Ocean anoxic events in the mid-Cretaceous simulated by a 3-D biogeochemical general circulation model

The mid-Cretaceous is well known for its ocean anoxic events. The causal mechanisms are controversial: stagnant deepwater, high biological productivity in the surface waters, and other possibilities have been suggested. Our study simulated the mid-Cretaceous ocean, using general circulation models combined with a marine biogeochemical cycle model to explore the relationship between thermohaline circulation and biogeochemical cycles and investigate the causes of ocean anoxic events. The simulated thermohaline circulation shows an unsteady inactive state. Oxygen concentrations in the deepwater decrease under the inactive state, but a horizontal gradient develops, with higher oxygen concentrations in the Tethys and lower concentrations in eastern Panthalassa. This is not due to the different ages of the deepwater but rather to the differences in biological productivity in the surface water, meaning that the relationship between thermohaline circulation and biogeochemical cycles under the inactive state is different from that in the present ocean. In the standard simulation, assuming the present level of the total amount of phosphate in the ocean, 29% of the bottom water is anoxic. The experiments increasing the amount of phosphate show its high sensitivity for extending the anoxic region with global-scale anoxia simulated under the doubled amount of phosphate. The high amount of phosphate would be reasonable because the inactive state would induce an imbalance of phosphate between riverine input and sediment output. Therefore, both the inactive thermohaline circulation and the increase in the total amount of phosphate in the ocean induce the global-scale anoxic condition in the deepwater.     

A constitutive law for rock salt based on creep and relaxation tests

Summary The paper deals with uniaxial relaxation tests on rock salt which are the basis for a constitutive equation. Since so far no regard was paid to relaxation behaviour, corresponding test results are not available and hence a special device for performing of uniaxial relaxation tests had to be constructed. Some interesting test results are discussed in the paper. These results are useful for the verification of constitutive equations. A critical analysis of conventional constitutive laws and their fundamentals shows that these material laws have considerable imperfections and are rested on substantial restrictions. Particularly, they are not able to describe relaxation behaviour sufficiently. Consequently, a constitutive law is proposed consisting of a strain hardening approach with separate creep and relaxation functions. By post-calculation of different laboratory tests it could be shown that in comparison to conventional steady-state creep equations this material law describes the viscous behaviour of rock salt more realistically.     

Holocene climate variability in northernmost Europe

The sediments of a small lake on Nordkinnhalvøya, Finnmark, Norway, were investigated in order to test the hypothesis that this region was sensitive to centennial–millennial climatic fluctuations during the Holocene related to changes in ocean circulation. Sedimentation at the site began during the Younger Dryas, although the site chronology, developed using a series of ¹⁴C age measurements, reveals an early Holocene hiatus in accumulation. Pollen analysis confirmed that the regional vegetation responded to Holocene climatic variability at centennial–millennial time scales and provided data used to make quantitative palaeoclimate reconstructions. The latter indicate that marked changes in seasonality characterised Holocene climatic fluctuations. Intervals with warmer summers, higher temperature sums and higher precipitation, but cooler winters and generally reduced moisture availability, alternated with intervals with cooler summers, lower temperature sums, lower precipitation, warmer winters and greater moisture availability. The former conditions were more prevalent between ca 8950 and 3950 cal BP, whereas the latter were predominant before ca 8950 and since ca 3950 cal BP. Sediment geochemistry indicates minerogenic material deposited in the lake was probably derived from two or more distinct sources or transport pathways that differed in their responses to palaeoclimatic conditions. A series of cryptotephras were located, although the small size of the shards rendered them unsuitable for electron microprobe analyses. Time-series analysis of pollen analytical and sediment geochemical data indicates that each exhibits statistically significant periodic behaviour (at periods of ca 190, 410, 1050, 1650 and 1810 yr). The periods detected suggest this behaviour may reflect regional expression of climate system responses to solar variability and/or of effects upon tides and ocean circulation of periodic lunar orbital variation. Comparison with records of fluctuations in ocean thermohaline circulation strength indicate some concordance with respect to timing of warmer and cooler intervals, but also some differences. The 8.2 ka event, that is evident in marine records from the Barents Sea, is clearly expressed by both the palaeovegetation and geochemical records. Distinctive temporal behaviour of the palaeovegetation and of different geochemical components indicates complexity in the underlying causes and mechanisms of regional climatic variability; ocean circulation variability alone cannot account for the complex climatic variability observed.     

The emergence of life from iron monosulphide bubbles at a submarine hydrothermal redox and pH front

Here we argue that life emerged on Earth from a redox and pH front at c. 4.2 Ga. This front occurred where hot (c. 150 degrees C), extremely reduced, alkaline, bisulphide-bearing, submarine seepage waters interfaced with the acid, warm (c. 90 degrees C), iron-hearing Hadean ocean. The low pH of the ocean was imparted by the ten bars of CO2 considered to dominate the Hadean atmosphere/hydrosphere. Disequilibrium between the two solutions was maintained by the spontaneous precipitation of a colloidal FeS membrane. Iron monosulphide bubbles comprising this membrane were inflated by the hydrothermal solution upon sulphide mounds at the seepage sites. Our hypothesis is that the FeS membrane, laced with nickel, acted as a semipermeable catalytic boundary between the two fluids, encouraging synthesis of organic anions by hydrogenation and carboxylation of hydrothermal organic primers. The ocean provided carbonate, phosphate, iron, nickel and protons; the hydrothermal solution was the source of ammonia, acetate, HS-, H2 and tungsten, as well as minor concentrations of organic sulphides and perhaps cyanide and acetaldehyde. The mean redox potential (delta Eh) across the membrane, with the energy to drive synthesis, would have approximated to 300 millivolts. The generation of organic anions would have led to an increase in osmotic pressure within the FeS bubbles. Thus osmotic pressure could take over from hydraulic pressure as the driving force for distension, budding and reproduction of the bubbles. Condensation of the organic molecules to polymers, particularly organic sulphides, was driven by pyrophosphate hydrolysis. Regeneration of pyrophosphate from the monophosphate in the membrane was facilitated by protons contributed from the Hadean ocean. This was the first use by a metabolizing system of protonmotive force (driven by natural delta pH) which also would have amounted to c. 300 millivolts. Protonmotive force is the universal energy transduction mechanism of life. Taken together with the redox potential across the membrane, the total electrochemical and chemical energy available for protometabolism amounted to a continuous supply at more than half a volt. The role of the iron sulphide membrane in keeping the two solutions separated was appropriated by the newly synthesized organic sulphide polymers. This organic take-over of the membrane material led to the miniaturization of the metabolizing system. Information systems to govern replication could have developed penecontemporaneously in this same milieu. But iron, sulphur and phosphate, inorganic components of earliest life, continued to be involved in metabolism.     

Viscoelastic behaviour and temporal fractal properties of lherzolite and marble: possible extrapolation from experimental results to the geological time-scale

The viscoelastic relaxation behaviour of lherzolite and marble and their temporal fractal properties are studied. Based on the high‐temperature viscoelastic behaviour for these rock types derived from the time–temperature superposition principle, the relaxation function for the viscoelastic behaviour of lherzolite and marble can be expressed as a flow law from a power‐law function of temperature‐reduced time given by normalizing the various temperature behaviours, with a non‐integer exponent. The relaxation function is thus time‐scale invariant, i.e. there is a temporal fractal property to the temperature‐reduced time. Their rheological behaviour over geological time‐scales at low temperature can be extrapolated from the experimental high‐temperature behaviour based on the temporal fractal property. Our derived flow law satisfies not only transient behaviour but also steady‐state behaviour.     

Coupling Between the Coastal Ocean and Yaquina Bay,Oregon: Importance of Oceanic Inputs Relative to Other Nitrogen Sources

Understanding of the role of oceanic input in nutrient loadings is important for understanding nutrient and phytoplankton dynamics in estuaries adjacent to coastal upwelling regions as well as determining the natural background conditions. We examined the nitrogen sources to Yaquina Estuary (Oregon, USA) as well as the relationships between physical forcing and gross oceanic input of nutrients and phytoplankton. The ocean is the dominant source of dissolved inorganic nitrogen (DIN) and phosphate to the lower portion of Yaquina Bay during the dry season (May through October). During this time interval, high levels of dissolved inorganic nitrogen (primarily in the form of nitrate) and phosphate entering the estuary lag upwelling favorable winds by 2 days. The nitrate and phosphate levels entering the bay associated with coastal upwelling are correlated with the wind stress integrated over times scales of 4–6 days. In addition, there is a significant import of chlorophyll a to the bay from the coastal ocean region, particularly during July and August. Variations in flood-tide chlorophyll a lag upwelling favorable winds by 6 days, suggesting that it takes this amount of time for phytoplankton to utilize the recently upwelled nitrogen and be transported across the shelf into the estuary. Variations in water properties determined by ocean conditions propagate approximately 11–13 km into the estuary. Comparison of nitrogen sources to Yaquina Bay shows that the ocean is the dominant source during the dry season (May to October) and the river is the dominant source during the wet season with watershed nitrogen inputs primarily associated with nitrogen fixation on forest lands.     

Assessment of Submarine Groundwater Discharge (SGD) as a Source of Dissolved Radium and Nutrients to Moorea (French Polynesia) Coastal Waters

Previous work has documented large fluxes of freshwater and nutrients from submarine groundwater discharge (SGD) into the coastal waters of a few volcanic oceanic islands. However, on the majority of such islands, including Moorea (French Polynesia), SGD has not been studied. In this study, we used radium (Ra) isotopes and salinity to investigate SGD and associated nutrient inputs at five coastal sites and Paopao Bay on the north shore of Moorea. Ra activities were highest in coastal groundwater, intermediate in coastal ocean surface water, and lowest in offshore surface water, indicating that high-Ra groundwater was discharging into the coastal ocean. On average, groundwater nitrate and nitrite (N + N), phosphate, ammonium, and silica concentrations were 12, 21, 29, and 33 times greater, respectively, than those in coastal ocean surface water, suggesting that groundwater discharge could be an important source of nutrients to the coastal ocean. Ra and salinity mass balances indicated that most or all SGD at these sites was saline and likely originated from a deeper, unsampled layer of Ra-enriched recirculated seawater. This high-salinity SGD may be less affected by terrestrial nutrient sources, such as fertilizer, sewage, and animal waste, compared to meteoric groundwater; however, nutrient-salinity trends indicate it may still have much higher concentrations of nitrate and phosphate than coastal receiving waters. Coastal ocean nutrient concentrations were virtually identical to those measured offshore, suggesting that nutrient subsidies from SGD are efficiently utilized.     

Time and the crystallization of apatite in seawater

Carbonate fluorapatite has been synthesized in seawater in an experiment of nearly 10-years duration. The addition of phosphate to seawater whose fluoride concentration had been increased to 7.6 mg/l brought about an initial amorphous phosphate precipitate. After 20 months, a crystalline magnesium phosphate phase developed within the amorphous phosphate. Crystallization of apatite, which occurred during the last 3 years of the experiment, was accompanied by dissolution of the crystalline magnesium phosphate phase.The MgO content of the apatite (1.9 percent) is high in comparison to Tertiary and older apatite but similar to some young apatite; the CO₂ content (3.6 percent) is medium, and the fluorine content (2.2 percent) is low but again similar to some young apatite. The hydroxyl ion (OH^?) likely fills the need for additional fluorine-position atoms. The mole ratio of Ca plus substituent elements to P plus substituent elements (1.50) is low in comparison to the expected ratio of 1.67. The substitution of the hydronium ion (H₃O⁺) for Ca may account for this difference.The synthesis of apatite in seawater demonstrates that the factor of time overcomes the well known inhibiting effect of magnesium upon the crystallization of apatite. It also implies that given an adequate supply of phosphate, apatite can form in most ocean environments and likely plays a major pan in the control of the phosphate content of seawater.     

Earth rotation,ocean circulation and paleoclimate

During the 20 Ka glaciation maximum Earth's rate of rotation was significantly faster. The subsequent glacial eustatic rise in sea level meant an increase of the equatorial radius and hence led to a general deceleration in the Earth's rate of rotation. At about 6000 BP the glacial eustatic rise in sea level finished and a new situation began which was characterized by feedback interchanges of angular momentum between the solid Earth and the hydrosphere. There is a strong linkage between Earth's rate of rotation — total as well as differential — and the changes in ocean surface circulation. The ocean circulation changes are, in their turn, strongly linked to the paleoclimatic evolution of the boardering land masses. This is due to the high heat-storing capacity of the oceans, the ocean/ atmosphere heat flux, and the ocean/land interaction via heat transport by the winds. Consequently, we see a causal connection between Earth's rotation, oceanic circulation, ocean/atmosphere heating, atmospheric (wind) heat transport and continental paleoclimatic changes. We propose that the paleoclimatic changes on the decadal to millennial time scale are primarily driven by this mechanism. Observational data of changes in ocean water masses and paleoclimate are presented for the 20 Ka situation, for the high-amplitude changes 13-10 Ka ago, for the decadal-to-century changes during the Holocene, for the last centuries' instrumental data and for the ENSO-events. This implies that the oceanic system (the ocean surface circulation system) has a much more important role than previously appreciated.     

Chlorine in phosphorites and bone phosphate from oceanic and marine deposits

The content, distribution patterns, and occurrence forms of Cl in phosphorites and bone phosphate from the ocean bottom, as well as in a set of samples from the land, are studied. The total Cl content ranges from 0.05 to 4.25% in phosphorites and from 2.48 to 2.75% in recent phosphate-bearing sediments. Recent phosphorites are enriched in Cl relative to ancient ones. The bound Cl content (not extractable by washing), which increases with lithification, ranges from 0.17 to 0.60% in oceanic and land phosphorites and from 0.02% to 1.30% in the bone phosphate. The Na content in most samples is higher relative to NaCl due to its incorporation into the crystal lattice of apatite. However, the opposite relationship is observed in some samples, indicating a partial Cl incorporation into the anion complex of phosphate. The behavior of Cl in phosphorites from the present-day ocean bottom is controlled by early diagenetic processes, whereas the role of weathering, catagenesis, and hydrogeological factors may be crucial for phosphorites on continents.Translated from Litologiya i Poleznye Iskopaemye, No. 1, 2005, pp. 65–77.Original Russian Text Copyright © 2005 by Baturin.     

太平洋中部富REY深海粘土的地球化学特征及REY富集机制

深海沉积物中的稀土资源是一种新发现的、潜在的海底稀土资源.对太平洋中部重力活塞取样获得的90个深海粘土样品的矿物组分、常量和稀土化学分析结果进行了系统分析,并与中北太平洋以及西北太平洋南鸟岛附近海域深海沉积物稀土元素地球化学特征进行了对比.研究结果表明:太平洋中部深海粘土以富含沸石、富P及富REY为特征,其碎屑矿物中含有较多的鱼牙骨,其P₂O₅与CaO之间、P₂O₅、CaO与∑REY之间呈良好的正相关关系;其稀土分布模式表现为明显的Ce负异常、一定程度的重稀土元素富集和Y正异常.太平洋中部深海粘土REY富集的主要原因是深海粘土中含有过量的磷酸盐组分,推测过量的磷酸盐组分是由于深海粘土中鱼牙骨碎屑的加入引起的.在北太平洋海域,未受到热液活动影响的条件下,富REY的深海沉积物的稀土元素富集机制具有统一性和普遍性,可以归纳为深海沉积物中高REY磷酸盐的混入作用.      

四川雷波地区下寒武统麦地坪含磷地层研究及磷矿资源潜力分析

【研究目的】四川省雷波县至云南省永善县是寒武系麦地坪组磷矿聚集区,含磷地层的研究不仅有助于深入分析磷矿形成的古地理环境及其变化特征,而且结合构造背景的研究,可研究磷矿形成分布规律,为磷矿的开发提供理论依据。【研究方法】以岩心编录及剖面测量为基础,研究了雷波地区麦地坪组含磷层系厚度、岩性、沉积相、沉积模式、构造背景、盆地性质、磷矿成因机制、磷块岩岩石学特征及其变化等。【研究成果】阐明了雷波地区麦地坪组在50km范围内,岩性、岩相的巨大差异以及磷块岩特征,指出雷波地区在麦地坪组沉积时期呈隆、凹相间的格局,缺失浅水陆棚相。白云岩相区属潮坪相,是磷矿聚集的有利地段。硅质岩属深水陆棚相,是火山活动形成的热水作用成因。磷矿的聚集是硅质岩相区火山活动,生物发育,高温洋流由下向上运动,携带生物遗体分解的高P₂O₅浓度海水在凹陷区两侧白云岩相区沉积和改造的结果。从大地构造背景、盆地性质、磷质来源、磷的迁移、沉淀、富集阐述了磷矿成矿作用机制,提出雷波地区磷矿是多种因素作用形成,建立了相应的磷矿成矿模式。【结论】发现揭示了新元古代末期至寒武纪早期,裂谷盆地发育的晚期阶段,一种新的磷成矿作用——隆、凹相间的古地理格局及微弱的火山活动,在空间上有效配置,并由此提出在凹陷两侧白云岩相区寻找磷矿的预测评价新思路,指出针对麦地坪组磷矿找矿的新方向,在找矿空间可由凹陷区向四周拓展。     

全球冰-海洋耦合模式的海冰模拟

海冰是全球气候系统的重要分量 ,与大气和海洋的相互作用 ,直接影响大气环流和海洋环流 ,对气候及其变化具有重要影响。文中依据冰、海洋间的热力、动力耦合相互作用 ,改进冰海洋热力耦合方案 ,利用由中国科学院大气物理研究所的 30层海洋模式和基于Flato空化流体流变学的海冰动力模式和Hibler表面热收支平衡的零层海冰热力模式 ,建立全球冰海洋耦合模式。利用大气月平均气候资料 ,利用冰海洋耦合模式对全球海冰的分布及其季节性变化、海冰漂移进行了耦合模拟和分析。模拟的南半球海冰分布及季节变化与实际分析资料非常接近 ,比 2 0层冰海洋耦合模式的结果有显著改进。北半球海冰范围偏小 ,但季节变化的量值与实际相当一致。模拟的海冰速度场反映了南、北半球海冰漂移的主要特征 ,如北极的穿极漂流和南大洋的绕极环流等。对海冰密集度的分析表明 ,模拟结果得以改进原因在于改进的冰海洋热力耦合方案增强了融冰期冰海洋耦合系统海洋热通量增加—密集度减小—能量收支增加的正反馈机制。     

Fifteen Years of Ocean Observations with China Argo

For 15 years since the beginning of China Argo project, China has deployed over 350 profiling floats in Pacific and Indian ocean, and constructed China Argo ocean observing network. Moreover, we have setup the Argo data receiving, processing and distributing system, and developed various Argo data products using Argo observations, which has promoted the progress of ocean data sharing in China. The abundant Argo data have become a main data source in oceanic and atmospheric basic researches and operational applications. A batch of important achievements in basic research and operational application have been brought, e.g. in aspects of tropical cyclone (typhoon), ocean circulation, meso-scale eddy, turbulence, heat/salt storage and transport and water mass, as well as in ocean, atmosphere/climate operational forecasting and predicting. With the extension of the international Argo program from “Core Argo” to “Global Argo”, we are faced with great challenges in the long-term maintaining and sustained developing of our Argo ocean observing network. It is suggested that we should take the opportunity to construct China regional Argo ocean observing network as soon as possible in adjacent northwestern Pacific and Indian ocean using Chinese BeiDou profiling floats, which will make us to take responsibility and obligation of a big country for addressing global climate changes and preventing natural disasters.     

研究岩石破裂等弱化行为的力－位移组合控制方法

本文介绍了一种用力和位移的线性组合控制岩石试验的新方法。该方法已在一台自制的伺服实验系统上和一台MTS实验系统上得到了实现。用这种方法能够简便地求出通常难以求出的具有Ⅱ类特性岩石的全应力-应变曲线,而且能够变化出如广义应力松驰等其它实验类型,从而能够对时间依赖性进行深入的研究。由于其易于采用的特点,它在研究岩石破裂乃至摩擦等弱化过程方面有着广泛的应用前景。     

Coral skeleton P/Ca proxy for seawater phosphate: Multi-colony calibration with a contemporaneous seawater phosphate record

A geochemical proxy for surface ocean nutrient concentrations recorded in coral skeleton could provide new insight into the connections between sub-seasonal to centennial scale nutrient dynamics, ocean physics, and primary production in the past. Previous work showed that coralline P/Ca, a novel seawater phosphate proxy, varies synchronously with annual upwelling-driven cycles in surface water phosphate concentration. However, paired contemporaneous seawater phosphate time-series data, needed for rigorous calibration of the new proxy, were lacking. Here we present further development of the P/Ca proxy in Porites lutea and Montastrea sp. corals, showing that skeletal P/Ca in colonies from geographically distinct oceanic nutrient regimes is a linear function of seawater phosphate (PO_4 SW) concentration. Further, high-resolution P/Ca records in multiple colonies of Pavona gigantea and Porites lobata corals grown at the same upwelling location in the Gulf of Panamá were strongly correlated to a contemporaneous time-series record of surface water PO_4 SW at this site (r² = 0.7-0.9). This study supports application of the following multi-colony calibration equations to down-core records from comparable upwelling sites, resulting in ±0.2 and ±0.1 μmol/kg uncertainties in PO_4 SW reconstructions from P. lobata and P. gigantea, respectively.

     

Modeling estuarine nutrient geochemistry in a simple system

We present a model of estuarine mixing, removal, and input for dissolved constituents, and apply the model to 39 nutrient (P, N, Si) profiles collected over a 14-month period in a pristine river/ estuary: Ochlockonee Bay, Florida. Each profile is deconvolved into three component functions: linear mixing (conservative) first-order removal (biological productivity), and parabolic input (regeneration). After correction for temporal variations in the fluvial end-members, the model provides quantitative estimates of total estuarine primary production, net regeneration, and subsequent fluxes to the ocean over a year-long period. The modeled data set is internally self-consistent: virtually perfect mass balances are obtained for P and Si. All biological P-uptake is regenerated within the estuary so that virtually 100% of the fluvial reactive-P enters the ocean. One-third of the fluvial reactive-P enters the estuary as particles whose phosphate is released after deposition in estuarine sediments. About 20% of the dissolved fluvial silica flux is removed biologically; all of this biogenic silica dissolves in the estuary and enters the ocean. N cannot be mass balanced, probably because it enters and escapes the bay in unmeasured forms (as NH₄ or via denitrification to N₂ and N₂O). In the Ochlockonee, biological productivity removes nutrients in the ratios N:P ? 9:1 and Si:P ? 20:1.     

Nutrient Loading and Transformations in the Columbia River Estuary Determined by High-Resolution In Situ Sensors

The Columbia River estuary is characterized by relatively large tidal currents and water residence times of a few days or less. These and other environmental conditions tend to suppress water column productivity and favor the export of riverborne nutrients to the coastal ocean. However, hotspots of biological activity may allow for significant nutrient transformation and removal within the estuary, but these processes have previously been difficult to quantify due to the challenges of obtaining measurements at appropriate frequency and duration. In this study, nutrient biogeochemical dynamics within the salt-influenced region of the estuary were quantified using high-resolution in situ observations of nutrients and physical water properties. During 2010, three autonomous nutrient sensors (Satlantic SUNA, SubChem Systems Inc. APNA, WET Labs Cycle-PO4) that together measured nitrate?+?nitrite, orthophosphate, ammonium, silicic acid, and nitrite were deployed on fixed observatory platforms. Hourly measurements captured tidal fluctuations and permitted an analysis of river and ocean end-member mixing. The results suggested that during summer, the lower estuary released high concentrations of ammonium and phosphate despite low concentrations in the river and coastal ocean. This was likely a result of organic matter accumulation and remineralization in the estuarine turbidity maximum and the lateral bays adjacent to the main channel.     

海洋酸化对颗石藻的影响

工业革命以来人类活动产生了大量二氧化碳气体（CO2）并释放到大气中。CO2溶于海水,造成海水pH值降低,改变海洋碳酸系统的平衡。海洋酸化对海洋生态系统特别是钙化生物构成威胁。颗石藻作为主要的钙化浮游生物,在海洋碳循环过程中起着重要的作用。大多数培养实验表明CO2浓度上升会促进颗石藻光合作用。而海洋酸化对不同种或不同品系颗石藻钙化作用产生不同的影响。     

Irreversible thermodynamic and viscoelastic model for power-law relaxation and attenuation of rocks

A constitutive law for viscoelastic behaviour of rocks is derived from irreversible thermodynamics. To this model, two specific parameters are introduced; one is an internal state variable which is a variable concerning the microstructures such as defects in crystals or microcracks, and the other is a temperature reduced time obtained by normalizing the various temperature behaviours. A large number of internal state variables have the respective relaxation times and show the respective time evolutions, while a set of the time evolutions generates temporal power-law behaviour of rocks. The time evolutions of internal states are regarded as dynamics of elements of the generalized Maxwell model, and the stress–strain relation is represented by a response function following a temporal power-law in terms of linear system theory. This relation is inversely formulated to investigate the source field from output data. This model enables us to explain experimentally-based constitutive laws for transient and steady-state behaviour of rocks (e.g., lherzolite) following a temporal power-law and for attenuation behaviour of polycrystals (e.g., olivine) represented by a relation between the quality factor and frequency. Both laws show power-laws on deformation time or frequency depending on the fractal structure in polycrystals or rocks, and the experimental high-temperature behaviours can be extrapolated to long deformation time or high frequency behaviour.