from geoscilabs.em.TDEMHorizontalLoopCylWidget import TDEMHorizontalLoopCylWidget APP = TDEMHorizontalLoopCylWidget()
from matplotlib import rcParams rcParams['font.size'] = 16
Here, we show the transient fields and fluxes that result from placing a vertical magnetic dipole (VMD) source over an Earth model containing a spherical structure and an overburden layer. The transient response in this case refers to the fields and fluxes that are produced once a long-standing primary magnetic field is removed.
There are two commonly used models for describing the VMD source that produces a transient response: 1) as an infinitessimally small bar magnet that experiences a long-standing vertical magnetization which is then instantaneously removed at $t=0$, and 2) as an infinitessimally small horizontal loop of wire carrying a constant current which is then instantaneously shut off at $t=0$ (step-off current waveform).
True dipole sources do not exist in nature however they can be approximated in practice. For geophysical applications, we use small current loops to approximate transient VMD sources. These EM sources may be placed on the Earth's surface (ground-based surveys) or flown through the air (airborne surveys). According to the Biot-Savart law, a primary magnetic field is produced whenever there is current in the loop. When the current is shut-off, the sudden change in magnetic flux induces anomalous currents in the Earth which propagate and diffuse over time. The distribution and propagation of the induced currents depends on the subsurface conductivity distribution and how much time has passed since the current in the VMD source was shut off. The induced currents ultimately produce secondary magnetic fields which can be measured by a receiver.
In this app, we explore the following:
The geological scenario being modeled is shown in the figure below. Here, the Earth is comprised of a spherical structure and overburden layer within a homogeneous background. Each of the three geological units has its own conductivity ($\sigma$). However, a constant magnetic susceptibility ($\chi$) is used for all units; where $\mu_0$ is the magnetic permeability of free space and $\mu = \mu_0 (1 +\chi)$. The depth to the layer is given by $d_1$ and $h$.
In this case, a transient VMD source (Tx) is used to excite the Earth, and the Earth's TEM response (secondary magnetic field) is measured by a receiver (Rx). In practice, the transmitter and receiver may be placed near the Earth's surface or in the air. The receiver may also measure secondary fields at a variety of times after the source is shut off.
To understand the fields and currents resulting from a transient VMD source we have two apps:
Follow the exercise in a linear fashion. Some questions may use parameters set in a previous question.
We use this app to simulate the fields and currents everywhere due to a transient VMD source. The fields and induced currents depend on time and the subsurface conductivity distribution. You will use the app to change various parameters in the model and see how the fields and currents change.
Using this app, we show how the fields observed at the receiver location depend on the parameters set in the previous app. Note that if you want to see changes in the data due to changes in the model, you MUST re-run the previous app.
EM fields will be depenent upon a number of parameters, using a simple half-space model ($\sigma_1=\sigma_2=\sigma_3$) explore how EM fields and data changes upon below four parameters.