Practical considerations in the application of simulated annealing to stochastic simulation

Deutsch, Clayton V.; Cockerham, Perry W.

doi:10.1007/bf02065876

Cited by 112 publications

(64 citation statements)

References 7 publications

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“…In this study, initial random images, which reproduce the variogram, were disturbed by the change of Z values in two randomly selected sites. The preestablished contrast was the reproduction of the variogram, and the correspondent function was minimized using a standard annealing procedure (Deutsch & Cockerham, 1994).…”

Section: Methodsmentioning

confidence: 99%

Stochastic simulations of calcium contents in sugarcane area

Pereira

Teixeira

Souza

et al. 2015

Rev. bras. eng. agríc. ambient.

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A B S T R A C TThe aim of this study was to quantify and to map the spatial distribution and uncertainty of soil calcium (Ca) content in a sugarcane area by sequential Gaussian and simulatedannealing simulation methods. The study was conducted in the municipality of Guariba, Simulações estocásticas dos teores de cálcio em área de cana-de-açúcar R E S U M O Objetivou-se, neste trabalho, quantificar e mapear a distribuição espacial e a incerteza do teor de cálcio (Ca) do solo, em área sob o cultivo de cana-de-açúcar por meio da simulação sequencial gaussiana e simulação do arrefecimento simulado. O estudo foi conduzido no município de Guariba, nordeste do estado de São Paulo. Foi estabelecida uma malha amostral contendo 206 pontos separados por uma distância de 50 m totalizando aproximadamente 42 ha. Os teores de cálcio foram avaliados na profundidade de 0-0,20 m. Foram utilizadas técnicas geoestatísticas de estimação, krigagem ordinária e de simulações estocásticas: simulação sequencial gaussiana e a simulação de arrefecimento simulado. A técnica da krigagem ordinária não reproduz satisfatoriamente as estatísticas globais do teor de Ca. A utilização das técnicas da simulação permite a reprodução do padrão da variabilidade espacial do teor de Ca e as técnicas de simulação da sequencial gaussiana e a simulação do arrefecimento simulado mostraram variações significativas dos teores de Ca na pequena escala.

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Section: Methodsmentioning

confidence: 99%

Stochastic simulations of calcium contents in sugarcane area

Pereira

Teixeira

Souza

et al. 2015

Rev. bras. eng. agríc. ambient.

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“…Continuous Markov chain models (MCM) are used to represent the model of spatial variability (Krumbein and Dacey, 1969;Carle and Fogg, 1997;Ritzi, 2000). TProGS allows for the simulation of multiple realizations by utilizing a sequential indicator simulation (SIS) (Seifert and Jensen, 1999) and by performing simulated quenching (Deutsch and Cockerham, 1994;Carle, 1997). These two steps are mutually dependent and they make sure that the realizations honor local conditioning data as well as the defined model of spatial variability.…”

Section: Tprogs -Transition Probability Geostatistical Softwarementioning

confidence: 99%

“…An initial configuration of facies distribution is produced by the SIS algorithm (Deutsch and Journel, 1992). Secondly, the initial configuration is reshuffled by the simulation quenching optimization algorithm (Deutsch and Cockerham, 1994). The TProGS simulation domain of this study is discretized into 20 m × 20 m × 2 m cells on a 450 ×600 × 40 cell grid.…”

Section: Tprogs -Transition Probability Geostatistical Softwarementioning

confidence: 99%

Challenges in conditioning a stochastic geological model of a heterogeneous glacial aquifer to a comprehensive soft data set

Koch

Jensen

et al. 2014

Hydrol. Earth Syst. Sci.

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Abstract. In traditional hydrogeological investigations, one geological model is often used based on subjective interpretations and sparse data availability. This deterministic approach usually does not account for any uncertainties. Stochastic simulation methods address this problem and can capture the geological structure uncertainty. In this study the geostatistical software TProGS is utilized to simulate an ensemble of realizations for a binary (sand/clay) hydrofacies model in the Norsminde catchment, Denmark. TProGS can incorporate soft data, which represent the associated level of uncertainty. High-density (20 m × 20 m × 2 m) airborne geophysical data (SkyTEM) and categorized borehole data are utilized to define the model of spatial variability in horizontal and vertical direction, respectively, and both are used for soft conditioning of the TProGS simulations. The category probabilities for the SkyTEM data set are derived from a histogram probability matching method, where resistivity is paired with the corresponding lithology from the categorized borehole data. This study integrates two distinct data sources into the stochastic modeling process that represent two extremes of the conditioning density spectrum: sparse borehole data and abundant SkyTEM data. In the latter the data have a strong spatial correlation caused by its high data density, which triggers the problem of overconditioning. This problem is addressed by a work-around utilizing a sampling/decimation of the data set, with the aim to reduce the spatial correlation of the conditioning data set. In the case of abundant conditioning data, it is shown that TProGS is capable of reproducing non-stationary trends. The stochastic realizations are validated by five performance criteria: (1) sand proportion, (2) mean length, (3) geobody connectivity, (4) facies probability distribution and (5) facies probability-resistivity bias.In conclusion, a stochastically generated set of realizations soft-conditioned to 200 m moving sampling of geophysical data performs most satisfactorily when balancing the five performance criteria. The ensemble can be used in subsequent hydrogeological flow modeling to address the predictive uncertainty originating from the geological structure uncertainty.

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“…To reduce the computational effort, Deutsch and Cockerham (1994) proposed an efilcient method of updating y '(h,).…”

Section: ! mentioning

confidence: 99%

“…c c Conditioning data is then read in (if available) and assigned to the nearest node if within the grid network. ',Iagfl tite(*,*y****** ***************************************r ead(1in,*,er&7) isas write(*,111) isas write(ldbg,l 11) isas 111 forrnat(flAnnealing schedule: ',i2/, +' ( &user, l:defarrl~2fas~3:very fast )') read(lin,*,err=97) (sas(i),i=I,6) read(Iin,*,en=97) part read(1in,*,err=97) seed read(lin,*,es-r=97) nsim read(lin,*,err=97) nx,xnm,xsiz read(lin,*,err=97) ny,yrnn,ysiz read(lin,*,err=97) nz,zrnn,zsiz rcad(Iin, (Deutsch and Cockerham, 1994) c sas(3)=sas(3)*dble(nx*ny*nz) sas(4)=sas(4)*dbIe(nx*ny*nz) if(isas.eq.1) then Sas(l) = I.odo sas(2) = O.ldO sas(3) = 100.dO*dble(nx*ny*nz) 555(4)= 10.dO*dble(nx*ny*nz) sas(5) = 3.dO sas(6) = 0.001dO elseif(isas.eq.2) then 555(I)= l.odo sas(2) =0.05d0 SSS(3)= 50.dO*dble(nx*ny *nz) sas(4) = 5.dO*dble(nx*ny*nz) sas(5) = 3.dO SSS(6)= 0.001dO elseif(isas.eq.3) then sa.s(l) = 0.5d0 sas(2) = O.OldO sas(3) = 10.dO*dble(nx*ny*nz) SSS(4)= 2.dO*dbIe(nx*ny*nz) sas(5) = 3.dO sas(6) = 0.001dO endif write(*,112)(sas(i),i=l,6),part write(ldbg,112)(sas(i),i=l ,6),part 112 forrnat('User set schedule:'/ + 'To = ',f5.lj + 'T factor= ',f5.1J + ' Knrax = ',e7.lj + ' Kaccept = ',e7.l/ + 's =',f5.lJ + 'Ornirs = ',e7.1J + 'Part = ',i2) write(*,*~*********************************************q read(lin,*,en=97) nst,cO,isiIl sill = CO wnte(*, 100) isill,nst,cO if(nst.Ie.0) then write(*,9997) nst 9997 forrnat('nst must beat least 1, it has been set to ',i4J, + 'The c or a values can be set to zero') stop endif + '#of neighborhood = ',i4) write(*,*~*********************************************' read(lbr,*)ymean,ystd,itrans read(lin,*) peut,aspcut,xcrr~ptarget c c Read which annealing algorithm should be used: …”

Section: ------------------------------------------------------------mentioning

confidence: 99%

Statistical analysis of liquid seepage in partially saturated heterogeneous fracture systems

Liou¹

1999

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Practical considerations in the application of simulated annealing to stochastic simulation

Cited by 112 publications

References 7 publications

Stochastic simulations of calcium contents in sugarcane area

Stochastic simulations of calcium contents in sugarcane area

Challenges in conditioning a stochastic geological model of a heterogeneous glacial aquifer to a comprehensive soft data set

Statistical analysis of liquid seepage in partially saturated heterogeneous fracture systems

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