1 
Signatures of reductive magnetic mineral diagenesis from unmixing of first-1 
order reversal curves 2 
 3 
Andrew P. Roberts
1
, Xiang Zhao
1
, Richard J. Harrison
2
, David Heslop
1
, Adrian R. Muxworthy
3
, 4 
Christopher J. Rowan
4
, Juan-Cruz Larrasoaña
5
, and Fabio Florindo
6
 5 
 6 
1. Research School of Earth Sciences, Australian National University, Canberra, ACT 2601, 7 
Australia 8 
2. Department of Earth Sciences, University of Cambridge, Cambridge, CB2 3EQ, UK 9 
3. Department of Earth Science and Engineering, Imperial College London, South Kensington 10 
Campus, London, SW7 2AZ, UK 11 
4. Department of Geology, Kent State University, 325 Lincoln Street, Kent, OH 44240, USA 12 
5. Instituto Geológico y Minero de España, Unidad de Zaragoza, C/ Manuel Lasala 44, 9B, 13 
Zaragoza 50006, Spain 14 
6. Institute of Earth Sciences Jaume Almera, Consejo Superior de Investigaciones Científicas, 15 
Barcelona 08028, Spain 16 
7. Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, 00143 Rome, Italy 17 
 18 
Abstract 19 
 Diagenetic alteration of magnetic minerals occurs in all sedimentary environments and 20 
tends to be severe in reducing environments. Magnetic minerals provide useful information about 21 
sedimentary diagenetic processes, which makes it valuable to use magnetic properties to identify 22 
the diagenetic environment in which the magnetic minerals occur and to inform interpretations of 23 
paleomagnetic recording or environmental processes. We use a newly developed first-order 24 
reversal curve (FORC) unmixing method on well-studied samples to illustrate how magnetic 25 
 2 
properties can be used to assess diagenetic processes in reducing sedimentary environments. From 26 
our analysis of multiple data sets, consistent magnetic components are identified for each stage of 27 
reductive diagenesis. Relatively unaltered detrital and biogenic magnetic mineral assemblages in 28 
surficial oxic to manganous diagenetic environments undergo progressive dissolution with burial 29 
into ferruginous and sulfidic environments, and largely disappear at the sulfate-methane transition 30 
(SMT). Below the SMT, a weak superparamagnetic to largely non-interacting stable single 31 
domain (SD) greigite component is observed in all studied data sets. Moderately interacting stable 32 
SD authigenic pyrrhotite and strongly interacting stable SD greigite are observed commonly in 33 
methanic environments. Recognition of these characteristic magnetic components enables 34 
identification of key diagenetic processes and should help to constrain interpretation of magnetic 35 
mineral assemblages in future studies. A key question for future studies concerns whether stable 36 
SD greigite forms in the sulfidic or methanic zones, where formation in deeper methanic 37 
sediments will cause greater delays in paleomagnetic signal recording. Authigenic pyrrhotite 38 
forms in methanic environments, so it will usually record a delayed paleomagnetic signal. 39 
 40 
1. Introduction 41 
 Magnetic mineral diagenesis involves the post-depositional modification of magnetic 42 
particles either by alteration of detrital sedimentary minerals or by authigenic growth of secondary 43 
magnetic minerals (Roberts, 2015). Diagenesis affects all sedimentary magnetic mineral 44 
assemblages, which makes it important to assess the extent of its effects. Diagenetic effects range 45 
from subtle (e.g., minor surficial oxidation of detrital/biogenic magnetic particles) to pervasive 46 
(e.g., complete dissolution of detrital/biogenic particles or growth of new authigenic phases that 47 
dominate the magnetic signal). Diagenetic magnetic mineral modification occurs over the full 48 
range of oxidizing to reducing conditions (Figure 1). Under oxic conditions, Fe
2+
 within magnetic 49 
minerals is oxidized progressively to Fe
3+
. Under reducing conditions, Fe
3+
 within magnetic 50 
 3 
minerals is reduced to Fe
2+
, which is achieved by corrosion of detrital/biogenic magnetic minerals, 51 
and incorporation of the liberated Fe
2+
 into authigenic pyrite or other paramagnetic phases. 52 
Reductive diagenesis is driven by microbial degradation of organic matter where different 53 
oxidants are used progressively with the following order of electron acceptor use: oxygen, nitrate, 54 
manganese oxides, iron (oxyhydr-)oxides, sulfate, and organic matter itself (Figure 1). When one 55 
oxidant is depleted, the next most efficient (i.e., most energy producing) oxidant is used, etc., until 56 
either all oxidants or all reactive organic matter are consumed (Froelich et al., 1979). In some 57 
settings, two respiration processes can occur simultaneously (e.g., Oremland and Taylor, 1978; 58 
Canfield and Thamdrup, 2009). The treatment provided here is based on the normal progression of 59 
environments expected during steady-state diagenesis (Figure 1). 60 
Magnetic minerals start to dissolve in ferruginous environments in association with iron 61 
reduction, and dissolution becomes pervasive in sulfidic environments where pore water sulfate is 62 
consumed entirely via microbial sulfate reduction or by anaerobic oxidation of methane (AOM) in 63 
underlying methanic environments, where the dominant process by which organic matter is 64 
degraded is via methanogenesis (Canfield and Thamdrup, 2009; Roberts, 2015). The ferruginous, 65 
sulfidic, and methanic diagenetic zones represent the more strongly reducing end of the spectrum 66 
in which the effects of diagenesis on magnetic mineral assemblages become pervasive. These 67 
environments are encountered frequently in paleomagnetic and environmental magnetic studies, 68 
which makes it important to have a thorough understanding of the types of magnetic mineral 69 
assemblages that occur in these settings and the diagenetic processes that modify or control them. 70 
A key aim in rock magnetism over the last 20 years has been to develop techniques that 71 
enable identification of individual magnetic mineral components. This is important in most 72 
paleomagnetic and environmental magnetic applications where magnetic signals are carried by 73 
mixed magnetic mineral assemblages. For example, even in seemingly simple pelagic carbonate 74 
sediments, four or five distinct magnetic mineral components are identified commonly (Roberts et 75 
 4 
al., 2013). Each component can potentially carry valuable environmental information; being able 76 
to unmix rigorously the magnetic signals carried by such materials can unlock this environmental 77 
information. Magnetic unmixing is also valuable in paleomagnetic studies, where, for example, 78 
sedimentary relative paleointensity signals are recorded with different efficiency by co-occurring 79 
detrital and biogenic magnetite (Ouyang et al., 2014; Chen et al., 2017). Various unmixing 80 
methods have been developed, which generally involve fitting of functions to derivatives of 81 
isothermal remanent magnetization (IRM) acquisition or direct current demagnetization curves 82 
(e.g., Robertson & France, 1994; Kruiver et al., 2001; Heslop et al., 2002; Heslop & Dillon, 2007) 83 
or to alternating field demagnetization curves of an anhysteretic remanent magnetization or IRM 84 
(Egli, 2004a, b, c). A key issue with magnetic unmixing is that, like any geophysical inversion 85 
method, potentially infinite combinations of components can be fitted to a given coercivity 86 
spectrum unless independent evidence is available concerning magnetic components (Heslop, 87 
2015). So-called semi-supervised or supervised unmixing is, therefore, needed to minimize 88 
ambiguities associated with spectral unmixing approaches (Heslop, 2015). 89 
First-order reversal curve (FORC) diagrams (Pike et al., 1999; Roberts et al., 2000) are 90 
used widely in rock magnetism because of their diagnostic value in identifying magnetic domain 91 
states and magnetostatic interactions for magnetic mineral components (Roberts et al., 2014). 92 
FORC measurements provide information about the magnetic response of all particles in a sample 93 
in terms of magnetization (represented by the magnitude of the FORC distribution), and the 94 
coercivity and magnetic interaction field distributions (Bc and Bi axes of the FORC diagram, 95 
respectively), where contrasting features can be used to diagnose the full range of magnetic 96 
domain states in fine magnetic particle systems. FORC distributions are, therefore, powerful for 97 
exploring subtle magnetization processes that are unrecognizable in standard hysteresis 98 
measurements. For readers who are less familiar with FORC diagrams, we show typical FORC 99 
diagrams in Figure 2 and refer here to papers that describe the key features for the following types 100 
 5 
of particle systems: superparamagnetic (SP; Pike et al., 2001a), stable single domain (SD) with 101 
and without interactions (Pike et al., 1999; Roberts et al., 2000, 2014), vortex (Pike & Fernandez, 102 
1999; Roberts et al., 2000, 2017; Muxworthy & Dunlop, 2002), and multi-domain (MD; Pike et 103 
al., 2001b). Despite their widespread use, most applications of FORC diagrams have only 104 
involved qualitative domain state identification or quantitative assessment of interactions (e.g., 105 
Muxworthy & Dunlop, 2002; Carvallo et al., 2006) without quantifying the contributions from 106 
each magnetic mineral component present in a sample, although some more quantitative attempts 107 
have had limited success (Muxworthy et al., 2005). This situation has changed with development 108 
of tools that enable quantitative simulation of FORC distributions (Harrison & Lascu, 2014) and 109 
with introduction of principal component analysis (PCA) to unmix FORC distributions (Heslop et 110 
al., 2014) into end-member (EM) components (Lascu et al., 2015). An important aspect of 111 
unmixing is to solve the linear mixing equation (Heslop, 2015), which was not achieved in the 112 
FORC-PCA approach of Lascu et al. (2015). Harrison et al. (2018), therefore, further developed 113 
FORC unmixing to solve this equation.  114 
In this paper, we use the new FORC unmixing algorithm of Harrison et al. (2018), which is 115 
built into the FORCinel software package (Harrison & Feinberg, 2008), to illustrate its power for 116 
understanding magnetic particle assemblages in sedimentary sequences that have undergone 117 
reductive diagenesis. Our aim is to reveal diagenetic processes through identification of the 118 
magnetic minerals present in these diagenetic systems. The identified magnetic components 119 
should be useful for future studies of similar diagenetic environments in which these components 120 
are expected to be encountered, where FORC unmixing can enable quantitative assessment of 121 
their respective contributions. Typical FORC diagrams for each domain state shown in Figure 2 122 
can be used as a guide to EM interpretation in the discussion below. 123 
 124 
  125 
 6 
2. Methods 126 
 The FORC measurements used in this study were all made with Princeton Measurements 127 
Corporation vibrating sample magnetometers in various laboratories around the world, with 128 
averaging times of 250 ms. The sample collections subjected here to FORC unmixing were treated 129 
with VARIFORC processing (Egli, 2013), where the parameters used are indicated in the 130 
respective figure captions for each data set presented. 131 
 While progressive reductive diagenesis might be expected to transform an initially more 132 
complex detrital/biogenic magnetic particle assemblage into one with simpler and less variable 133 
magnetic properties with either weak relict or authigenically enhanced magnetizations, we treat 134 
most sample sets independently. This approach maintains the integrity of the respective sample 135 
sets, and it recognises an important limitation associated with visualization of unmixing results. 136 
Multiple-component systems are readily represented in binary mixing lines, ternary diagrams, or 137 
in tetrahedra for quaternary mixtures, but higher-order mixing becomes more difficult to represent. 138 
This is not because of the mathematics, which can cope with many components, but because of the 139 
difficulty in visualizing results for so many components. Treating each sample set independently 140 
reduces the number of components identified, which helps to simplify data visualization. 141 
 142 
2.1 The new FORC unmixing algorithm 143 
 PCA is used routinely in many disciplines to estimate unknown EMs by providing a low-144 
rank approximation to data that facilitates definition of an empirical mixing space (Heslop, 2015). 145 
Details of FORC unmixing are described by Harrison et al. (2018); a brief outline is provided here 146 
to help readers to understand essential aspects of the approach. The principal advance in the 147 
FORC unmixing algorithm of Harrison et al. (2018) compared to that of Lascu et al. (2015) is that 148 
PCA is now performed on a representation of the magnetization curves rather than on processed 149 
FORC diagrams: this enables identification of both irreversible (i.e., remanence-bearing) and 150 
 7 
reversible magnetization components so that the total magnetization is the sum of linearly additive 151 
components that satisfy the linear mixing equation. With this approach, contributions due to SP 152 
and MD components, which either have no or little irreversible magnetization, are recognised and 153 
quantified. With the graphical user interface available in FORCinel (Harrison & Feinberg, 2008), 154 
EMs can be visualized and selected interactively using the FORC-PCA algorithm. EM selection is 155 
not physically constrained and is based on user selection; best solutions are obtained when users 156 
have other constraints with which to “supervise” EM selection. To facilitate EM selection, newly 157 
devised feasibility metrics are included to define an unmixing space within which EMs are 158 
physically realistic (Harrison et al., 2018). The feasibility metrics are contoured to help users to 159 
select EMs that satisfy reasonable criteria such as requiring FORCs to change monotonically and 160 
to not cross each other. Demarcation of this physically realistic space helps users to avoid manual 161 
selection of unrealistic EMs. Even with these feasibility constraints, EM selection within the 162 
“allowable space” depends on the user. It is generally desirable to select EMs that lie close to 163 
measured data points, but an EM can also represent a mixture (e.g., Heslop, 2015), so it can be 164 
desirable to select an EM that lies further from measured data points to obtain a less mixed EM. 165 
These aspects of EM selection are subjective, which emphasizes the need for independent 166 
information about samples and the value of user expertise. 167 
Smoothing of measurement noise is a key challenge for FORC processing (Roberts et al., 168 
2000, 2014; Harrison & Feinberg, 2008; Egli, 2013). To ensure that results for EMs and individual 169 
samples are comparable, all samples within a given dataset are treated in the FORC-PCA approach 170 
with the same VARIFORC parameters. This poses particular challenges when studying diagenesis 171 
because signal/noise ratios will contrast strongly because sample sets tend to contain either typical 172 
detrital or diagenetically enhanced magnetic mineral assemblages along with diagenetically 173 
depleted assemblages. This issue is discussed below where relevant. Following Egli (2013), areas 174 
where the FORC distribution equals zero are white. The positive FORC signal is then scaled from 175 
 8 
zero to the maximum value, and the negative region is scaled to its highest negative value. As 176 
discussed below, negative regions are important; more blue shades are evident when a negative 177 
region is deeper than for shallow negative regions. 178 
 While FORC unmixing has significant strengths, it also has limitations. The unmixing 179 
approach is as good as the data fed into it. For example, in the present study, FORC measurements 180 
focus on the <120 mT coercivity range. This biases explicitly against visualization of high 181 
coercivity minerals such as hematite and goethite. The weak spontaneous magnetizations of these 182 
minerals can also be swamped by more strongly magnetic co-existing minerals such as magnetite 183 
in FORC diagrams (e.g., Muxworthy et al., 2005; Roberts et al., 2014). Hematite tends to have 184 
broad coercivity spectra that extend from low to high values, so hematite will usually be partially 185 
evident in FORC diagrams with the field ranges used in this study (Roberts et al., 2006). As 186 
shown by Zhao et al. (2017), its detection can still be difficult when magnetite is present, and 187 
visualization of a hematite component is facilitated by use of adjustable non-linear color maps for 188 
FORC diagrams. Goethite has exceptionally high coercivity (Rochette et al., 2005), which makes 189 
it generally invisible in FORC diagrams in the adopted <120 mT coercivity range (cf. Roberts et 190 
al., 2006). Semi-quantitative determination of hematite and goethite concentrations is better 191 
achieved with low-temperature magnetic measurements (e.g., Lagroix & Guyodo, 2017). Our aim 192 
here is to understand diagenetic effects on typical detrital magnetic mineral assemblages and 193 
authigenic magnetic minerals that form during reductive diagenesis. Limitations associated with 194 
recognising hematite and goethite are acknowledged and readers with interests in understanding 195 
the diagenetic fate of these minerals should bear in mind that they will be largely invisible in the 196 
data representations in this paper. Overall, quantitative FORC analysis enabled by FORC 197 
unmixing has considerable potential because the domain state and interaction field distribution can 198 
be identified for each constituent magnetic component, which provides unprecedented levels of 199 
valuable information even for samples that comprise complex magnetic mixtures. 200 
 9 
 201 
3. Samples and setting 202 
 We present here reanalysed FORC data from several of our own published studies of 203 
reductive magnetic mineral diagenesis. We use well studied sample sets so that the identified 204 
components are known and can be used as references for such diagenetic systems in future studies. 205 
The studied samples include modern depositional systems in which detrital/biogenic magnetic 206 
mineral assemblages at the seafloor undergo progressive magnetic property changes associated 207 
with down-core reductive dissolution. This type of environment is represented by hemipelagic 208 
sediments recovered in sediment cores CD143-55705 from the Oman margin, Arabian Sea 209 
(Rowan et al., 2009; Chang et al., 2016a) and LC13-81-G138 from the Northern California 210 
margin, Pacific Ocean (Rowan et al., 2009). These cores progress from the oxic to methanic 211 
diagenetic zones and are dominated by sulfidic diagenesis (see Figure 1 and Roberts (2015) for 212 
nomenclature). Sulfidic to methanic diagenetic systems with more complete diagenetic reduction 213 
are represented by tectonically uplifted marine sediments from Neogene sequences that crop out 214 
throughout eastern North Island, New Zealand (Rowan and Roberts, 2006), Pleistocene marine 215 
sediments from Crostolo River, Italy (Roberts et al., 2005), and middle Pleistocene alluvial 216 
sediments from a drill core on the Tiber River coastal plain near Rome, Italy (Florindo et al., 217 
2007). Methanic environments are represented by sediment cores from Hydrate Ridge, Cascadia 218 
margin, offshore of Oregon, USA, which were recovered during Ocean Drilling Program (ODP) 219 
Leg 204 (Larrasoaña et al., 2007). 220 
 221 
4. Results 222 
4.1 Progressive down-core dissolution: ferruginous to sulfidic diagenesis 223 
 Many studies of coastal, hemipelagic, and pelagic sediments document progressive down-224 
core diagenetic dissolution of detrital iron oxides in reducing environments (Karlin & Levi, 1983, 225 
 10 
1985; Channell and Hawthorne, 1990; Karlin, 1990a, 1990b; Leslie et al., 1990a, 1990b; Roberts 226 
and Turner, 1993; Richter et al., 1999; Robinson et al., 2000; Yamazaki et al., 2003; Emiroglu et 227 
al., 2004; Liu et al., 2004; Garming et al., 2005; Rey et al., 2005; Riedinger et al., 2005; Dillon & 228 
Bleil, 2006; Kawamura et al., 2007; Rowan et al., 2009; Mohamed et al., 2011; Bouilloux et al., 229 
2013; Roberts, 2015; Chang et al., 2016b). These studies provide a common picture of surface 230 
sediments, generally with all stages of organic matter diagenesis recognised in pore water profiles 231 
(Figure 1) (Roberts, 2015). Surface sediments generally contain trace abundances of detrital iron 232 
oxide minerals, including ferric oxyhydroxides and biogenic magnetite. With ongoing burial, 233 
reactive magnetic minerals start to undergo dissolution in ferruginous diagenetic environments and 234 
more pervasive dissolution occurs once sulfide is produced in pore waters, with the finest particles 235 
dissolving first, and pyrite becoming increasingly abundant in sulfidic environments. The depth at 236 
which the magnetic mineral content declines precipitously depends on the organic carbon content 237 
and sedimentation rate, and can vary significantly (e.g., Karlin & Levi, 1983; Kawamura et al., 238 
2007; Roberts, 2015). We provide below two examples of FORC unmixing in environments that 239 
progress through the ferruginous and sulfidic diagenetic stages (Figure 1). 240 
 241 
4.1.1 Core CD143-55705, Oman margin 242 
 FORC unmixing results are shown in Figure 3 for 50 samples from core CD143-55705. 243 
This core has been studied extensively in relation to magnetic mineral diagenesis (Rowan et al., 244 
2009; Chang et al., 2016a) and is used here to illustrate diagenetic alteration of surface magnetic 245 
mineral assemblages. High initial IRM values (Figure 3j, gray curve) associated with a surface 246 
detrital/biogenic magnetic mineral assemblage decrease in two sharp steps at depths of ~2 m and 247 
~4.2 m to low values below ~5 m. The large IRM contrast between the upper and lower parts of 248 
the core presents a challenge for calculating FORC distributions because of the variable signal/ 249 
noise ratio and the need to smooth FORCs more for weakly magnetized samples. This challenge is 250 
 11 
illustrated in Figure 3a, b, where data are presented with respect to 3 principal components (PCs). 251 
In Figure 3a, data are plotted in the PC1-PC2 plane where it is clear that data from the upper part 252 
of the core (above ~4.2 m) fall on a single trend and data from the lower part of the core are 253 
scattered. Data that fall on a linear trend with positive PC1 values and near-zero PC2 values in 254 
Figure 3a for the upper part of the core define a triangular region in the PC1-PC3 plane in Figure 255 
3b, where data from the lower part of the core (below ~4.2 m) are also scattered. Therefore, we 256 
treat separately data from the upper and lower parts of the core. The triangular region identified in 257 
the PC1-PC3 plane in Figure 3b is used to define a 3 EM system for the upper part of the core, 258 
where FORC diagrams for the 3 EMs are shown in Figure 3d-f and the vertices of the triangle that 259 
represent each EM are shown with respect to the data in Figure 3g. As should be the case for a 260 
physically meaningful solution, the triangle for the 3 EM mixing system falls within a broader 261 
zone enclosed by shaded contours (Figure 3g) in which FORCs increase monotonically without 262 
crossing each other (Harrison et al., 2018). Noisier data from the lower part of the core are treated 263 
separately and are represented in the PC1-PC2 plane in Figure 3h. The conventional unmixing 264 
procedure is to define a mixing region in PC space from which EMs are identified. Due to the 265 
noisy nature of the data, we chose a single component that represents the entire magnetic mineral 266 
assemblage for the lower part of the core. With this approach, the scatter in the PC1-PC2 plane is 267 
considered to be due to the noisy data for weakly magnetized samples rather than due to a mixed 268 
magnetic mineral assemblage. A FORC diagram for this component is shown in Figure 3i, which 269 
is represented by the point where PC1 and PC2 equal zero (Figure 3h). An equivalent approach 270 
would be to average all FORC measurements from this interval to improve the signal/noise ratio. 271 
 The three components identified in the upper part of core CD143-55705 (Figure 3d-f) are 272 
represented by a stable single domain (SD)/fine vortex state component (EM1), a coarse vortex 273 
state/MD component (EM2), where vortex states are identified following the arguments of Roberts 274 
et al. (2017), and a noisier superparamagnetic (SP) to SD component (EM3). Down-core 275 
 12 
variations for the 3 components identified for the upper part of the core are shown in Figure 3j. 276 
EM1 is dominant in the uppermost part of the core, where the sharp non-interacting central ridge 277 
signal is interpreted to be due to biogenic magnetite (cf. Egli et al., 2010; Roberts et al., 2012). 278 
EM1 also has a fine vortex state detrital contribution. Chang et al. (2016a) demonstrated that 279 
biogenic and detrital magnetite record the low-temperature Verwey transition at different 280 
temperatures and that biogenic magnetite is present in this core to depths of 4.60 m. This 281 
interpretation is consistent with the down-core profile for EM1 in Figure 3j. EM2 represents a 282 
coarser detrital magnetic mineral fraction whose relative importance increases to depths of ~4.6 m 283 
at which point it drops sharply. EM3 is interpreted to represent an authigenic SP/SD component 284 
that has trivial relative concentrations in the upper part of the core except for within the minimum 285 
between two IRM peaks (Figure 3j). Its relative importance also increases sharply at ~4.6 m. The 286 
contribution from EM1 drops at the base of the upper IRM peak and EM2 is responsible for all of 287 
the lower IRM peak, and EM3 is always weak. The FORC diagram for EM3 (Figure 3f) is 288 
indicative of an SP/SD greigite assemblage and is similar to the average FORC result for the lower 289 
part of the core (Figure 3i), except that the latter has a greater stable SD contribution and a lesser 290 
SP contribution. Interpretation of these trends in terms of diagenesis is discussed further below. 291 
 292 
4.1.2 Core LC13-81-G138, Northern California margin 293 
 FORC unmixing results are shown in Figure 4 for core LC13-81-G138 (15 samples). This 294 
core has also been studied previously in relation to magnetic mineral diagenesis (Rowan et al., 295 
2009). Contrasting magnetizations in the upper and lower, diagenetically depleted, parts of the 296 
core mean that these two intervals are treated separately, as we did for core CD143-55705. Two 297 
data clusters occur in the PC1-PC2 plane (Figure 4a): a tight cluster at PC1 1 x 10-4, and a noisy 298 
one at PC1 < 0. In the PC1-PC3 plane (Figure 4b), the cluster at PC1 1 x 10-4 has a wider 299 
distribution along a line at constant PC1 values. This trend defines a binary mixing line (Figure 300 
 13 
4g) where EM1 is represented by a non-interacting stable SD component with a strong central 301 
ridge (Figure 4d) that is typical of biogenic magnetite (e.g., Egli et al., 2010; Roberts et al., 2012), 302 
and EM2 is a coarse detrital component dominated by the vortex state (Figure 4e). The measured 303 
data lie closer to EM2 and selection of EM1 in a position some distance away from the measured 304 
data (Figure 4g) is done to isolate an EM with a pure central ridge signature (Figure 4d) without 305 
admixture of EM2 (Figure 4e). Identical EM1 and EM2 components were identified by Channell 306 
et al. (2016), which they also identified as due to biogenic and detrital magnetite, respectively. 307 
Again, instead of fitting multiple components to the noisy FORC distributions from the lower part 308 
of the core, a single FORC distribution is selected to represent this interval (Figure 4f) where PC2 309 
and PC3 equal zero (Figure 4c). 310 
 As is the case for core CD143-55705, the upper part of core LC13-81-G138 is dominated 311 
by SD biogenic and coarser detrital magnetite components. This biogenic component declines 312 
throughout the upper part of the record at the expense of the coarser detrital component in both 313 
cores LC13-81-G138 (Figure 4i) and CD143-55705 (Figure 3j). The diagenetically depleted lower 314 
part of core LC13-81-G138 (Figure 4f) has a similar average SP/SD FORC signature as the same 315 
zone in core CD143-55705 (Figure 3i). Interpretation of the LC13-81-G138 record in terms of 316 
diagenesis is discussed further in the Discussion section. 317 
 318 
4.2 Magnetic enhancement via greigite authigenesis: sulfidic diagenesis 319 
 In the examples discussed above, reductive diagenesis has depleted initial surficial detrital/ 320 
biogenic magnetic mineral assemblages via dissolution, followed by weak magnetic enhancement 321 
via authigenic growth of SP/SD greigite. During early diagenesis, dissolved Fe
2+
 and H2S react to 322 
form authigenic greigite, which can grow from initially fine SP/SD assemblages to stable SD 323 
particle assemblages with strong magnetostatic interactions that dominate magnetic mineral 324 
 14 
assemblages. Greigite can also grow in methanic environments in association with AOM. We now 325 
consider greigite-forming environments with two sets of examples. 326 
 327 
4.2.1 Greigite formation in Pleistocene sediments from Italy 328 
4.2.1.1 Middle Pleistocene alluvial sediments, Tiber River plain 329 
 We present results here for Middle Pleistocene alluvial sediments from a drill core on the 330 
Tiber River plain near Rome, Italy (Florindo et al., 2007). Harrison et al. (2018) used FORC 331 
results from this group of 16 samples to illustrate FORC unmixing, which we show in Figure 5. 332 
Three EMs are identified, all of which are due to greigite. EM1 (Figure 5a) has less vertical spread 333 
than EM2 (Figure 5b), and a negative peak that starts from below the main positive peak of the 334 
FORC distribution with a trend at –45° from the positive peak (Figure 5a). EM2 has a strong 335 
positive contribution with a broad, concentric distribution, and a deeper negative contribution 336 
along the negative Bi axis (Figure 5b) that is typical of interacting SD greigite (Roberts et al., 337 
2006, 2011). EM3 comprises a SP/SD component (Figure 5c) that is present in all sample sets 338 
analysed here. FORC measurements for 4 weakly magnetized samples were averaged to increase 339 
the signal/noise ratio to obtain an average result that was included in the PCA to identify EM3. 340 
The identified three-EM system is defined within the contoured region for physically realistic 341 
solutions in the PC1-PC2 plane (Figure 5d). Typical FORC diagrams for real samples are shown 342 
for comparison with the calculated EMs in Figure 5e-h. These samples are dominated by EM2 343 
(Figure 5g, 5h), but also clearly represent mixtures with the other EMs (Figure 5e, 5f). Details of 344 
the EMs and the processes that they represent are discussed further below. 345 
This example also illustrates challenges associated with FORC unmixing. The horizontal 346 
stripes in FORC diagrams for EM2 and EM3 are due to VARIFORC smoothing (Egli, 2013), 347 
where the unmixing space is defined using noisy experimental data and the same VARIFORC 348 
parameters are used to unmix the entire sample set (Harrison et al., 2018). These “stripes” are 349 
 15 
mostly present in weak samples or EMs. The weak EM3 is dominated by a horizontal ridge; 350 
measurement noise coupled with the chosen VARIFORC parameters produces the artefact stripes. 351 
Despite the visually and technically unappealing artefact stripes associated with FORC smoothing 352 
for weakly magnetized samples and calculated EMs, the overall FORC pattern is clear. Smoothing 353 
of noisy measurement data is a key challenge in FORC data processing (e.g., Roberts et al., 2000, 354 
2014; Harrison and Feinberg, 2008; Egli, 2013); this example illustrates some of the compromises 355 
associated with the second derivative calculation used to obtain FORC distributions. 356 
 357 
4.2.1.2 Lower Pleistocene marine sediments, Crostolo River 358 
 We present results here for tectonically uplifted Lower Pleistocene greigite-bearing marine 359 
sediments from Crostolo River, Italy (Tric et al., 1991; Roberts et al., 2005). Three EMs are 360 
identified from 12 analysed samples (Figure 6a-c), which are similar to those from the Tiber River 361 
plain, with two distinct interacting SD components (EM1 and EM2; Figure 5a, 5b) and one SP/SD 362 
component (EM3; Figure 5c). In PC1-PC2 space, most data points cluster around EM2 (Figure 363 
6e), so that measured FORC diagrams are mainly like those of EM2 (Figure 6f). Only four data 364 
points reveal more scatter (Figure 6d, e); these samples represent mixtures of the three identified 365 
EMs, where sample CR01B (Figure 6i) is a mixture of EM1 and EM2, sample CR03B is closer to 366 
EM1 (Figure 6g), and sample CR02D lies closest to EM3 but has contributions from both EM1 367 
and EM2 (Figure 6h). Like the Tiber River plain example, the three EMs are all authigenic 368 
components that grew during diagenesis, as discussed further below. 369 
 370 
4.2.2 Greigite formation in Neogene marine sediments, New Zealand 371 
 We present results here for tectonically uplifted Neogene marine sediments that crop out 372 
throughout eastern New Zealand (Rowan and Roberts, 2006). We group FORC results for 129 373 
samples from wide-ranging mudstone outcrops of varying age because they appear to have 374 
 16 
undergone diagenesis in similar environments. Four EMs are identified from FORC unmixing 375 
(Figure 7). These sediments have been altered strongly by reductive diagenesis, but a detrital 376 
magnetic component persists in some tuffaceous samples, and iron-titanium oxides are also likely 377 
to occur as inclusions within detrital silicate particles (Chang et al., 2016c). EM1 is identified as a 378 
coarse detrital iron oxide MD component carried by four tuffaceous samples from the NR locality 379 
of Rowan and Roberts (2006) (Figure 7a). By contrast, EM2 is represented by pure SD greigite 380 
with strong magnetostatic interactions (Figure 7b) that is a typical signature of authigenic greigite 381 
(e.g., Roberts et al., 2006, 2011; Rowan & Roberts, 2006; Florindo et al., 2007; Vasiliev et al., 382 
2007; Chang et al., 2014; Liu et al., 2016). EM3 and EM4 link the other two components (Figure 383 
7e, f), where both have a strong SP signal but EM3 contains a SD/vortex state detrital fraction 384 
(Figure 7c), while EM4 comprises a less strongly interacting SP/SD greigite component (Figure 385 
7d). These four components are typical of the New Zealand sediments studied by Rowan and 386 
Roberts (2006). Mixing among the four EMs is illustrated in Figure 7e and 7f, and FORC 387 
diagrams for typical samples with intermediate properties are shown in Figure 7g-7j. Details of the 388 
EMs and the processes that they represent are discussed further below. 389 
 390 
4.3 Magnetic mineral diagenesis in methanic environments 391 
 Methanic environments are represented by sediment cores from Hydrate Ridge, Cascadia 392 
margin, offshore of Oregon, USA, which were recovered during ODP Leg 204 (Larrasoaña et al., 393 
2007). FORC diagrams for 20 samples can be represented by four components (Figure 8), the first 394 
three of which are common to sulfidic environments (Figures 5, 6). EM1 is a coarse vortex state 395 
component due to detrital magnetic minerals (Figure 8a), which is associated with terrigenous 396 
inputs via turbidites (Larrasoaña et al., 2007). EM2 is a strongly magnetostatically interacting SD 397 
greigite component (Figure 8b), while EM3 corresponds to the authigenic SP/SD component that 398 
is seen in all examples above (Figure 8c). EM4 (Figure 8d) is typical of methanic environments, 399 
 17 
and is due to authigenic pyrrhotite (e.g., Weaver et al., 2002; Larrasoaña et al., 2007; Roberts et 400 
al., 2010; Kars & Kodama, 2015a, b; Horng, 2018). Relationships among the EMs for this data set 401 
are shown in Figure 8e, 8f. Typical FORC diagrams for intermediate samples that fall between 402 
EMs are shown in Figure 8g, 8h. The EM2-EM3 trend represents the dominant variation between 403 
fine SP/SD greigite and stable SD greigite assemblages. EM1 represents an isolated component 404 
where coarse detrital particles have been admixed via exogenous turbidite inputs, while EM4 405 
represents an additional authigenic pyrrhotite component that has formed during methanic 406 
diagenesis. Details of the EMs and the processes that they represent are discussed further below. 407 
 408 
5. Discussion 409 
5.1 Domain states and magnetocrystalline anisotropy types in EMs 410 
 Expected FORC signatures for all domain states (Figure 2) can be compared with those 411 
identified for each EM in Figures 3-8. When using PCA, any EM can represent a mixture of 412 
magnetic components (Heslop, 2015), and various EMs evidently consist of such mixtures (e.g., 413 
EM1 in Figure 3; EM3 in Figure 7). Nevertheless, the domain states represented by each EM are 414 
understandable in terms of the framework provided in Figure 2. In addition to recognising domain 415 
states, FORC results can reveal features related to the type of magnetic anisotropy that controls the 416 
magnetization in different minerals. For example, SD particles with uniaxial anisotropy always 417 
have a negative peak along the Bi axis (Muxworthy et al., 2004; Newell, 2005). Harrison & Lascu 418 
(2014) demonstrated that FORC distributions for SD particles with cubic anisotropy also have 419 
such a peak (feature 1 in Figure 5f) as well as an additional negative peak below the main positive 420 
peak with elongation at –45° (feature 2 in Figure 5f). Such negative elongated peaks can be 421 
obscured by various features, including mixtures of domain states and strong magnetostatic 422 
interactions (Harrison & Lascu, 2014), but when they are present they indicate the presence of 423 
magnetic particles with multi-axial rather than uniaxial anisotropy. The presence of negative peaks 424 
 18 
such as feature 2 in Figure 5f in greigite-bearing samples and EMs as documented here (Figure 5a) 425 
confirms that greigite has cubic magnetocrystalline anisotropy (Roberts, 1995; Roberts et al., 426 
2011). This type of negative peak is also seen systematically in FORC diagrams for authigenic 427 
pyrrhotite (Figure 8d, 8g) that forms in methanic environments (e.g., Weaver et al., 2002; 428 
Larrasoaña et al., 2007; Roberts et al., 2010; Kars & Kodama, 2015a, b; Horng, 2018). This is due 429 
to triaxial anisotropy in the basal plane of pyrrhotite crystals (Martín-Hernández et al., 2008). 430 
Such features provide diagnostic information about magnetocrystalline anisotropy type, which is 431 
relevant to magnetic mineral identification, in addition to providing information about domain 432 
state. Importantly, even though pyrrhotite and greigite give rise to negative peaks with elongation 433 
at –45°, FORC distributions for authigenic pyrrhotite typically have lower coercivity and negative 434 
slopes (Figures 6a, 6g, 7j, 8d, 8g) than those for greigite (Figure 5a, 5f). 435 
 436 
5.2 Diagenetic processes and interpretation of FORC unmixing results 437 
The EMs identified in the above examples from well-studied settings provide a consistent 438 
and systematic view of the magnetic properties associated with different diagenetic zones and of 439 
well documented diagenetic processes in these reducing sediments. Linking these characteristic 440 
FORC results to diagenetic processes (Figure 9) should assist future studies of sediments that have 441 
undergone similar magnetic mineral diagenesis. Below we outline the main magnetic properties 442 
and diagenetic processes that affect magnetic minerals in the oxic to ferruginous, sulfidic, and 443 
methanic zones (Figure 9), respectively. 444 
 445 
5.2.1 Oxic to ferruginous diagenesis 446 
Surficial seafloor, lake bed, or river bed sediments are likely to contain primary magnetic 447 
mineral assemblages with relatively little diagenetic modification, especially if bottom waters are 448 
oxic. Compared to the pervasive diagenetic modification of magnetic minerals that occurs in the 449 
 19 
sulfidic and methanic zones, modification of magnetic minerals is relatively minor in the oxic, 450 
nitrogenous, and manganous zones and starts to become more significant in the ferruginous zone 451 
(Roberts, 2015). Cores CD143-55705 and LC13-81-G138 lack pore water chemistry data, but a 452 
diagenetic zonation can be developed by combining FORC results with the scanning electron 453 
microscope (SEM) observations of Rowan et al. (2009) and the SEM and transmission electron 454 
microscope (TEM) observations of Chang et al. (2016a) because observed biogenic and authigenic 455 
minerals can be linked to the biogeochemistry of sedimentary environments (Berner, 1981). 456 
Addition of biogenic magnetite to primary detrital magnetic mineral assemblages 457 
contributes significantly to the magnetic properties of surface sediments in cores CD143-55705 458 
and LC13-81-G138. Magnetotactic bacteria generally biomineralize magnetite at the base of the 459 
nitrogenous zone (Figure 9), which may occur in the water column or uppermost sediment 460 
column, where iron is bioavailable due to upward diffusion of dissolved Fe
2+
 from the underlying 461 
ferruginous zone (Roberts, 2015). Contributions from the inorganic post-mortem remains of 462 
magnetotactic bacteria are evident from a central ridge signature (Figures 3d, 4d) in FORC 463 
diagrams (Egli et al., 2010; Roberts et al., 2012) from the uppermost sediments in cores CD143-464 
55705 and LC13-81-G138 (Figure 9). TEM observations (Chang et al., 2016a) demonstrate the 465 
presence of fossil magnetosomes in these surficial sediments and confirm our interpretation of the 466 
central ridge FORC signature. Fine-grained bacterial magnetite is highly reactive under reducing 467 
conditions and EM1 is depleted progressively with depth in both cores (Figures 3j, 4i). This loss 468 
of the finest magnetite population can occur in association with iron reduction in the ferruginous 469 
diagenetic zone or with sulfate reduction in the sulfidic zone, and enhances the contribution of a 470 
coarser EM2 vortex state/MD component (Figures 3j, 4i). Chang et al. (2016a) demonstrated that 471 
detrital and biogenic magnetite have different Verwey transition temperatures and used this to 472 
demonstrate that biogenic magnetite persists to depths of ~4.6 m in core CD143-55705 at which 473 
point the IRM is depleted to low values. From SEM observations, Rowan et al. (2009) 474 
 20 
documented minor sedimentary pyrite at depths of 0.1 m below the top of core CD143-55705, 475 
which indicates that sulfidic conditions were established close to the sediment-water interface (cf. 476 
Berner, 1981), and that the overlying diagenetic zones must be extremely thin. Both studied 477 
sediment cores occur in regions with an oceanic oxygen minimum zone (OMZ), but were both 478 
taken from below the modern OMZ (Levin, 2003). Bottom waters in these settings are oxic and 479 
the rapid progression to sulfidic conditions at shallow depths is likely due to high organic carbon 480 
inputs and microbial respiration of this organic matter near the sediment-water interface. Oxic to 481 
ferruginous diagenetic zones in the studied cores are likely to have been present because upward 482 
diffusion of bioavailable Fe
2+
 from the ferruginous zone is likely to have been used by 483 
magnetotactic bacteria to biomineralize magnetite at the base of the nitrogenous zone. 484 
Nevertheless, these zones would have been thin considering the shallow depths at which pyrite is 485 
present in these sediments. All further magnetic mineral diagenesis in these cores will have 486 
occurred under sulfidic or methanic conditions, as discussed below. 487 
 488 
5.2.2 Sulfidic diagenesis 489 
Dissolution of magnetite and hematite becomes ubiquitous in sulfidic sediments (Canfield 490 
and Berner, 1987). Dissolved Fe
2+
 released from detrital and biogenic iron-bearing minerals reacts 491 
with dissolved H2S, which is a by-product of sulfate reduction, to form sedimentary iron sulfides, 492 
particularly pyrite (Berner, 1984). Dissolution of detrital magnetite and hematite during sulfidic 493 
diagenesis, and replacement by paramagnetic pyrite, which does not carry a permanent 494 
magnetization, progressively destroys the primary paleomagnetic record. Hematite is less reactive 495 
than magnetite in reducing environments (Robinson et al., 2000; Yamazaki et al., 2003; Emiroglu 496 
et al., 2004; Liu et al., 2004; Garming et al., 2005; Rey et al., 2005; Kawamura et al., 2007; 497 
Rowan et al., 2009; Roberts, 2015; Korff et al., 2016), but it will also undergo progressive 498 
dissolution with depth. We do not discuss the fate of hematite further in this context because it is 499 
 21 
less visible in FORC diagrams than magnetite (see Section 2.1 above). Progressive loss of detrital 500 
and biogenic magnetic minerals via dissolution and pyrite formation is evident in the upper parts 501 
of cores CD143-55705 and LC13-81-G138 (Figures 3j, 4i). The presence of pyrite at shallow 502 
depths in core CD143-55705 (Rowan et al., 2009; Chang et al., 2016a) indicates that sulfidic 503 
conditions existed just below the sediment-water interface, which raises the question of why 504 
surficial IRM values decrease to low values down-core in two steps rather than one (Figures 3j) in 505 
core CD143-55705. The lower IRM peak is depleted in biogenic magnetite (EM1) and is enriched 506 
in the coarser vortex state/MD detrital component (EM2). In core CD143-55705, there is a local 507 
increase in the diagenetic SP/SD greigite component (EM3) in the minimum between IRM peaks. 508 
EM3 is then the only component below the lower IRM peak. These features indicate that the base 509 
of the upper IRM peak represents the modern sulfate-methane transition (SMT; Figure 9). The 510 
base of the lower IRM peak likely represents a former SMT position, which migrated upward with 511 
a change in sedimentary conditions to leave a relict coarse detrital component (EM2) between the 512 
old and new sulfidic dissolution fronts (Riedinger et al., 2005; Rowan et al., 2009). Even though 513 
biogenic magnetite is fine-grained and reactive to dissolved sulfide, low-temperature magnetic 514 
measurements indicate that minor magnetofossil concentrations remain in core CD143-55705 to 515 
depths of ~4.6 m in correspondence with the former SMT position (Chang et al., 2016a). 516 
Once detrital and biogenic magnetic components have been dissolved by sulfidic 517 
diagenesis, the only magnetic minerals that are likely to remain are authigenic minerals that form 518 
in reducing environments, relict minerals that are unreactive or slowly reactive to sulphide, such 519 
as chromite (Hounslow, 1996), titanohematites (Franke et al., 2007; Garming et al., 2007), or iron 520 
oxide inclusions within silicate minerals that are protected from sulfidization by their silicate hosts 521 
(Roberts, 2015; Chang et al., 2016b, 2016c). The only component detected with FORC unmixing 522 
below the former SMT position at ~4.6 m in core CD143-55705 (Figure 3i) is an authigenic 523 
SP/SD greigite component (EM3). This component is fine-grained, weak, and lacks strong 524 
 22 
magnetostatic interactions. It is possible that the magnetically non-interacting SD part of EM3 525 
(Figure 3i, 4f) is a central ridge signature (Egli et al., 2010) associated with greigite-bearing 526 
magnetotactic bacteria. Identification of ancient magnetite magnetofossils has expanded greatly 527 
with joint use of FORC diagrams and TEM observations (e.g., Yamazaki, 2008, 2009; Roberts et 528 
al., 2012; Yamazaki & Ikehara, 2012). Roberts (2015) suggested that greigite magnetofossils 529 
should be more abundant in the geological record than magnetite magnetofossils, particularly if 530 
they are gradient organisms (Bazylinski & Frankel, 2004) that live near the so-called oxic-anoxic 531 
interface (i.e., nitrogenous to ferruginous boundary in Figure 1), because magnetite dissolves 532 
when buried into the sulfidic diagenetic zone, whereas greigite remains stable. The potential for 533 
widespread greigite magnetofossil occurrences remains undemonstrated, and is an important 534 
research avenue. The link between central ridge FORC signatures and greigite magnetofossils is 535 
established (Reinholdsson et al., 2013; Chang et al., 2014; Chen et al., 2014), but the challenge 536 
will be to provide convincing evidence from TEM observations of greigite magnetosomes, which 537 
do not have the ideal crystal morphology or chain arrangement of magnetite magnetosomes 538 
(Farina et al., 1990; Mann et al., 1990; Pósfai et al., 1998a, 1998b; Kasama et al., 2006). 539 
Greigite formation has been documented in modern continental margin marine sediments 540 
at depths of several meters to tens of meters below the sediment-water interface (Kasten et al., 541 
1998; Jørgensen et al., 2004; Liu et al., 2004; Neretin et al., 2004; Riedinger et al., 2005, 2014; 542 
Larrasoaña et al., 2007; Fu et al., 2008; Rowan et al., 2009). Strongly magnetized stable SD 543 
greigite with strong magnetostatic interactions that is typically associated with sulfidic diagenesis 544 
(EM2 in Figures 5-8) is not evident in the relatively short sediment cores discussed here. There is, 545 
therefore, a disconnect in our understanding of early diagenesis and the point at which the strongly 546 
interacting stable SD greigite grows. It has been assumed that initial SP/SD greigite assemblages 547 
(EM3 in Figure 3-8) continue to grow through the stable SD blocking volume with progressive 548 
sulfidization at depth to transform into such assemblages (Rowan and Roberts, 2006; Rowan et al., 549 
 23 
2009), but marine sediment cores are usually not long enough to assess whether this progressive 550 
greigite formation mechanism is correct. Liu et al. (2016) documented strongly interacting stable 551 
SD greigite in discrete sediment layers from a long sediment core from the South Yellow Sea 552 
starting from depths of ~6 m below the sediment-water interface. However, this shallow water 553 
setting has been subjected to major non-steady state diagenetic changes associated with large-554 
amplitude Quaternary sea level variations and lack of a pore-water profile makes it difficult to 555 
assess the diagenetic environment in which this greigite formed. Stable SD greigite has been 556 
documented extensively within sediments in methanic environments in association with AOM 557 
(Housen & Musgrave, 1996; Horng & Chen, 2006; Musgrave et al., 2006; Enkin et al., 2007; 558 
Larrasoaña et al., 2007; Kars & Kodama, 2015a, b; Shi et al., 2017), so the possibility of greigite 559 
formation in either the sulfidic or methanic zones should be considered (Figure 9). The depth of 560 
this greigite formation has important consequences for the timing of sedimentary paleomagnetic 561 
signal acquisition. Rowan et al. (2009) estimated from widely distributed sediment cores that the 562 
onset of early greigite formation at the SMT (with properties like EM3) starts from 0.6 to >220 563 
kyr after deposition depending on the sedimentation rate, with SD greigite formation in underlying 564 
sediments occurring over periods of ≥1 to ≥160 kyr. Later formation in the methanic zone can lead 565 
to remanence acquisition delays of a few kyr to Myr (Larrasoaña et al., 2007), including complete 566 
remagnetization (Roberts and Weaver, 2005). Assessing recording delays associated with greigite 567 
growth is a key issue in magnetic studies of diagenetically reduced sediments. 568 
 569 
5.2.3 Methanic diagenesis 570 
 In the methanic diagenetic zone, AOM is the most important known process that affects 571 
magnetic mineral assemblages (Roberts, 2015). Sulfate reduction via AOM consumes pore water 572 
methane and sulfate to depletion at the SMT (Figure 1) and provides a secondary, relatively 573 
mobile, source of H2S (Murray et al., 1978; Devol & Ahmed, 1981; Niewöhner et al., 1998; 574 
 24 
Kasten & Jørgensen, 2000; Jørgensen & Kasten, 2006) that can cause both reductive dissolution of 575 
detrital iron oxides and formation of secondary ferrimagnetic iron sulfides. If the SMT occurs at 576 
shallow depths, as in the examples shown in Figures 3 and 4, early diagenetic greigite growth will 577 
result in relatively short delays in paleomagnetic signal acquisition. If Fe
2+
 and H2S are available 578 
at greater depths (Figure 9), however, greigite can form at any time during diagenesis (Roberts 579 
and Weaver, 2005). Fe
2+
 concentrations can increase within the methanic zone due to coupling of 580 
AOM to Fe and Mn reduction (Beal et al., 2009; Sivan et al., 2011; Segarra et al., 2013; Riedinger 581 
et al., 2014; Egger et al., 2015). While dissolved sulfide production is expected at the SMT during 582 
steady-state diagenesis (Figure 1), methane is often mobilized through fracture and fault networks 583 
in tectonically active settings. AOM of this mobile methane can release H2S that will react with 584 
any available Fe
2+
 to cause magnetic iron sulfide formation at any time during diagenesis (Figure 585 
9), which makes AOM an important process in magnetic mineral diagenesis. Greigite is known to 586 
occur in methane-rich sediments or in methane hydrates (e.g., Housen and Musgrave, 1996; Horng 587 
and Chen, 2006; Musgrave et al., 2006; Enkin et al., 2007), while greigite and pyrrhotite also form 588 
in association with methane diffusion (Figures 5, 8, 9; Larrasoaña et al., 2007). 589 
Potential greigite formation during both sulfidic and methanic diagenesis (Figure 9) raises 590 
questions about the diagenetic zone in which the stable SD greigite formed in the case studies 591 
illustrated in Figures 5-8. The presence of greigite in methanic environments is generally 592 
associated with its formation during earlier sulfidic diagenesis, but this is not necessarily the case. 593 
The common occurrence of remagnetizations in greigite-bearing sediments of eastern North 594 
Island, New Zealand, led Rowan and Roberts (2008) to suggest that late greigite formation was 595 
associated with deeper diagenetic processes such as gas hydrate formation and AOM. Likewise, 596 
van Dongen et al. (2007) demonstrated from organic geochemical evidence that AOM occurred 597 
within greigite-bearing nodules. Nevertheless, assumed linkages between greigite formation and 598 
sulfidic environments have not been questioned widely. In addition to greigite, pyrrhotite has been 599 
 25 
documented widely in association with methane hydrates (Housen and Musgrave, 1996; Horng 600 
and Chen, 2006; Musgrave et al., 2006; Enkin et al., 2007; Rudmin et al., 2018) and in tectonically 601 
fractured areas that support active methane diffusion or venting (Larrasoaña et al., 2007), which 602 
suggests that authigenic pyrrhotite is an indicator of methanic environments (Figure 9). The 603 
authigenic pyrrhotite that forms in methanic environments is magnetic so it has been assumed 604 
widely to be monoclinic pyrrhotite (e.g., Weaver et al., 2002; Larrasoaña et al., 2007; Kars & 605 
Kodama, 2015a; Roberts, 2015). Horng (2018) and Horng and Roberts (2018) demonstrated 606 
recently that authigenic pyrrhotite in methanic sediments has an unambiguous hexagonal rather 607 
than monoclinic crystal structure. Hexagonal pyrrhotite is expected to be antiferromagnetic, so 608 
further work is needed to understand and explain its magnetic structure. 609 
The above observations raise the question of whether sulfidic and methanic diagenetic 610 
environments can be distinguished from each other from the magnetic properties of magnetic 611 
mineral assemblages. Characteristic kidney-shaped FORC distributions with negative slopes for 612 
SD pyrrhotite and a negative region also with negative slope (Weaver et al., 2002; Wehland et al., 613 
2005; Larrasoaña et al., 2007; Roberts et al., 2010; Kars & Kodama, 2015a, b; Horng, 2018) 614 
suggest that pyrrhotite can be identified readily from FORC distributions (Figure 8d, 8g). This 615 
negative region is sometimes not evident because of the scaling of FORC diagrams, but it can be 616 
made more visible through manual adjustment of the color scale. Nevertheless, the negative slope 617 
of the positive part of FORC distributions for pyrrhotite-bearing samples is distinct from FORC 618 
distributions for greigite-bearing samples. Additionally, the peak coercivity of FORC distributions 619 
for our SD greigite-bearing samples is ~60-70 mT, while it is ~20-40 mT for our pyrrhotite-620 
bearing samples. Based on these observations, we suggest that the Crostolo River sediments 621 
contain previously unidentified pyrrhotite (Figures 6a, 6g, 6h). In contrast, Tric et al. (1991) 622 
argued that the Crostolo Rover sediments contain a detailed Upper Olduvai polarity transition 623 
record associated with greigite that grew during earliest burial. Roberts et al. (2005) demonstrated 624 
 26 
from detailed SEM observations that different generations of greigite formed in these sediments, 625 
but they could not constrain the timescales involved and concluded that it was relatively early. 626 
Thus, these sediments record magnetic signatures associated with both sulfidic and methanic 627 
stages, which illustrates the potential difficulties in discriminating in which of these two stages 628 
greigite formed. Magnetic signatures due to pyrrhotite have not been detected previously in the 629 
Crostolo River sediments, which provides new information about the diagenetic history of these 630 
sediments. It is important to note that pyrrhotite is not always identified in association with 631 
methane hydrates (e.g., Shi et al., 2017). Also, even though remagnetization of sediments from 632 
eastern North Island, New Zealand, has been attributed to tectonically driven methane migration 633 
(Rowan & Roberts, 2008), no pyrrhotite is evident in FORC diagrams from these sediments 634 
(Figure 7). However, pyrrhotite FORC signatures are evident in four samples from the NC locality 635 
(Figure 7j) in northeastern South Island (Rowan & Roberts, 2006), which indicates that these 636 
sediments experienced methanic diagenesis. Overall, though, key markers for diagenetic processes 637 
of interest may not always be present. As ever, positive evidence is important and an absence of 638 
evidence provides neither confirmation nor disproof of a process. 639 
 640 
6. Conclusions 641 
FORC unmixing with PCA provides clear detection of magnetic properties associated with 642 
magnetic mineral diagenesis during early sediment burial. From our analysis of multiple data sets 643 
(FORC measurements for > 240 samples), consistent magnetic components are identified from 644 
sediments that have undergone various stages of reductive diagenesis (Figure 9). Relatively 645 
unaltered magnetic assemblages in oxic to manganous diagenetic zones are rich in coarse detrital 646 
magnetic minerals and fine biogenic magnetite. These minerals dissolve progressively in 647 
ferruginous and sulfidic diagenetic environments and largely disappear when buried to the base of 648 
the sulfidic zone at the SMT. Below the SMT, authigenic phases dominate magnetic mineral 649 
 27 
assemblages. An initial weak and magnetostatically weakly interacting authigenic SP/SD greigite 650 
component is identified in all studied sulfidic and methanic settings, along with stable and 651 
strongly interacting SD greigite. An additional magnetostatically interacting pyrrhotite component 652 
is identified in methanic environments. Mixtures of the components are common in the respective 653 
environments; FORC unmixing enables quantification of the contributions of each component. 654 
Identification of FORC signatures for each component and association of their magnetic properties 655 
with the diagenetic processes to which they have been subjected provides information concerning 656 
sedimentary magnetic signatures that will enable researchers to grapple with relevant questions 657 
that arise when considering diagenesis and its effects on paleomagnetic and environmental signals. 658 
Despite the clarity of our results concerning the magnetic mineral components that occur in 659 
reducing diagenetic environments, our work raises a key unresolved question. Greigite can form in 660 
both sulfidic and methanic diagenetic environments (Figure 9); in most cases where greigite has 661 
been identified, it remains unknown in which of these diagenetic zones greigite formed. 662 
Significant smoothing can affect paleomagnetic and environmental signal acquisition in both 663 
cases, but smoothing will be a more significant complication in deeper methanic environments. 664 
Determining the environment in which greigite formed is important for understanding magnetic 665 
signals associated with sedimentary reductive diagenetic processes. It is important to gain a better 666 
understanding in future studies of the extent to which stable SD greigite grows in sulfidic versus 667 
methanic diagenetic environments. It is also important to note that authigenic pyrrhotite forms in 668 
methanic environments, so it will usually record a delayed paleomagnetic signal. 669 
 670 
Acknowledgements 671 
This work was supported financially by the Australian Research Council through grant 672 
DP160100805, by the European Research Council under the European Union’s Seventh 673 
Framework Programme (FP/2007–2013)/ERC grant agreement number 320750, and by National 674 
 28 
Institute of Advanced Industrial Science and Technology, Ministry of Economy, Trade and 675 
Inustry, Japan. We thank Luca Lanci and Tilo von Dobeneck for constructive reviews that 676 
improved this paper, Michael Walter for editorial handling, and Mrs Sue Wigley for organizing a 677 
writing week that enabled the first five authors of this paper to finalize the unmixing algorithm 678 
and prepare manuscripts for publication. The authors are in the process of creating a global FORC 679 
database to which the data presented in this paper will be added after publication. 680 
 681 
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Neogene marine sediments from New Zealand. Earth and Planetary Science Letters, 241, 119–1003 
137. 1004 
Rowan, C. J., & Roberts, A. P. (2008). Widespread remagnetizations and a new view of Neogene 1005 
tectonic rotations within the Australia-Pacific plate boundary zone, New Zealand. Journal of 1006 
Geophysical Research: Solid Earth, 113, B03103, doi:10.1029/2006JB004594. 1007 
Rowan, C. J., Roberts, A. P., & Broadbent, T. (2009). Reductive diagenesis, magnetite dissolution, 1008 
greigite growth and paleomagnetic smoothing in marine sediments: A new view. Earth and 1009 
Planetary Science Letters, 277, 223–235. 1010 
Rudmin, M., Roberts, A. P., Horng, C. S., Mazurov, A., Savinova, O., Ruban, A., Kashapov, R., 1011 
& Veklich, M. (2018). Ferrimagnetic iron sulfide formation and methane venting across the 1012 
 42 
Paleocene-Eocene Thermal Maximum in shallow marine sediments, ancient West Siberian 1013 
Sea. Geochemistry, Geophysics, Geosystems, 19, 21–42. 1014 
Segarra, K. E. A., Comerford, C., Slaughter, J., & Joye, S. B. (2013). Impact of electron acceptor 1015 
availability on the anaerobic oxidation of methane in coastal freshwater and brackish 1016 
wetland sediments. Geochimica et Cosmochimica Acta, 115, 15–30. 1017 
Shi, M. N., Wu, H. C., Roberts, A. P., Zhang, S. H., Zhao, X. X., Li, H. Y., Su, X., Yang, T. S., 1018 
Chang, L., Hu, P. X., Zhao, X., & Wang, H. Q. (2017). Tectonic, climatic, and diagenetic 1019 
control of magnetic properties of sediments from Kumano Basin, Nankai margin, 1020 
southwestern Japan. Marine Geology, 391, 1–12. 1021 
Sivan, O., Adler, M., Pearson, A., Gelman, F., Bar-Or, I., & John, S. G. (2011). Geochemical 1022 
evidence for iron-mediated anaerobic oxidation of methane. Limnology and Oceanography, 1023 
56, 1536–1544. 1024 
Tric, E., Laj, C., Jehanno, C., Valet, J. P., Kissel, C., Mazaud, A., & Iaccarino, S. (1991). High-1025 
resolution record of the Upper Olduvai transition from Po Valley (Italy) sediments: Support 1026 
for dipolar transition geometry? Physics of the Earth and Planetary Interiors, 65, 319–336. 1027 
van Dongen, B. E., Roberts, A. P., Schouten, S., Jiang, W. T., Florindo, F., & Pancost, R. D. 1028 
(2007). Formation of iron sulfide nodules during anaerobic oxidation of methane. 1029 
Geochimica et Cosmochimica Acta, 71, 5155–5167. 1030 
Vasiliev, I., Dekkers, M. J., Krijgsman, W., Franke, C., Langereis, C. G., & Mullender, T. A. T. 1031 
(2007). Early diagenetic greigite as a recorder of the palaeomagnetic signal in Miocene-1032 
Pliocene sedimentary rocks of the Carpathian foredeep (Romania). Geophysical Journal 1033 
International, 171, 613–629. 1034 
Weaver, R., Roberts, A. P., & Barker, A. J. (2002). A late diagenetic (syn-folding) magnetization 1035 
carried by pyrrhotite: Implications for paleomagnetic studies from magnetic iron sulphide-1036 
bearing sediments. Earth and Planetary Science Letters, 200, 371–386. 1037 
 43 
Wehland, F., Stancu, A., Rochette, P., Dekkers, M. J., & Appel, E. (2005). Experimental 1038 
evaluation of magnetic interaction in pyrrhotite bearing samples. Physics of the Earth and 1039 
Planetary Interiors, 153, 181–190. 1040 
Yamazaki, T. (2008). Magnetostatic interactions in deep-sea sediments inferred from first-order 1041 
reversal curve diagrams: Implications for relative paleointensity normalization. 1042 
Geochemistry, Geophysics, Geosystems, 9, Q02005, doi:10.1029/2007GC001797. 1043 
Yamazaki, T. (2009). Environmental magnetism of Pleistocene sediments in the North Pacific and 1044 
Ontong-Java Plateau: Temporal variations of detrital and biogenic components. 1045 
Geochemistry, Geophysics, Geosystems, 10, Q07Z04, doi:10.1029/2009GC002413. 1046 
Yamazaki, T., Abdeldayem, A. L., & Ikehara, K. (2003). Rock-magnetic changes with reduction 1047 
diagenesis in Japan Sea sediments and preservation of geomagnetic secular variation in 1048 
inclination during the last 30,000 years. Earth, Planets and Space, 55, 327–340. 1049 
Zhao, X., Roberts, A. P., Heslop, D., Paterson, G. A., Li, Y. L., & Li, J. H. (2017). Magnetic 1050 
domain state diagnosis using hysteresis reversal curves. Journal of Geophysical Research: 1051 
Solid Earth, 122, 4767–4789. doi:10.1002/2016jb013683. 1052 
  1053 
 44 
Figure captions 1054 
Figure 1 Cartoon representation of the depth distribution of sedimentary redox-driven 1055 
diagenetic zones. Electron acceptors and respiration processes by which reactants are consumed 1056 
are indicated on the left. Idealized pore water profiles of reactants (O2, NO2
−, NO3
−) and products 1057 
(NO3
−, Mn
2+
, Fe
2+
, H2S, CH4) and associated chemical zones are shown on the right (modified 1058 
from Jørgensen and Kasten (2006), Canfield and Thamdrup (2009), and Roberts (2015)). The 1059 
names used for chemical zones are from Canfield and Thamdrup (2009). Authigenic iron 1060 
minerals that can form in the respective chemical zones are listed in the far right-hand column 1061 
(modified from Berner, 1981). 1062 
Figure 2 Representative FORC diagrams for fine magnetic particle systems with different 1063 
dominant domain states. Examples are individual samples discussed later in this study, except 1064 
(f). (a) Non-interacting SD particles with part of the particle assemblage near the SP/SD 1065 
threshold size (see Pike et al. (2001a) for details). Sample MH30 from New Zealand, with the 1066 
following VARIFORC smoothing parameters (Egli, 2013): sc,0 = 8, sc,1 = 10, sb,0 = 7, sb,1 = 10, 1067 
and c = b = 0.2. Such diagenetically reduced samples are usually weakly magnetized and 1068 
noisy. (b) Strongly interacting stable SD particles (see Pike et al. (1999) and Roberts et al. 1069 
(2000, 2014) for details). Sample WB26 from New Zealand, with the following VARIFORC 1070 
smoothing parameters (Egli, 2013): sc,0 = 5, sc,1 = 7, sb,0 = 4, sb,1 = 7, and c = b = 0.1. (c) 1071 
Moderately magnetostatically interacting stable SD particles with multi-axial anisotropy (see 1072 
Harrison & Lascu (2014) for details). Sample SDC3950 from Italy, with the following 1073 
VARIFORC smoothing parameters (Egli, 2013): sc,0 = 5, sc,1 = 8, sb,0 = 5, sb,1 = 8, and c = b = 1074 
0.1. (d) SD/vortex state particles (see Pike and Fernandez (1999) and Roberts et al. (2017) for 1075 
details). Sample CD1431056 from the Arabian Sea, with the following VARIFORC smoothing 1076 
parameters (Egli, 2013): sc,0 = 5, sc,1 = 8, sb,0 = 5, sb,1 = 8, and c = b = 0.1. (e) MD particles 1077 
typically seen in natural samples (Roberts et al., 2000; Pike et al., 2001b). Sample NR27 from 1078 
 45 
New Zealand, with the following VARIFORC smoothing parameters (Egli, 2013): sc,0 = 5, sc,1 1079 
= 7, sb,0 = 4, sb,1 = 7, and c = b = 0.1. (f) MD particles seen in coarser systems dominated by 1080 
domain wall pinning (see Pike et al. (2001b) and Roberts et al. (2014) for details). Geological 1081 
samples rarely have such behaviour; the example is a silicon steel sample with conventional 1082 
FORC smoothing with smoothing factor = 4. 1083 
Figure 3 FORC unmixing results for ferruginous to sulfidic diagenetic environments in core 1084 
CD143-55705. Distribution of PCs for 50 measured FORC diagrams in (a) PC1-PC2 space, (b) 1085 
PC1-PC3 space, and (c) PC2-PC3 space. Data for the lower part of the core (enclosed by an 1086 
ellipse in (a)) are noisy and are treated separately (26 samples)). Data for the upper part of the 1087 
core (enclosed by an ellipse in (a); 24 samples) define a triangular region in (b) from which 1088 
three EMs are defined where (d) is a non-interacting stable SD/vortex state component (EM1) 1089 
due to biogenic and detrital magnetite, (e) is a coarser vortex state to MD component (EM2) 1090 
due to detrital magnetic minerals, and (f) is an authigenic SP-SD component (EM3) that formed 1091 
during early diagenesis. Sets of FORCs shown for EMs in this and other figures are usually 1092 
incomplete representations. For experimental measurements, a set of FORCs provides an 1093 
outline of the major hysteresis loop and is approximately symmetrical, whereas the lower part 1094 
of the set of FORCs for EMs is usually not shown because the lowermost FORCs represent 1095 
areas that lie outside the limits defined for the EM FORC diagrams. In such a representation, 1096 
EM FORCs will, thus, usually appear truncated and asymmetrical, and can possibly appear 1097 
distorted. The triangular mixing space with positions of the three EMs is shown in (g), where 1098 
contours indicate the space where FORC distributions start to become physically unrealistic 1099 
(see Harrison et al. (submitted ms)). The arrow indicates the general down-core trend from 1100 
EM1 to EM2 to EM3. (h) Representation of the noisy data from the lower part of the core 1101 
(ellipse in (a)) that were averaged to obtain (i) a FORC diagram defined where PC1 and PC2 1102 
equal zero in (h). (j) Down-core IRM profile (gray) with relative contributions of EM1, EM2, 1103 
 46 
and EM3. VARIFORC parameters (see Egli (2013)) for smoothing of the PCA solution are: sc,0 1104 
= 5, sc,1 = 8, sb,0 = 5, sb,1 = 8, and c = b = 0.1. The maximum applied field for FORC 1105 
measurements was 500 mT, which is sufficient to saturate magnetically the low-coercivity 1106 
minerals in the studied samples. 1107 
Figure 4 FORC unmixing results for ferruginous to sulfidic diagenetic environments in 1108 
marine sediment core LC13-81-G138. Distribution of PCs for 15 measured FORC diagrams in 1109 
(a) PC1-PC2 space, (b) PC1-PC3 space, and (c) PC2-PC3 space for core LC13-81-G138. Data 1110 
for the lower part of the core (scattered data to the left in (a) and (b)) are noisy and are treated 1111 
separately (10 samples)). Data for the upper part of the core (enclosed by an ellipse in (b); 5 1112 
samples) define a binary mixing line from which 2 EMs are defined where (d) is a non-1113 
interacting stable SD component (EM1) due to biogenic magnetite and (e) is a coarser vortex 1114 
state component (EM2) due to detrital magnetic minerals. (f) An authigenic SP-SD component 1115 
(EM3) that formed during early diagenesis is obtained by averaging the noisy FORC data 1116 
indicated in (h) where PC1 and PC2 equal zero. (g) Binary mixing space with positions of 2 1117 
EMs for the upper part of the core. (i) Down-core IRM profile (gray) with relative contributions 1118 
of EM1 and EM2 for the upper part of the core. VARIFORC parameters (see Egli (2013)) for 1119 
smoothing of the PCA solution are: sc,0 = 5, sc,1 = 8, sb,0 = 5, sb,1 = 8, and c = b = 0.1. The 1120 
maximum applied field for FORC measurements was 500 mT, which is sufficient to saturate 1121 
magnetically the low-coercivity minerals in the studied samples. 1122 
Figure 5 FORC unmixing results for sulfidic diagenetic environments in Middle Pleistocene 1123 
Italian fluvial clays (Florindo et al., 2007). (a) EM1 is magnetostatically interacting stable SD 1124 
greigite, where the negative region at –45° is indicative of multi-axial anisotropy (see Harrison 1125 
& Lascu (2014)). (b) EM2 is a magnetostatically interacting stable SD greigite component with 1126 
higher coercivity than EM1. (c) EM3 is an authigenic SP-SD component that is observed in all 1127 
environments analysed here (defined by the average for 4 weakly magnetized samples). (d) The 1128 
 47 
triangular mixing space with positions of the three EMs for 16 samples, where the contours 1129 
indicate the space where FORC distributions start to become physically unrealistic. (e-h) FORC 1130 
diagrams for measured samples, which fall dominantly near (g, h) EM2, with mixtures with (e) 1131 
EM3 and (f) EM1. VARIFORC parameters (see Egli (2013)) for smoothing of the PCA 1132 
solution are: sc,0 = 8, sc,1 = 10, sb,0 = 7, sb,1 = 10, and c = b = 0.1. The maximum applied field 1133 
for FORC measurements was 500 mT, which is sufficient to saturate magnetically the low-1134 
coercivity minerals in the studied samples. 1135 
Figure 6 FORC unmixing results for sulfidic (and methanic) diagenetic environments in 1136 
tectonically uplifted Lower Pleistocene marine mudstones from Crostolo River, Italy (Roberts 1137 
et al., 2005). (a) EM1 represents magnetostatically interacting pyrrhotite, where the negative 1138 
region at –45° is indicative of multi-axial anisotropy (see Harrison & Lascu (2014)). (b) EM2 is 1139 
a magnetostatically interacting stable SD greigite component. (c) EM3 is an authigenic SP-SD 1140 
component that is observed in all environments analysed here. (d, e) Triangular PC1-PC2 1141 
mixing space (12 samples) with (d) 4 scattered weakly magnetized samples from which 3 EMs 1142 
are defined and (e) all samples, where the dominant behavior is scattered around EM2. 1143 
Contours in (d, e) indicate the space where FORC distributions start to become physically 1144 
unrealistic. (f-i) FORC diagrams for measured samples, which range from (f) being dominated 1145 
by EM2, (g) near EM1, (h) mixture of EM1 and EM3, and (i) mixture of EM2 and EM3. 1146 
VARIFORC parameters (see Egli (2013)) for smoothing of the PCA solution are: sc,0 = 8, sc,1 = 1147 
10, sb,0 = 7, sb,1 = 10, and c = b = 0.1. The maximum applied field for FORC measurements 1148 
was 500 mT, which is sufficient to saturate magnetically the low-coercivity minerals in the 1149 
studied samples. 1150 
Figure 7 FORC unmixing results for sulfidic diagenetic environments in tectonically 1151 
uplifted Neogene marine sediments from eastern New Zealand (Rowan and Roberts, 2006). 1152 
Four EMs are identified, where (a) EM1 is a coarse detrital iron oxide component, and (b) EM2 1153 
 48 
is stable SD greigite with strong magnetostatic interactions. EM3 and EM4 link the other two 1154 
components, where both have a strong SP signal, but (c) EM3 contains a SD/vortex state 1155 
detrital fraction, and (d) EM4 comprises a less strongly interacting SP/SD greigite component. 1156 
(e, f) Visualizations of a tetrahedral mixing space (129 samples) for: (e) PC1-PC2 and (f) PC1-1157 
PC3. (g-j) Representative FORC diagrams for measured samples that represent mixtures 1158 
between (g) EM1 and EM3, (h) EM1, EM3, and EM4, (i) EM2, EM3, and EM4, and (j) EM2, 1159 
EM3, and EM4. VARIFORC parameters (see Egli (2013)) for smoothing of the PCA solution 1160 
are: sc,0 = 8, sc,1 = 10, sb,0 = 7, sb,1 = 10, and c = b = 0.1. The maximum applied fields for 1161 
FORC measurements were either 500 or 1000 mT, which is sufficient to saturate magnetically 1162 
the low-coercivity minerals in the studied samples. 1163 
Figure 8 FORC unmixing results for sulfidic and methanic diagenetic environments in 1164 
sediments with active methane venting from Hydrate Ridge, Cascadia margin, offshore of 1165 
Oregon, USA (Larrasoaña et al., 2007). Four EMs are identified, where (a) EM1 is a coarse 1166 
detrital iron oxide component (in turbidite samples), (b) EM2 is stable SD greigite with strong 1167 
magnetostatic interactions, (c) EM3 is an authigenic SP-SD component, and (d) EM4 is 1168 
magnetostatically interacting pyrrhotite, where the negative region at –45° is indicative of 1169 
multi-axial anisotropy (see Harrison & Lascu (2014)). (e, f) Visualizations of tetrahedral 1170 
mixing (20 samples) for: (e) PC1-PC2 and (f) PC1-PC3. (g, h) Representative FORC diagrams 1171 
for measured samples that represent mixtures between (g) EM2 and EM4, and (h) EM2 and 1172 
EM3. The mixing space is well defined by measured samples that represent each EM, so 1173 
contours are not shown to indicate the space for physically realistic FORCs. VARIFORC 1174 
parameters (see Egli (2013)) for smoothing of the PCA solution are: sc,0 = 5, sc,1 = 7, sb,0 = 4, 1175 
sb,1 = 7, and c = b = 0.1. The maximum applied field for FORC measurements was 500 mT, 1176 
which is sufficient to saturate magnetically the low-coercivity minerals in the studied samples. 1177 
 49 
Figure 9 Illustration of typical FORC diagrams encountered in different diagenetic 1178 
environments. (a) Schematic pore water profile for progressive steady state diagenesis and (b) 1179 
chemical zones from Figure 1. FORC diagrams that are typical of (c) biogenic magnetite and 1180 
(d) biogenic magnetite and a fine detrital magnetite fraction are encountered typically in oxic to 1181 
ferruginous environments. Biogenic magnetite ceases to be stable in ferruginous environments. 1182 
Variable FORC diagrams are typically observed for detrital magnetic mineral assemblages 1183 
containing magnetite with variable grain sizes as illustrated in (e-g), where coarse magnetite 1184 
remains stable in oxic to manganous zones and starts to dissolve in the ferruginous zone. Iron 1185 
oxides are unstable in the sulfidic and methanic zones and are unlikely to survive (unless they 1186 
occur as inclusions within silicate particles; e.g., Chang et al. (2016b, c)). At the SMT, 1187 
dissolved sulfide reacts with any available Fe
2+
 to form (h) SP/SD greigite. If Fe
2+
 is available 1188 
in the methanic zone, stable SD authigenic pyrrhotite can grow (i). Stable SD greigite (j) is 1189 
encountered widely in reducing diagenetic environments, but it has not been linked definitively 1190 
to the SMT and it could form deeper within the sediment column where Fe
2+
 is available and 1191 
AOM creates a source of H2S to enable greigite formation. The location of stable SD greigite 1192 
formation is, therefore, indicated with question marks. Note that while the FORC diagrams 1193 
presented in this figure are typical of the environments in question they are not necessarily 1194 
unique to these environments. 1195 
 1196 
Figure 1.
Electron acceptor
O2
NO2-
NO3-
MnO2
FeOOH
SO42-
CO2
Chemical zone
O2
NO2- NO3
-
Mn2+
Fe2+
CH4
Respiration process
Aerobic
respiration
Nitrate reduction
Manganese
reduction
Iron reduction
Methanogenesis
Oxic
Nitrogenous
Manganous
Ferruginous
Sulfidic
Methanic
Authigenic iron
mineral formation
FeOOH/hematite/
magnetite
Magnetite/FeOOH
Pyrite ±
mackinawite/greigite
Greigite/pyrrhotite/
siderite
De
pt
h 
(a
rb
itr
ar
y)
Fe2+
Anaerobic oxidation
of methane
Sulfate reduction
H2S SMT
SMT = sulfate-methane transition
Figure 2.
-150
-100
-50
0
50
12080400
140
120
100
80
60
40
20
0
 Bc (mT)
 B
i (m
T)
Am2/T2
-150
-100
-50
0
50
100
12080400
140
120
100
80
60
40
20
 Bc (mT)
 B
i (m
T)
Am2/T2 -40
-20
0
20
40
403020100
400
300
200
100
0
 Bc (mT)
 B
i (m
T)
Am2/T2
-200
-100
0
100
200
80400
5
4
3
2
1
0
 Bc (mT)
 B
i (m
T)
Am2/T2
-150
-100
-50
0
50
12080400
200
150
100
50
0
 Bc (mT)
 B
i (m
T)
Am2/T2 -150
-100
-50
0
50
12080400
300
200
100
0
 Bc (mT)
 B
i (m
T)
Am2/T2
(a) (b) (c)
(d) (e) (f)
SP/non-
interacting SD
Interacting SD Multi-axial
interacting SD
SD/vortex MD Coarse
MD
SD
SP
SD
vortex
vortex
Figure 3.
4(d)
(g)
(j)
(e) (f)
(i)(h)
EM3EM2
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
EM1
Lower part
IR
M
 (A
m
2 )
Re
lat
ive
 co
nt
rib
ut
ion
 o
f E
M
s
0
5e-06
1e-05
1.5e-05
2e-05
2.5e-05
3e-05
3.5e-05
Depth (m)
0 2 4 6 8 10
 
0.2
0.4
0.6
0.8
1
EM1
IRM
EM2
EM3
-1.0 x 104
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
PC
2
x 100.80.60.40.20.0-0.2-0.4
PC1
EM3
EM1EM2
-1.0 x 104
-0.5
0.0
0.5
1.0
PC
2
-1.0 x 104 -0.5 0.0 0.5 1.0
PC1
PC
3
PC1
PC
3
PC2
Upper part
Lower part
scatter due to noisy data
(a) (b) (c)
-1.0 x 104
-0.5
0.0
0.5
1.0
-1.0 x 104 -0.5 0.0 0.5 1.0
-1.0 x 104
-0.5
0.0
0.5
1.0
-1.0 x 104 -0.5 0.0 0.5 1.0
-2 x104
-1
0
1
2
PC
2
-2 x104 -1 0 1 2
PC1
Upper part Lower part
Figure 4.
IR
M
 (A
m
-1
)
0
2
4
6
8
10
12
0 1 2 3 4
0
0.2
0.4
0.6
0.8
1
EM1
IRM
EM2
Re
lat
ive
 co
nt
rib
ut
ion
 o
f E
M
s
Depth (m)
(d)
(i)
(e) (f)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
EM1 EM2 Lower part
(g) (h)
EM1 EM2
Lower part
-1.0 x104 -0.5 0.0 0.5 1.0
PC1
-10000
-5000
0
5000
10000
PC
2
-10000 -5000 0 5000 10000
PC1
Bc (mT)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
-2 x 104
-1
0
1
2
PC
2
-1 0 1 2
PC1
PC
3
PC1 PC2
(a) (b) (c)
-2 x 104
-1
0
1
2
-1 0 1 2
PC
3
-2 x 104
-1
0
1
2
-1 0 1 2-2 x 104 -2 x 104 -2 x 104
Figure 5.
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
EM1 EM2 EM3(a)
-6 x104
-4
-2
0
2
4
6
PC
2
-6 x104 -4 -2 0 2 4 6
PC1
 0.99  0.98 
 0.97 
 0.96  0.95  0.94 
 0.93  0.92 
 0.91 
EM1
EM2
EM3
(d) (e)
250
200
150
100
50
0
SDC3500
200
150
100
50
0
SDC4320
150
100
50
0
SDC3570
100
80
60
40
20
0
-20
SDC5424
-150
-100
-50
0
50
12080400
Am2/T2
1
2
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(b)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(c)
B i 
(m
T)
Bc (mT)
(h)
-150
-100
-50
50
12080400
B i 
(m
T)
Bc (mT)
0
(g)
-150
-100
-50
50
12080400
B i 
(m
T)
Bc (mT)
0
(f)
-150
-100
-50
50
12080400
B i 
(m
T)
Bc (mT)
0
Am2/T2Am2/T2Am2/T2
Figure 6.
6 x104
4
2
0
-2
-4
-6
PC
2
-6 x104 -4 -2 0 2 4 6
PC1
 0.99  0.98 
 0.97 
 0.96 
 0.95 
 0.94  0
.93 
 0.92 
 0.91 
EM1
EM3 EM2
All CR samples
 0.99  0.98 
 0.98 
 0.97 
 0.9
7 
 0.96 
 0.96 
 0.95 
 0.95 
 0.94 
 0.94
 
 0.93 
 0.93 
 0.92 
 0.92 
 0.91 
 0.91 
EM1
EM3
EM2
4 scattered CR samples
(d) (e)
6 x104
4
2
0
-2
-4
-6
PC
2
-6 x104 -4 -2 0 2 4 6
PC1
EM1 EM2 EM3
140
120
100
80
60
40
20
0
CR08C
120
100
80
60
40
20
0
CR01B
200
150
100
50
0
CR03B
100
80
60
40
20
0
CR02D
Am2/T2
Am2/T2Am2/T2Am2/T2
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(a)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(b)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(c)
(f)
-150
-100
-50
0
50
12080400
B i 
(m
T)
Bc (mT)
(h)
-150
-100
-50
0
50
12080400
B i 
(m
T)
Bc (mT)
(i)
-150
-100
-50
0
50
12080400
B i 
(m
T)
Bc (mT)
(g)
-150
-100
-50
0
50
12080400
B i 
(m
T)
Bc (mT)
Figure 7.
-4 x104
-2
0
2
4
PC
2
-4 x104 -2 0 2 4
PC1
EM1
EM2
EM4
EM3
PC
3
PC1
EM1 EM2EM3
EM4
(e) (f)
EM1
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(a)
EM2
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(b)
EM3
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(c)
EM4
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(d)
(g)
Am2/T2
BR03A
140
120
100
80
60
40
20
0
-150
-100
-50
0
50
12080400
B i 
(m
T)
Bc (mT)
80
60
40
20
0
-20
-40
Am2/T2
NR40A
(h)
12080400
Bc (mT)
Am2/T2
200
150
100
50
0
TC11A
(i)
12080400
Bc (mT)
-4 x104
-2
0
2
4
-4 x104 -2 0 2 4
150
100
50
0
Am2/T2
12080400
Bc (mT)
(j)
NC14
Figure 8.
EM3
EM2EM1
EM4
150
100
50
0
H15
120
100
80
60
40
20
0
-20
H3
PC
3
PC1
EM4 EM2
EM1
EM3
-3 x104
-2
-1
0
1
2
3
PC
2
-3 x104 -2 -1 0 1 2 3
PC1
EM4
EM3
EM2
EM1
(e) (f)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(a)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(b)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(c)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(d)
Am2/T2
(g)
-150
-100
-50
0
50
12080400
B i 
(m
T)
Bc (mT)
Am2/T2
(h)
-150
-100
-50
0
50
12080400
B i 
(m
T)
Bc (mT)
-3 x104
-2
-1
0
1
2
3
-3 x104 -2 -1 0 1 2 3
Figure 9.
O2
NO2-
NO3-
Mn2+
Fe2+
CH4
H2S
Fe2+
SMT
De
pt
h 
(a
rb
itr
ar
y)
Chemical zone
Oxic
Manganous
Ferruginous
Sulfidic
Methanic
(a) (b)
(c)
(e)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Biogenic magnetite
Detrital magnetite
Bc (mT)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(h) SP/SD greigite
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(d)
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
Biogenic/detrital
magnetite
Coarse detrital
magnetite
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(g)Detrital magnetite
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(f)
Stable SD pyrrhotite
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(i)
Stable SD greigite
-100
-80
-60
-40
-20
0
20
40
B i 
(m
T)
12080400
Bc (mT)
(j)
Biogenic magnetite formation:
oxic to nitrogenous zones
Magnetite stability:
oxic to lower 
manganous zones
SP/SD greigite 
formation:
sulfidic zone
Authigenic pyrrhotite
formation: methanic
zone
?
?
Fe2+ + AOM
Stable SD greigite
formation: sulfidic or
methanic zone?
Nitrogenous
Iron oxides unstable: 
sulfidic and 
methanic zones
Iron oxide dissolution
starts in the
ferruginous zone