情報地質 第26巻 第2号 078-079頁 2015年
Geoinformatics, vol.26, no.2, pp.078-079, 2015

A geostatistical approach of ore grade modeling in combination with aphysical law
Lei Lu*, Taiki Kubo*, Risa Uchikura*, Chunxue Liu**, Koki Kashiwaya*, Katsuaki Koike* andRyoichi Yamada****Graduate School of Engineering, Kyoto University, C1-2-214, Kyoto Daigaku Katsura, Nishikyo-ku,
Kyoto, Japan. E-mail: lu.lei.62a@st.kyoto-u.ac.jp**School of Urban and Environment, Yunnan University of Finance and Economics, China***Graduate School of Science, Tohoku University, Japan

Key words: Kuroko deposit, Kriging, Physical-based model, 3D modeling, Ore grade

1. Introduction
Despite small sizes in ore productions, there weremany, various kinds of metalliferous mines in Japan. In
addition, potential mapping resource investigations had
been conducted over Japan for a long period. To utilize
such information on the closed mines and investigations
can contribute to clarify the ore genesis mechanisms
and control factors of metal deposits in Japan andfurthermore, to resource exploration for the same typedeposit such as volcanogenic massive sulfide (VMS) typeover the world.
From a viewpoint of geological processes, four basic
requirements are needed for ore deposits (McQueen,2005): ore components source, process that transportsore components and removes non-ore components,
depositional mechanism to fix the components, andgeological setting that preserves ore deposit. The
unifying characteristics of VMS deposit are associatedwith volcanic activity and mineralization byhydrothermal solutions at or near the seafloor. The key
distinction is that VMS deposits were formed as seafloor
massive sulfides from hydrothermal fluids driven by themagmatic heat. This mineralizing process may involve
convecting seawater that evolves by water/rockinteraction into a slightly acidic metalliferous fluid,which may contain a significant component of magmatic
volatiles (Shanks, 2012).
Characterizing the ore deposits often involves
imaging 2D and 3D structures，physical and chemical
properties, and interactions of materials. In general,
imaging techniques use irregularly-spaced data thathave originated from field surveys, borehole
investigations, well-logging, core tests, and laboratory
analyses. However，these data are limited in quantity,
sampling location, areal (or volumetric) distribution,and spatial and temporal resolution. In addition,
geomaterials tend to have heterogeneous structures andproperties and behave nonlinearly due to geologicaldiscontinuities such as faults and unconformities, andthe limited local influence of many geological processes.
Therefore, this study is aimed to develop a spatialmodeling technique covering the heterogeneity andnonlinearity of ore grade data by combing geostatistics
and a physical law of hydrothermal fluids flows foraccurate imaging.

2. Methods
2.1 Review of previous studies
Early ideas about the origin of metal-rich submarinehydrothermal solutions and the formation of seafloor
deposits were advanced by taking the role of thermal
crack propagation into a heat source admitting seawaterand establishing convective fluid flow (Corliss, 1971).
Then, a simple numerical model was developed bydescribing the convection of hydrothermal fluids andleading to potential ore body formation (Cathles, 1977).
A general descriptive model of kuroko massive sulfide byFranklin (1981) is shown in Fig. 1.
A more comprehensive modeling approach was taken
by Cathles (1983), who studied fluid flow requirements
for several deposit settings. A more recent study used abasic single-pass model by employing expression ofconservation of mass and momentum, and integrating
version of Darcy's law to model fluid flow of VMS deposit(Lowell et al., 2008). A recent noteworthy study likesurface-based model or process-based model, byreproducing the deposit genesis, provides realistic
representation of the subsurface structures (Bertoncelloet al., 2013).
Although the results from those studies have beenused successfully to investigate a number of important
aspects such as rock permeability, the role of basement
relief and heat source, or the importance of fault
structures, few studies have integrated all thesefeatures. Moreover, traditional methods focus only on
analyzing and processing the deposit geometry as they
exist at the end of sedimentation process. However, theemergence of specific deposit structures is driven bycomplex physical processes, such as ejected metal
solution by an advection-diffusion process near theseafloor, that occur both in space and time. Byneglecting the advection-diffusion (reaction-advectiondiffusion) process, traditional modeling methods fail toreproduce the complex interactions of topography, flow,deposition, and erosion.
2.2 Proposed method for ore grade modeling
The proposed modeling workflow consists three parts,
geological structure modeling, ore grade estimation, and79

this direction are continued in the distributions ofsilicious ore and rhyolite. This may imply the main
paths of ore solutions.

4. Concluding remarks
The importance of considering hydrothermal fluids
flow for VMS ore grade modeling was summarized witha case study. Our next step is to improve the grade
model by incorporating the convection–diffusion
equation into kriging system. The authors wish toexpress their gratitude to Dowa Metals & Mining Co.,
Ltd. and Hanaoka Eco-System Co., Ltd. for providing
the precious drilling investigation materials.

Figure 1. Kuroko massive sulfide deposit model, modified fromFranklin et al. (1981).

physical-based convection-diffusion model.
The vast majority of fluid compositions in the modern
and ancient VMS deposits indicate that seawater orevolved seawater was the dominant source ofmineralizing fluids. The resulting convection systemproduces compositionally evolved seawater following
reactions with host rocks along the flow path and thehydrothermal vent site on the seafloor (Shanks, 2012).
The convection–diffusion equation is a combination of
the diffusion and convection (advection) equations, anddescribes physical phenomena where particles, energy,
or other physical quantities are transferred inside aphysical system by diffusion and convection. The
general convection–diffusion equation is expressed as:
where c is variable of interest, D is diffusivity,
isaverage velocity, R describes "sources" of quantity c,represents gradient, andrepresents divergence.

3. Ongoing case study of kuroko deposits
The Hokuroku basin in Akita Pref., northern Japan, isa volcano sedimentary basin that was developed within
the rift graben and designated as the most important
kuroko ore field in Japan. The Matsumine deposit of theHanaoka mine, found in 1963, is the largest kuroko
deposit, located in the western margin of the Hokuroku
basin. For considering the boreholes distribution with
dense record data, 77 boreholes were chosen for an ore
grade analysis in this study. Lithology record in theboreholes contains clay, tuff, mud stone, rhyolite, siliceousore, yellow ore, kuroko, dolerite, gypsum, and pyrite.
The ore grades of three principal metals, Cu, Zn, andPb were estimated by kriging. Cross-section comparison
between the Cu grade and geological model suggeststhat the high concentration of Cu has a coherent
distribution with kuroko and yellow ores (Fig. 2).
Next, the advective velocities and the diffusion
coefficients were calculated at each grid point by acombination of the ore grade model and theconvection–diffusion equation. The advective velocities
are mainly directed upward and the grid points withFigure 2. Relationship between grade distribution (Cu) andgeological models. Grade increases from blue to red colors.

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