Computational Geo-electromagnetics: Methods, Models, and Forecasts: Volume 5

COMPUTATIONAL GEO-ELECTROMAGNETICS: Methods, Models, and Forecasts
Copyright
Preface
	References
1 - 3-D EM forward modeling techniques
	1.1 Introduction
	1.2 Methods of integral equations
		1.2.1 The method of volume integral equations
		1.2.2 The method of surface integral equations
	1.3 Methods of differential equations
		1.3.1 The finite difference technique
		1.3.2 The finite element technique
	1.4 Hybrid schemes
	1.5 Analog (physical) modeling approaches
	1.6 Balance technique for EM field computation
		1.6.1 Governing equations
		1.6.2 Boundary conditions
		1.6.3 Discretization scheme
		1.6.4 Calculation of the magnetic field
		1.6.5 Controlling the accuracy of the results
			1.6.5.1 Criteria for accuracy
			1.6.5.2 Comparison with analytical solution
			1.6.5.3 Comparison with results obtained by other techniques
	1.7 Method of the EM field computation in axially symmetrical media
		1.7.1 Governing equations
		1.7.2 Boundary conditions
		1.7.3 Discrete equations and their numerical solution
			1.7.3.1 Discrete equations
			1.7.3.2 Basis functions
			1.7.3.3 Numerical solution of discrete equations
		1.7.4 Code testing
	1.8 Conclusions
	References
2 - Three-dimensional Bayesian statistical inversion
	2.1 Introduction
	2.2 Technique for solving inverse problem using Bayesian statistics
		2.2.1 Bayesian approach
		2.2.2 Inversion algorithm
		2.2.3 Software implementation
			2.2.3.1 Computation hints
			2.2.3.2 Testing of the software package INVSTAT3D
	2.3 Assessment of prior information and data effects on the inversion results
		2.3.1 Effect of prior information
		2.3.2 Trade-off between the data and prior information
		2.3.3 Effect of the data volume and structure
	2.4 Case study: modeling of the aquifer salinity assessment with AMT data
		2.4.1 Statement of the problem
		2.4.2 Data
		2.4.3 Prior information
		2.4.4 Posterior conductivity distribution
	2.5 Conclusions
	References
3 - Methodology of the neural network estimation of the model macro-parameters
	3.1 Introduction
	3.2 Backpropagation technique
	3.3 Statement of the modeling problem
	3.4 Artificial Neural Network architecture
		3.4.1 Activation functions
		3.4.2 Number of neurons in a hidden layer
		3.4.3 Effect of the second hidden layer
		3.4.4 Threshold level
	3.5 Effect of the type, volume, and structure of the teaching data pool
		3.5.1 Effect of the data transformation type
		3.5.2 Effect of the data volume
		3.5.3 Effect of the data structure
			3.5.3.1 Random choice of synthetic data sets
			3.5.3.2 Gaps in the training data pool
			3.5.3.3 “No target” case
	3.6 ANN generalization ability
	3.7 Effect of noise
	3.8 Case study: ANN reconstruction of the Minou fault parameters
		3.8.1 Geological and geophysical setting
		3.8.2 CSAMT data acquisition and processing
		3.8.3 3-D imaging Minou fault zone using 1-D and 2-D inversion
			3.8.3.1 Synthesis of Bostick transforms
			3.8.3.2 2-D inversion results
		3.8.4 ANN reconstruction of the Minou geoelectrical structure
			3.8.4.1 ANN recognition in terms of macro-parameters
			3.8.4.2 Testing ANN inversion result
		3.8.5 Discussion
	3.9 Conclusions
	References
4 - Building of 3-D geoelectrical models at the lack of magnetotelluric data
	4.1 Introduction
	4.2 Single profile case
		4.2.1 Effect of data used
		4.2.2 Effect of prior information on the background section
			4.2.2.1 Test model and synthetic data
			4.2.2.2 3-D inversion of profile MT data
	4.3 Effect of additional profile
		4.3.1 Test model and synthetic data
		4.3.2 3-D inversion results
			4.3.2.1 Effect of data transforms used
			4.3.2.2 Effect of sparse profiles location
	4.4 Effect of using scalar archive data around profile (case study of Eastern Siberia profile)
		4.4.1 Geology and magnetotelluric data
		4.4.2 Algorithm for joint inversion of tensor and scalar MT data
		4.4.3 Building of 3-D model of the apparent resistivity from archive scalar data
		4.4.4 2-D inversion of tensor MT data
		4.4.5 2-D+ resistivity model
		4.4.6 Discussion
	4.5 Conclusions
	References
5 - Methods for joint inversion and analysis of EM and other geophysical data
	5.1 Introduction
	5.2 Simultaneous inversion
		5.2.1 Deterministic techniques
		5.2.2 Stochastic techniques
	5.3 Cooperative inversion
	5.4 Classification methods
		5.4.1 Probabilistic clustering
		5.4.2 Neural network classification
			5.4.2.1 Maximal correlation similarity technique
			5.4.2.2 Self-organizing map (SOM) technique
		5.4.3 Hybrid approaches
	5.5 Conclusions
	References
Introducation
6 - Electromagnetic study of geothermal areas
	6.1 Introduction
	6.2 Conceptual models of geothermal areas
	6.3 Factors affecting electrical resistivity of rocks
		6.3.1 Temperature
		6.3.2 Rock porosity and permeability
		6.3.3 Alteration mineralogy
	6.4 EM imaging of geothermal areas
		6.4.1 Magnetotelluric sounding
		6.4.2 3-D resistivity models
		6.4.3 Other electromagnetic techniques
		6.4.4 Joint analysis of electrical resistivity and temperature models
	6.5 Electromagnetic mapping faults and fracturing
	6.6 EM monitoring of the geothermal reservoirs
	6.7 Constraining locations for drilling boreholes
	6.8 Conclusions
	References
7 - 3-D magnetotelluric sounding of volcanic interiors: methodological aspects
	7.1 Introduction
	7.2 Geological noise and relief topography treatment (Kilauea volcano, Hawaii, case study)
		7.2.1 Upward analytical continuation of MT field
		7.2.2 Imaging of the structure using MT data collected over the relief surface
	7.3 Fast 3-D inversion of MT data (Komagatake volcano, Japan, case study)
	7.4 Assessment of the magma chamber parameters (Vesuvius volcano, Italy, case study)
		7.4.1 Simplified 3-D conductivity model and synthetic MT data
		7.4.2 Assessment of the geometrical parameters of the magma chamber
			7.4.2.1 Lateral boundaries
			7.4.2.2 Upper and lower boundaries
		7.4.3 Assessment of the magma conductivity
			7.4.3.1 Effect of prior information about magma conductivity
			7.4.3.2 Effect of prior information about magma chamber depth
		7.4.4 Discussion
	7.5 Modeling of remote MT monitoring of the melt condition in the magma chamber
		7.5.1 Effects of the cone and magma channel
		7.5.2 Estimating of the melt temperature variation
	7.6 Remote imaging magma chamber from MT sounding data and satellite photo (Elbrus volcano, Caucasus, case study)
		7.6.1 Resistivity cross-section of the Elbrus lithosphere
		7.6.2 Estimation of the tectonic fracturing of the lithosphere from satellite photo
		7.6.3 Focusing magma chambers using electrical resistivity and tectonic fracturing data
			7.6.3.1 Neural network training
			7.6.3.2 2-D+ electrical resistivity model
	7.7 Conclusions
	References
8 - A conceptual model of the Earth’s crust of Icelandic type
	8.1 Introduction
	8.2 Geological and geophysical information
		8.2.1 Geology and volcanic activity in the region
		8.2.2 Electromagnetic soundings
		8.2.3 Seismic tomography
		8.2.4 Seismicity
	8.3 Building of 3-D resistivity model
		8.3.1 EM data
			8.3.2 3-D electrical resistivity model
	8.4 Temperature recovering from EM data
		8.4.1 Temperature well logs
		8.4.2 EM geothermometer calibration
		8.4.3 EM geothermometer validation
	8.5 3-D temperature model
		8.5.1 Background temperature
		8.5.2 Local temperature anomalies
	8.6 Heat sources
	8.7 Seismicity sources
	8.8 Conceptual model of the crust
	8.9 Conclusions
	References
9 - Conceptual model of a lens in the upper crust (Northern Tien Shan case study)
	9.1 Introduction
		9.1.1 Geology and seismicity
		9.1.2 Seismic velocity models
		9.1.3 Electrical resistivity model
			9.1.3.1 General analysis of resistivity distribution
			9.1.3.2 2-D cross-section along MT profile
	9.2 Density model
		9.2.1 Gravity studies
		9.2.2 2-D cross-section
	9.3 Model of lithotypes
	9.4 Temperature model
		9.4.1 Geothermic studies
		9.4.2 Data and calibration of EM geothermometer
		9.4.3 2-D temperature model
	9.5 Porosity and fluid saturation
		9.5.1 Porosity estimation
		9.5.2 Fluid saturation estimation
	9.6 Conceptual model
		9.6.1 Petrophysical properties of the lens
		9.6.2 Nature of geophysical anomalies
		9.6.3 Mechanism of the lens formation
		9.6.4 The lifetime of the lens
		9.6.5 Relationship between fluid dynamics and geodynamic processes
	9.7 Conclusions
	References
10 - Conceptual model of the copper–porphyry ore formation (Sorskoe copper–molybdenum ore deposit case study)
	10.1 Introduction
	10.2 Geological and geophysical setting
	10.3 Characteristics of the Sorskoe copper–molybdenum deposit
	10.4 Electromagnetic studies
		10.4.1 Inversion of MT data
		10.4.2 3-D electrical resistivity model
	10.5 Seismic tomography
		10.5.1 Seismic survey
		10.5.2 3-D seismic velocity models
	10.6 3-D density model
	10.7 3-D lithology model
	10.8 Conceptual model of the deposit
	10.9 Conclusions
	References
11 - Electromagnetic sounding of hydrocarbon reservoirs
	11.1 Introduction
	11.2 Mapping zones of hydrocarbon fluids migration
	11.3 Decreasing the probability of drilling dry holes
	11.4 Ranking drilling targets
	11.5 Oil or water?
	11.6 Estimation of porosity beyond boreholes
	11.7 Constraining spatial boundaries of a deposit
	11.8 Optimization of a working cycle
	11.9 Forecasting reservoir rock properties while drilling
	11.10 Conclusions
	References
12 - Temperature forecasting from electromagnetic data
	12.1 Introduction
	12.2 Electromagnetic geothermometer
	12.3 Interpolation in the interwell space
		12.3.1 Effect of the data volume
		12.3.2 Effect of the neuronet training strategy
		12.3.3 Effect of the geology and hydrological conditions
	12.4 EM temperature extrapolation in depth
		12.4.1 Sedimentary cover
			12.4.1.1 Data and thermometer calibration
			12.4.1.2 Temperature extrapolation
		12.4.2 Geothermal area
			12.4.2.1 Data and thermometer calibration
			12.4.2.2 Temperature extrapolation
		12.4.3 Robustness evaluation
	12.5 Building temperature model from MT sounding data (Soultz-sous-Forêts, France, case study)
		12.5.1 Geological setting
		12.5.2 Previous temperature assessments
		12.5.3 Magnetotelluric sounding
		12.5.4 Geothermometer validation
			12.5.4.1 Retro-modeling of the temperature forecast
			12.5.4.2 Effect of the resistivity\'s uncertainty
		12.5.5 Temperature model
		12.5.6 Discussion
	12.6 Conclusions
	References
13 - Recovering seismic velocities and electrical resistivity from the EM sounding data and seismic tomography
	13.1 Introduction
	13.2 Geological setting
	13.3 Geophysical surveys
		13.3.1 Magnetotelluric sounding
		13.3.2 Seismic survey
	13.4 Methodology of modeling
	13.5 Recovering of seismic velocities from electrical resistivity
		13.5.1 Recovering of VP
		13.5.2 Recovering of VS
	13.6 Recovering of electrical resistivity from seismic velocities
		13.6.1 Recovering of resistivity from VP
		13.6.2 Recovering resistivity from VS
	13.7 Conclusions
	References
14 - Porosity forecast from EM sounding data and resistivity logs
	14.1 Introduction
	14.2 Lithology and porosity data
	14.3 Electrical resistivity data
		14.3.1 Electromagnetic sounding data
		14.3.2 Electrical resistivity logs
		14.3.3 Electrical resistivity pseudo logs
		14.3.4 Estimating parameters of Archie formula
	14.4 Modeling methodology
	14.5 Porosity forecast in depth
		14.5.1 Prediction variants
		14.5.2 Results of prediction
	14.6 Porosity forecast in the interwell space
		14.6.1 Prediction variants
		14.6.2 Results of prediction
	14.7 Conclusions
	References
A - Empirical formulas relating electrical conductivity, seismic velocities, and porosity
	A.1 Relations between electrical conductivity and porosity
		A.1.1 Archie formula and its modifications
		A.1.2 Formulas for two-phase media
	A.2 Relations between seismic velocities and porosity
	A.3 Cross-property relations of electrical conductivity and seismic velocities in the wet rocks
	References
Index