Applicability of landslide susceptibility and hazard zoning at different scales

Landslide susceptibility and hazard zoning can notably improve land-use planning, and thus can be considered an efficient way to reduce future damage and loss of lives caused by landslides. However, the lack of standard procedures restricts the use of susceptibility and hazard-zoning maps, notwithstanding their extensive development over the last decades.JTC-1, the Joint Technical Committee on Landslides and Engineered Slopes, fills this void by proposing International Guidelines for Landslide Susceptibility, Hazard and Risk Zoning for land-use planning, which provide definitions, terminology and international standards for methods, levels, scales and types of zoning. The Guidelines also promote the use of quantitative risk-management principles, essential to compare risk from landslides with risks related to other hazards and with loss of life tolerance criteria.This paper focuses on the applicability of landslide susceptibility and hazard zoning at different scales. Several zoning examples, referring to active, dormant and occasionally reactivated slides, provide insights into and highlight the relationships among different methods, levels and types of zoning. The examples also stress the importance of a correct characterization of the processes leading to landsliding to produce reliable susceptibility and hazard-zoning maps.     

Peak metamorphic temperatures from cation diffusion zoning in garnet

A model that relates the characteristic diffusion length and average cooling rate to peak temperature was developed for chemical diffusion in spherical geometries on the basis of geospeedometry principles and diffusion theory. The model is quantitatively evaluated for cation diffusion profiles in garnet. Important model parameters were calibrated empirically using diffusion zoning of Ca in garnet from the Pikwitonei Granulite Domain, a terrane for which the thermal history has been well characterized. The results are used: (i) to empirically test diffusion parameters for Mg and Fe(II) and (ii) to develop a tool that uses the diffusion zoning of these cations in garnet to constrain peak temperature conditions for garnet‐bearing rocks. The thermometric approach was externally tested by applying it to garnet crystals from various metamorphic terranes worldwide and comparing the results to published peak temperature estimates. The results overlap within uncertainties in all cases, but result that are based on Fe(II) and Mg chemical‐diffusion profiles are up to three times more precise than those acquired by conventional methods. The remarkable consistency of the results implies that the model is robust and provides a reliable means of estimating peak temperatures for different types of high‐grade metamorphic rock. The tool could be of particular advantage in rocks where critical assemblages for conventional thermometry do not occur or have been replaced during retrogression.     

On the mechanism of resorption zoning in metamorphic garnet

Abstract An analytical electron microscope study of almandine garnet from a metamorphosed Al–Fe‐rich rock revealed detailed composition profiles and defect microstructures of resorption zoning along fluid‐infiltrated veins and even into the garnet/ilmenite (inclusion) interface. This indicates a limited volume diffusion for the cations in substitution (mainly Ca and Fe) and an interface‐controlled partition for the extension of a composition‐invariant margin. A corrugated interface between the Ca‐rich margin/zone and the almandine garnet core is characterized by dislocation arrays and recovery texture further suggesting a resorption process facilitated by diffusion‐induced recrystallization, diffusion‐induced dislocation migration and diffusion–induced grain boundary migration. Integrated microstructural and chemical studies are essential for understanding the underlying mechanisms of processes such as garnet zoning and its modification. Without this understanding, it will not be possible to reliably use garnet compositions for thermobarometry and other applications that rely on garnet chemical information.     

Growth zoning of garnet porphyroblasts: Grain boundary and microtopographic controls

Chemical zoning in the outer few 10s of microns of garnet porphyroblasts has been investigated to assess the scale of chemical equilibrium with matrix minerals in a pelitic schist. Garnet porphyroblasts from the Late Proterozoic amphibolite facies regional metamorphic mica schists from Glen Roy in the Scottish Highlands contain typical prograde growth zoning patterns. Edge compositions have been measured via a combination of analysis of traverses across the planar edges of porphyroblast surfaces coupled to X-ray mapping of small areas within polished thin sections at the immediate edge of the porphyroblasts. These approaches reveal local variation in garnet composition, especially of grossular (Ca) and almandine (Fe) components, with a range at the edge from <7 mol.% grs to >16 mol.% grs, across distances of less than 50 µm. This small-scale patchy compositional zoning is as much variation as the core–rim compositional zoning across the whole of a 3 mm porphyroblast. Ca and Fe heterogeneity occurs on a scale suggesting a combination of inefficient diffusive exchange across grain boundaries during prograde growth and the evolving microtopography of the porphyroblast surface control garnet composition. The latter creates haloes of compositional zoning adjacent to some inclusions, which typically extend from the inclusion towards the porphyroblast edge during further growth. The lack of a consistent equilibrium composition at the garnet edge is also apparent in the internal zoning of the porphyroblast and so processes occurring during entrapment of some mineral inclusions have a profound influence on the overall chemical zoning. Garnet compositions and associated zoning patterns are widely used by petrologists to reconstruct P–T–t paths for crustal rocks. The evidence of extremely localized (10–50 µm scale) equilibrium during growth further undermines these approaches.     

Statistical microanalysis applied to garnet growth zoning and to cordierite fluid content

An analytical study to evaluate quantitatively weak zoning of a garnet from a high-grade kinzigite has been performed with an electron microprobe. The technique consists of the reconstruction of a profile step-by-step by successive analyses performed during relatively long counting times (30 s), along a radial profile of 2,500 μm length. The successive analytical data along this profile are statistically treated by Fisher's test and compared with the χ² values (Pearson's law). These statistical tests were applied to assess microprobe stability and analysis homogeneity, and as a consequence to assure high credibility of the radial variations of the garnet. From core to rim, and for each element, zoning appears as the radial juxtaposition of stationary Poissonian samples. These samples being associated, the garnet appears to be constituted of successive concentric domains with stationary compositions. Different substitutions between Mg, Fe, Mn and Ca are evidenced. Such an analytical approach to chemical zoning can be useful for understanding growth mechanisms, and the possible diffusion reactions with the environment at each growth step. In addition, such a procedure can be used to evaluate accurately the fluid content of cordierite, and to appreciate the nature of the fluids concerned. As an example, the fluid content of a cordierite from a similar high-grade kinzigite has been evaluated.     

Pressure-temperature path of Sanbagawa prograde metamorphism deduced from grossular zoning of garnet

The zonal structure of prograde garnet in pelitic schists from the medium-grade garnet zone and the higher-grade albite-biotite zone was examined to investigate the evolution of prograde P–T paths of the Sanbagawa metamorphism. The garnet studied shows a bell-shaped chemical zoning of the spessartine component, which decreases in abundance from the core towards the rim. Almandine and pyrope contents and X_Mg [=Mg/(Mg+Fe²⁺)] increase monotonously outwards. The general scheme of the zonal structure for grossular content [X_Grs=Ca/(Fe²⁺+Mn+Mg+Ca)] can be summarized as: (1) X_Grs increases outwards (inner segment) and reaches a maximum at an intermediate position between the crystal core and the rim, then decreases towards the outermost rim (outer segment) (2) the inner segment of garnet in the garnet zone samples tends to have a higher X_Grs/X_Sps values for a given X_Sps than those in the albite–biotite zone samples (3) average X_Sps at the maximum X_Grs position in the albite–biotite zone samples ranges from 0.02 to 0.12 and is lower than that in the garnet zone samples (0.13–0.32) (4) the maximum X_Grs in the albite–biotite zone samples (0.34–0.39 on average) tends to be higher than that in the garnet zone samples (0.26–0.36), and (5) differences of X_Grs between the maximum and rim in the albite–biotite zone samples are between 0.10 and 0.14 and higher than those in the garnet zone samples (< 0.11). These facts imply that albite–biotite zone materials (a) were recrystallized under lower dP/dT conditions at an early stage of the prograde metamorphism (b) began their exhumation under higher P–T conditions and (c) have been continuously heated during exhumation for a longer duration than the garnet zone materials. The systematic changes of prograde P–T paths can be interpreted as documenting the evolution of the Sanbagawa subduction zone.     

浅层地下水氟的溶解／沉淀作用的定量研究

以河北邢台山前平原浅层高氟地下水为例，根据氟的化学热力学分析，确定了控制浅层地下水中氟迁移和富集的固相沉淀物，以及不同化学类型的浅层地下水中含氟固相沉淀物的溶解／沉淀条件；利用浅层地下水化学平衡反应模型和ＰＨＲＥＥＱＥ软件，确定了氟化的稳定区域，计算了氟化钙的饱和指数．研究结果表明，在浅层高氟地下水的整个形成过程中，都表现为氟由固相转入水相的趋势，有利于氟的迁移和富集     

Well-preserved garnet growth zoning in granulite from the Dabie Mountains, central China

Ultra-high pressure eclogites and granulites both occur in the Dabie Mountains, central China. A garnet porphyroblast from felsic granulite in the Dabie Mountains has been analysed for compositional zoning by electron microprobe. Two segments of the porphyroblast have opposite compositional variations. Segment I (from centre outward 9  mm to analytical point 18) has decreasing X_Sps and increasing X_Pyr, while Segment II (from analytical point 18, 1  mm outward to the rim) has increasing X_Sps and X_Alm and decreasing X_Pyr and X_Grs. The compositional zoning in segment I is considered as growth zoning and that in Segment II as diffusive retrograde zoning. Garnet growth zoning records a P–T  path prior to the peak granulite metamorphism. The minimum P – T  conditions are estimated to be 1.35  GPa and 850  °C for peak metamorphism, based on the highest Mg/(Fe+Mg) composition in the garnet (analytical point 18) and matrix hypersthene, biotite and plagioclase. A symplectitic corona surrounds the porphyroblast and appears to have formed at 0.6  GPa and 700  °C. The well-preserved growth zoning in garnet suggests a short residence time for the granulite at peak metamorphism and thus rapid tectonic uplift history. The P–T  path is consistent with that of ultra-high-pressure eclogite in the area. Tectonic movements during a collisional event could have brought both the granulite and the eclogite to their present positions.     

Mechanical and transport constitutive models for fractures subject to dissolution and precipitation

Transient changes in the permeability of fractures in systems driven far‐from‐equilibrium are described in terms of proxy roles of stress, temperature and chemistry. The combined effects of stress and temperature are accommodated in the response of asperity bridges where mineral mass is mobilized from the bridge to the surrounding fluid. Mass balance within the fluid accommodates mineral mass either removed from the flow system by precipitation or advection, or augmented by either dissolution or advection. Where the system is hydraulically closed and initially at equilibrium, reduction in aperture driven by the effects of applied stresses and temperatures will be augmented by precipitation on the fracture walls. Where the system is open, the initial drop in aperture may continue, and accelerate, where the influent fluid is oversaturated with respect to the equilibrium mineral concentration within the fluid, or may reverse, if undersaturated. This simple zero‐dimensional model is capable of representing the intricate behavior observed in experiments where the feasibility of fracture sealing concurrent with net dissolution is observed. This zero‐order model is developed as a constitutive model capable of representing key aspects of changes in the transport parameters of the continuum response of fractured media to changes in stress, temperature and chemistry. Copyright © 2009 John Wiley & Sons, Ltd.     

高压-超高压变质岩石中石榴石的环带和成因

在俯冲带变质过程中,石榴石是高压-超高压变质榴辉岩和片麻岩的常见变质矿物。由于石榴石具有难熔和流体中的低溶解能力的特点,通常可以很好地保存下来,并且能够保留复杂的化学成分环带,以及不同类型的矿物或流体包裹体,为解释石榴石寄主岩石经历的变质演化历史提供了重要信息。石榴子石的主微量元素成分受控于很多因素,如全岩成分、变质的温压条件、控制石榴子石形成的相关变质反应、与石榴子石共生的矿物种类和成分等。因此,在利用石榴石探讨超高压变质的演化历史时,对石榴石进行系统的主要元素、微量元素、氧同位素以及矿物包裹体分析,以及相互间的成因关系。同时,对石榴石中的锆石或独居石包裹体并进行原位U-Pb定年和微量元素分析,可以为变质石榴石的形成时代提供直接的时间制约。深入研究超高压变质岩中石榴石的生长阶段,不仅可以为含石榴石寄主岩石的变质过程提供岩石学和地球化学证据,而且对于理解石榴石的形成机制、生长规律及其变质化学动力学过程具有重要的科学意义。     

The duration of near‐peak metamorphism from diffusion modelling of garnet zoning

Garnet in a staurolite–kyanite zone sample from central Vermont displays a bell‐shaped Mn growth zoning with diffusional modification over the outer 100 μm. The diffusion is driven by the prograde net transfer reaction garnet + chlorite = kyanite + biotite as is evidenced by a well‐defined resorption zone on the rim. Analysis of the reaction history and resorbed garnet composition suggests that the peak temperature attained was 620–660 °C. Diffusional modelling of the rim diffusion provides an estimate of the duration of the metamorphic episode over which significant garnet diffusion occurs. The duration is a function of the assumed peak temperature and garnet diffusivities and range from a few hundred thousand years to a few million years. Such short durations require rapid tectonic burial and exhumation of relatively thin tectonic slices.     

Genesis of monazite and Y zoning in garnet from the Black Hills, South Dakota

The paragenesis of monazite in metapelitic rocks from the contact aureole of the Harney Peak Granite, Black Hills, South Dakota, was investigated using zoning patterns of monazite and garnet, electron microprobe dating of monazite, bulk-rock compositions, and major phase mineral equilibria. The area is characterized by low-pressure and high-temperature metamorphism with metamorphic zones ranging from garnet to sillimanite zones. Garnet porphyroblasts containing euhedral Y annuli are observed from the garnet to sillimanite zones. Although major phase mineral equilibria predict resorption of garnet at the staurolite isograd and regrowth at the andalusite isograd, textural and mass balance analyses suggest that the formation of the Y annuli is not related to the resorption-and-regrowth of garnet having formed instead during garnet growth in the garnet zone. Monazite grains in Black Hills pelites were divided into two generations on the basis of zoning patterns of Y and U: monazite 1 with low-Y and -U and monazite 2 with high-Y and -U. Monazite 1 occurs in the garnet zone and persists into the sillimanite zone as cores shielded by monazite 2 which starts to form in the andalusite zone. Pelites containing garnet porphyroblasts with Y annuli and monazite 1 with patchy Th zoning are more calcic than those with garnet with no Y annuli and monazite with concentric Th zoning. Monazite 1 is attributed to breakdown of allanite in the garnet zone, additionally giving rise to the Y annuli observed in garnet. Monazite 2 grows in the andalusite zone, probably at the expense of garnet and monazite 1 in the andalusite and sillimanite zones. The ages of the two different generations of monazite are within the precision of chemical dating of electron microprobe. The electron microprobe ages of all monazites from the Black Hills show a single ca. 1713 Ma population, close to the intrusion age of the Harney Peak Granite (1715 Ma). This study demonstrates that Y zoning in garnet and monazite are critical to the interpretation of monazite petrogenesis and therefore monazite ages.     

西藏知不拉铜多金属矿床地质、石榴子石分带特征及其地质意义

西藏知不拉铜多金属床是冈底斯成矿带东段典型的矽卡岩矿床,石榴子石是矿区最主要的矽卡岩矿物,其颗粒间的空隙是金属矿物的主要赋存部位。本文通过详细的钻孔编录,结合岩矿鉴定及电子探针分析,划分出两种不同类型的石榴子环带,并在垂向上具有明显的分带:产于顶板凝灰岩中的石榴子石以钙铁榴石为主,环带中心颜色深,向外逐渐变浅,由纯钙铁榴石过渡到钙铝榴石;而位于底板大理岩附近石榴子石多以钙铝榴石为主,从环带核部向外颜色变深,化学组成由钙铝榴石向钙铁榴石变化,其它化学成分变化不大。反映该区上下两套不同性质围岩在石榴子石形成过程中所起的作用不同,其中上部凝灰岩主要提供了Fe,底部大理岩则是Ca的来源,热液流体贡献Si、Al及部分Fe,并随着环境和物质成分改变导致环带外侧具有不同于核部的变化趋势。这很好地解释了石榴子石矽卡岩在空间上具有上部为钙铁榴石、向下逐渐过渡到钙铝榴石的空间分带。石榴子石特征及分带显示了其属热液接触交代成因,这为矿床类型的确定提供了依据,也为在该区域内寻找类似矿床指明了方向。     

Chromium and manganese zoning in pelitic garnet and kyanite: Spiral,overprint, and oscillatory (?) zoning patterns and the role of growth rate

X‐ray composition maps and quantitative analyses for Mn, Ca and Cr have been made for six pelitic and calc‐pelitic garnet crystals and Al, Fe and Cr analyses maps have been made for two kyanite crystals, from lower and mid/upper amphibolite facies rocks from the Grenville Province of western Labrador, using an electron microprobe analyser and a laser ablation ICP‐MS. Garnet with spiral (‘snowball’) internal fabrics (S_i) has spiral zoning in major elements, implying that growth was concentrated in discrete regions of the crystal at any one time (spiral zoning). Cr zoning is parallel to S_i in low amphibolite facies garnet with both straight and spiral internal fabrics, indicating that the garnet overprinted a fabric defined by Cr‐rich (mica±chlorite±epidote) and Cr‐poor (quartz±plagioclase) layers during growth (overprint zoning) and that Cr was effectively immobile. In contrast, in mid/upper amphibolite facies garnet porphyroblasts lacking S_i, Cr zoning is concentric, implying that Cr diffusion occurred. Cr zoning in kyanite porphyroblasts appears superficially similar to oscillatory zoning, with up to three or four annuli of Cr enrichment and/or depletion present in a single grain. However, the variable width, continuity, Cr concentration and local bifurcation of individual annuli suggest that an origin by overprint zoning may be more likely. The results of this study explain previously observed nonsystematic Cr zoning in garnet and irregular partitioning of Cr between coexisting metamorphic mineral pairs. In addition, this study points to the important role of crystal growth rate in determining the presence or absence of inclusions and the type of zoning exhibited by both major and trace elements. During fast growth, inclusions are preferentially incorporated into the growing porphyroblast and slow diffusing elements such as Cr are effectively immobile, whereas during slow growth, inclusions are not generally included in the porphyroblast and Cr zoning is concentric.     

安徽池州铜山铜矿床元素地球化学分带特征及意义

铜山铜矿是长江中下游成矿带内安庆-贵池矿集区中的一个中型矽卡岩型矿床,矿体赋存于铜山岩体与下二叠统栖霞组碳酸盐岩间的接触带内.典型剖面系统取样分析结果显示:从岩浆岩、矽卡岩到碳酸盐岩,元素地球化学组成总体上表现为渐变分带特征,即靠近岩体的矽卡岩富集Si、Fe、Mg及亲铁元素Co和亲铜元素Cu、Ag;远离岩体的矽卡岩富集Ca、Mn、Al、Ti、REE和亲铜元素Pb、Zn;远离大理岩带的强硅化蚀变岩富集Si、Fe、Li和Co,而强烈亏损Ca、Sr和REE.这种分带可以依据元素活化迁移理论加以解释.在矽卡岩形成过程中,岩浆热液携带Si、Fe、Mg、Al、Li、REE、大离子亲石元素Rb、Cs、亲铁亲铜元素Co、V、Zn以及高场强元素Ta、Zr、Nb、Hf、Ga、Be向大理岩迁移并富集于形成的矽卡岩中;大理岩中的Ca被活化后进入矽卡岩体系,而Sr、K及Pb则随流体搬运迁出.蚀变及矿化较弱的矽卡岩稀土总量较高(ΣREE=122.0×10-6),LREE富集[(La/Sm)N =3.99],HREE亏损[(Gd/Yb)N=2.85],Eu显示负异常(δEu =0.69),重稀土配分形式与新鲜石英二长斑岩相似,但La、Ce等轻稀土元素相对亏损.矽卡岩剖面元素分带特征及稀土配分模式指示铜山矽卡岩铜矿床为接触交代成因.结合已有氢氧同位素结果,认为铜山铜矿成矿流体主要来自岩浆热液,在矽卡岩退化蚀变和成矿期间有大气降水混入成矿流体.     

Prograde reactions and garnet zoning reversals in staurolite schist, British Columbia: significance for thermobarometric interpretations

Abstract An outcrop of staurolite-bearing pelitic schist from the Solitude Range in the south-western Rocky Mountains, British Columbia, was examined in order to determine the nature of prograde garnet- and staurolite-producing reactions using information from garnet zoning and inclusion mineralogy. Although not present as a matrix phase, chloritoid is present as inclusions in garnet and is interpreted to have participated in the simultaneous growth of garnet and staurolite by a reaction such as chloritoid + quartz = garnet + staurolite + H₂O.
A garnet zoning trend reversal, which is most pronounced with respect to almandine and grossular components, is present in the outer core of garnets. The location of the zoning reversal corresponds to the outer limit of chloritoid inclusions in garnet. As there is no evidence for polymetamorphism, the zoning reversal is interpreted to indicate continued garnet growth by prograde reaction(s) during a single metamorphic event after the exhaustion of chloritoid as a matrix phase.
Metamorphic conditions recorded by mineral rim compositions are 550–600° C at 6–7 kbar. Because there is no evidence for partial resorption of garnet during production of staurolite, we interpret these results to represent peak conditions.     

Strontium isotope zoning in garnet: implications for metamorphic matrix equilibration,geochronology and phase equilibrium modelling

In principle, garnet growth rates may be calculated from ⁸⁷Rb/⁸⁶Sr and ⁸⁷Sr/⁸⁶Sr measurements in garnet subsamples and the surrounding rock matrix. Because of low Rb/Sr, garnet should passively record the matrix decay of ⁸⁷Rb to ⁸⁷Sr as a progressive increase in ⁸⁷Sr/⁸⁶Sr from core to rim. This concept was tested by collecting Rb‐Sr data for five garnet grains from four major orogenic belts: eastern Vermont (c. 380 Ma), western New Hampshire (c. 320 Ma), southern Chile (c. 75 Ma) and northwestern Italy (c. 35 Ma). Both normal Sr isotope zoning (increasing ⁸⁷Sr/⁸⁶Sr from core to rim) and inverse Sr zoning (decreasing ⁸⁷Sr/⁸⁶Sr from core to rim) were observed. Garnet and matrix isotope data commonly yielded grossly inaccurate model ages. Incomplete Rb and Sr equilibration among matrix minerals is invoked to explain the deviations between theoretical v. measured zoning patterns and the age disparities. Initially, the reactive matrix is dominated by rapidly equilibrating Rb‐rich mica, which imparts high ⁸⁷Sr/⁸⁶Sr values in garnet cores. Progressive participation of slower equilibrating Sr‐rich plagioclase buffers or even reduces ⁸⁷Sr/⁸⁶Sr, possibly leading to flat or decreasing ⁸⁷Sr/⁸⁶Sr from garnet cores to rims. Unusually high ⁸⁷Sr/⁸⁶Sr in garnet in combination with bulk matrix compositions causes erroneously young apparent ages, so metamorphic ages, growth rates, and associated heating and loading rates are likely suspect. Although Rb‐Sr may be the most susceptible because of the profound disparities between mica and feldspar, zircon reactivity might influence the Lu‐Hf system by up to a few per cent. The Sm‐Nd system seems generally immune to these effects. Pseudosection analysis and conventional garnet geochronology, which presume complete matrix equilibration during metamorphism, may require modification to account for differences between whole‐rock v. reactive matrix compositions.     

Petrological significance of prograde homogenization of growth zoning in garnet: an example from the Llano Uplift'pa

In the Llano Uplift of central Texas (USA), prograde homogenization of garnet growth zoning took place during moderate- to high-pressure dynamothermal metamorphism over a narrow temperature range near the transition from the amphibolite to the granulite facies. This subtle record of early dynamothermal metamorphism survived subsequent static metamorphism at low pressures in the middle-amphibolite facies, despite the destruction of most high-pressure mineral assemblages that originated in the early metamorphic episode. Geographically systematic variations in the degree of homogenization indicate that the uplift as a whole underwent high-pressure metamorphism, in accord with emerging tectonic models for the mid-Proterozoic evolution of the southern margin of the North American continent.     

金在碱性富硅热液中溶解和迁移的实验研究

实验测定了金在碱性富硅溶液中的溶解度，并标定了Ａｕ与ＳｉＯ２之间的配合关系Ａｕ＾＋Ｈ２ＳｉＯ＾－４＝ＡｕＨ３ＳｉＯ＾０４在８０￣２５０℃的温度范围内，其平衡常数为ｌｇＫ＝－１．９８８９＋１００８５。１８／Ｔ（Ｔ为绝对温度）各温度下的平衡常数值与Ａｕ－ＨＣｌ－ＳｉＯ２－Ｈ２Ｏ体系中得到的结果一致。它表明溶液在酸性和碱性条件下，ＳｉＯ２均作为配位体，与Ａｕ形成ＡｕＨ３ＳｉＯ＾０４在热液中溶解、迁移。Ａ     

Temperature–time path for the low-pressure Ryoke metamorphism, Japan, based on chemical zoning in garnet

Garnet crystals from low-pressure/high-temperature (LPHT) Ryoke metamorphic rocks in the Yanai district, south-western Japan, show several kinds of chemical zoning patterns that systematically vary with grain radius between c . 0.1 and 0.5  mm. Large grains (> c . 0.4  mm) show normal zoning and small grains (< c . 0.4  mm) show unzoned or reversely zoned cores. Observations of the chemical zoning and of the spatial and size distributions of the garnet grains between c . 0.1 and 0.5  mm in radius suggest that they were formed by continuous nucleation and diffusion-controlled growth.
A previously estimated temperature–time path ( T  – t path) for the Ryoke metamorphism, using 1-D numerical simulation, is characterized by a rapid increase in temperature, 0.0017  °C yr⁻¹ on average, and a period of high temperature (>600  °C) shorter than 0.5 Myr, which was presumably caused by the intrusion of a granodiorite sheet. Chemical zoning of garnet grains with different radii simulated for the T  – t path using a numerical model of continuous nucleation and diffusion-controlled growth, in combination with intracrystalline diffusion, compares well with the observed zoning patterns in garnet grains with different radii. This is in spite of the fact that the simulated zoning patterns vary greatly, depending on subtle differences in the T–t history. Therefore, they suggest that the T–t path gives a good explanation for the LPHT Ryoke metamorphism. Although this study only refers to the Ryoke metamorphism, the technique may be applicable to thermal modelling of other metamorphic terranes.