A cautionary tale: How phase compensation during surface nuclear magnetic resonance inversion conceals forward modelling errors

TY - JOUR

T1 - A cautionary tale

T2 - How phase compensation during surface nuclear magnetic resonance inversion conceals forward modelling errors

AU - Osterman, Gordon

AU - Haldrup, Jens

AU - Larsen, Jakob Juul

AU - Auken, Esben

AU - Grombacher, Denys

PY - 2020

Y1 - 2020

N2 - Surface nuclear magnetic resonance (NMR) data are sensitive to key hydrogeological parameters including water content and pore size. The measured data are modelled as a complex sinusoidal exponential decay where the phase is a function of the physics of the experiment and instrumental factors, parameters that are difficult to decouple. When inverting surface NMR data, practitioners typically account for these phases either by considering only the amplitudes of the complex signals, thus eliminating the influence of the phase, or by iteratively rotating the complex data during inversion so the data phase matches the theoretical phase generated during forward modelling. Each of these approaches assumes the user has an accurate forward model; if not, the data will be incorrectly rotated and forced to fit an erroneous forward model. Additionally, this rotation will artificially reduce the total data misfit, thus masking the effect of the erroneous forward model. We demonstrate the pitfalls of using inverse methods that correct for the phase by inverting synthetic data with three types of deliberate modelling errors that may occur during a surface NMR experiment: errors in the offset between the Larmor and transmit frequencies, errors in the subsurface resistivity model, and errors in the relative positioning of a separated transmitter-receiver coil pair. The inverted water content profiles show that the modelling errors can introduce inversion artifacts. However, the amplitude inversions and complex inversions with iterative phase correction frequently produce χ2 misfit values close to unity, showing that these inverse methods will fail to “raise the alarm” when an incorrect forward model is implemented.

AB - Surface nuclear magnetic resonance (NMR) data are sensitive to key hydrogeological parameters including water content and pore size. The measured data are modelled as a complex sinusoidal exponential decay where the phase is a function of the physics of the experiment and instrumental factors, parameters that are difficult to decouple. When inverting surface NMR data, practitioners typically account for these phases either by considering only the amplitudes of the complex signals, thus eliminating the influence of the phase, or by iteratively rotating the complex data during inversion so the data phase matches the theoretical phase generated during forward modelling. Each of these approaches assumes the user has an accurate forward model; if not, the data will be incorrectly rotated and forced to fit an erroneous forward model. Additionally, this rotation will artificially reduce the total data misfit, thus masking the effect of the erroneous forward model. We demonstrate the pitfalls of using inverse methods that correct for the phase by inverting synthetic data with three types of deliberate modelling errors that may occur during a surface NMR experiment: errors in the offset between the Larmor and transmit frequencies, errors in the subsurface resistivity model, and errors in the relative positioning of a separated transmitter-receiver coil pair. The inverted water content profiles show that the modelling errors can introduce inversion artifacts. However, the amplitude inversions and complex inversions with iterative phase correction frequently produce χ2 misfit values close to unity, showing that these inverse methods will fail to “raise the alarm” when an incorrect forward model is implemented.

KW - Inversion

KW - Phase

KW - Surface nuclear magnetic resonance

UR - http://www.scopus.com/inward/record.url?scp=85076826724&partnerID=8YFLogxK

U2 - 10.1016/j.jappgeo.2019.103905

DO - 10.1016/j.jappgeo.2019.103905

M3 - Journal article

AN - SCOPUS:85076826724

SN - 0926-9851

VL - 173

JO - Journal of Applied Geophysics

JF - Journal of Applied Geophysics

M1 - 103905

ER -