• TEM Smooth-model Inversion

  • One-dimensional In-loop TEM Inversion

  • One-dimensional In-loop TEM Forward Modelling

  • Two-dimensional Smooth-model CSAMT Inversion

  • Smooth-model CSAMT Inversion

  • One-dimensional CSAMT Inversion

  • Resistivity and IP Smooth-Model Inversion

  • Two-dimensional Electromagnetic Modelling

  • Smooth-model two-dimensional IP/Resistivity Inversion with Topography

TEM Smooth-model Inversion

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Smooth-model inversion is a robust method for transforming moving-in-loop TEM soundings to profiles of resistivity versus depth. Observed transient data for each sounding are used to determine the parameters of a layered-earth model. Layer thicknesses are fixed and set to sum to the soundings's maximum depth of investigation. Layer resistivities are then adjusted iteratively until model TEM responses are as close as possible to observed data. Smoothness constraints limit model resistivity variation from layer to layer.

STEMINV's algorithm for calculating the TEM response of a layered model includes the effects of rectangular transmitter loops and finite transmitter turn-off-ramp times. Accurate transient voltages are calculated for all window times.

The result of smooth-model inversion is a set of estimated resistivities which vary smoothly with depth. Lateral variation is determined by inverting successive soundings along a survey line. Results for a complete line can be presented in pseudosection form by contouring model resistivities. For contouring, model resistivity values are placed at the midpoint of each layer, forming a column below every station. The columns form an array representing a cross-section of model resistivity.

Inverting apparent resistivity and phase to smoothly varying model resistivities is an effective way to display the information inherent in TEM soundings. Smooth-model inversion does not require any a priori estimates of model parameters. The observed data are automatically transformed to resistivity as a function of depth. Models with smoothness constraints are complementary to more detailed models incorporating a priori geologic constraints.

One-dimensional In-loop TEM Inversion

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TCINV inverts the transient response of an in-loop TEM system to a layered earth model. TCINV uses an iterative inversion algorithm which constrains changes to layered model parameters while minimizing the difference between observed and calculated data. The forward modelling routine calculates the transient fields excited by a ramped current step in a large, circular transmitter loop. The in-loop transient response is measured as voltage in a small loop antenna placed at the center of the transmitter loop. TCINV supersedes NLSTCI with a more efficient inversion algorithm, compensation for finite transmitter turn-off time, and a simpler user interface.

One-dimensional In-loop TEM Forward Modelling

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TEM1D calculates the transient response of an induction loop system on the surface of a layered earth. Source fields are excited by a ramped current step in a large, rectangular transmitter loop antenna. The transient responses are calculated as voltages in receiver coil antennas placed at arbitrary locations on the earth's surface. TEM1D supersedes the program TCI. It allows rectangular loops, a finite transmitter turn-off time, and arbitrary placement of the receiver coil.

Two-dimensional Smooth-model CSAMT Inversion

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Smooth-model inversion is a robust method for converting far-field CSAMT or natural-source AMT data to resistivity model cross-sections. SCS2D inverts observed apparent resistivity and impedance phase data from a line of soundings to determine resistivities in a model cross-section. Either TM-mode data, TE-mode or both may be inverted. To start the inversion, the model cross-section is usually given a background resistivity generated from a moving average of apparent resistivity data or a 1d smooth-model inversion section. Specific geologic structure may be added to the background model if there is drill-log or geologic-mapping information available. During the inversion, model-section-pixel resistivities are adjusted iteratively until calculated apparent resistivity and impedance phases are as close as possible to observed data, consistent with model constraints. Model constraints include background-model constraints, which restrict the difference between the inversion model and a background model section, which represents known geology, and smoothness constraints, which limit resistivity variation from pixel to pixel.

To calculate apparent resistivity and impedance phase for a given model section, SCS2D uses a two-dimensional, finite-element algorithm to calculate far-field CSAMT or natural-source MT data. To model areas with rough terrain, the finite-element mesh is draped over an along-line topographic profile. Either TM or TE-mode data can be calculated for scalar, vector or tensor survey configurations for frequencies ranging from less than 0.01 Hz to 10 kHz.

Inverting apparent resistivity and impedance phase to smoothly varying model sections is an effective way to display the information inherent in CSAMT and AMT measurements. As smooth-model inversion does not require any preliminary information about geologic structure, observed data are automatically transformed to a resistivity model cross-section providing an image of the subsurface. Model sections generated with smoothness constraints are complementary to more specialized inversions incorporating specific geologic models.

Smooth-model CSAMT Inversion

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Smooth-model inversion is a robust method for transforming CSAMT soundings to profiles of resistivity versus depth. Observed apparent resistivity and phase data for each station are used to determine the parameters of a layered-earth model. Layer thicknesses are fixed by calculating source-field penetration depths for each frequency. Layer resistivities are then adjusted iteratively until model CSAMT responses are as close as possible to observed data. Smoothness constraints limit model resistivity variation from layer to layer.

The algorithm for calculating the CSAMT response of a layered model includes the effects of finite transmitter-receiver separation and a three- dimensional source field. Accurate impedance magnitude and phase values are calculated for all frequencies and transmitter-receiver separations.

Smooth-model inversion produces a set of estimated resistivities which vary smoothly with depth. Lateral variation is determined by inverting successive stations along a survey line. Results for a complete line can be presented in pseudosection form by contouring model resistivities. For contouring, model resistivity values are placed at the midpoint of each layer, forming a column below every station. The columns form an array representing a cross-section of model resistivity.

Inverting apparent resistivity and phase to smoothly varying model resistivities is an effective way to display the information inherent in CSAMT measurements. Smooth-model inversion does not require any a priori estimates of model parameters. The observed data are automatically transformed to resistivity as a function of depth. Models with smoothness constraints are complementary to more detailed models incorporating a priori geologic constraints.

One-dimensional CSAMT Inversion

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CSINV inverts CSAMT frequency-sounding data into a layered-earth model. The forward-modelling routines in CSINV include the effects of finite transmitter-receiver separation and a three-dimensional source. CSINV computes accurate impedances for near-field, transition, and far-field data. CSINV uses an iterative inversion algorithm which constrains changes to layered-model parameters while minimizing the difference between observed and calculated data.

CSINV can be used either as a stand-alone program or as one module in a group of programs designed for interactive interpretation. Supplemental programs distributed with CSINV provide utilities for data entry, editing, and display. The utilities include a program for direct inversion of far- field data. Also included are reformatting programs to convert data from or to specialized file formats. Screen and printer plotting capabilities allow quick review of modelling results.

Resistivity and IP Smooth-Model Inversion

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2DIP is a finite element program which computes the low-frequency electrical response of two-dimensional models. Models may include both subsurface structure and surface topography. Voltage responses for arbitrary electrode configurations may be calculated. Configurations may use up to ten transmitter electrodes and twenty receiver electrodes. The default survey configuration is dipole-dipole, with the model response calculated as apparent resistivity and phase. Up to nine resistivities may be specified. Voltages are calculated for all combinations of transmitter and receiver electrode locations. For the default dipole-dipole configuration, the model response is presented as pseudosections of apparent resistivity and phase.

Two-dimensional Electromagnetic Modelling

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EM2D calculates the electromagnetic fields excited by a plane-wave source over 2-D resistivity and topographic structures. The electric-field component of the source can be oriented at any angle relative to strike. EM2D calculates both transverse magnetic and transverse electric modes.

EM2D can evaluate models with arbitrary two-dimensional resistivity variations. An analytical solution is used to obtain exact values for electromagnetic field components over a layered earth. The effects of further two-dimensional variation relative to a layered-earth are approximated by a finite-difference algorithm. Fields over or within arbitrarily complex, two-dimensional models can be computed. The results are particularly accurate for models which are close to a layered earth.

Smooth-model two-dimensional IP/Resistivity Inversion with Topography

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Two-dimensional, smooth-model inversion of resistivity and induced polarization data produces image-like, electrical property sections which improve the data's interpretability.

Recent software improvements enable routine smooth-model inversion of resistivity and induced polarization (IP) data. Nearly uniform starting models are generated by running broad moving- average filters over lines of dipole-dipole or pole-dipole data. Model resistivity and IP properties are then adjusted iteratively until calculated data values match ovserved values as closely as possible, given constraints which keep the model section smooth.

Calculated values are generated with a finite element algorithm which can be adapted for accurate two-dimensional modelling of data collected in routh terrain. Smooth-model inversion of sample data show the method's utility as an interpretation aid and the importance of modelling topography in areas with significant relief.

Two-dimensional Smooth-model CSAMT Inversion

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Smooth-model inversion is a robust method for converting far-field CSAMT or natural-source AMT data to resistivity model cross-sections. SCS2D inverts observed apparent resistivity and impedance phase data from a line of soundings to determine resistivities in a model cross-section. Either TM-mode data, TE-mode or both may be inverted. To start the inversion, the model cross-section is usually given a background resistivity generated from a moving average of apparent resistivity data or a 1d smooth-model inversion section. Specific geologic structure may be added to the background model if there is drill-log or geologic-mapping information available. During the inversion, model-section-pixel resistivities are adjusted iteratively until calculated apparent resistivity and impedance phases are as close as possible to observed data, consistent with model constraints. Model constraints include background-model constraints, which restrict the difference between the inversion model and a background model section, which represents known geology, and smoothness constraints, which limit resistivity variation from pixel to pixel.

To calculate apparent resistivity and impedance phase for a given model section, SCS2D uses a two-dimensional, finite-element algorithm to calculate far-field CSAMT or natural-source MT data. To model areas with rough terrain, the finite-element mesh is draped over an along-line topographic profile. Either TM or TE-mode data can be calculated for scalar, vector or tensor survey configurations for frequencies ranging from less than 0.01 Hz to 10 kHz.

Inverting apparent resistivity and impedance phase to smoothly varying model sections is an effective way to display the information inherent in CSAMT and AMT measurements. As smooth-model inversion does not require any preliminary information about geologic structure, observed data are automatically transformed to a resistivity model cross-section providing an image of the subsurface. Model sections generated with smoothness constraints are complementary to more specialized inversions incorporating specific geologic models.