟 X 線透過率）も得ることができた．このようにして認定した境界を基に年縞を時系列化することで，年縞を構成する情報の年単位での変化や周波数解析等を容易に行うことができる．

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