Ground Water Source Depth analysis and application
of electrical source short offset transient electromagnetic detection.
Abstract
There
are several concepts of depth in transient electromagnetic method, including
diffusion depth, limit detection depth, effective detection depth and apparent
detection depth. In this paper, we conducted the calculation, analysis and
application to these different depths based on the SME The diffusion depth
represent the diffusion and propagation of the underground transient EM field,
the limit detection depth reveals the detectability of SOTEM and the results
indicate that the greatest depth will be obtained when the offset approximately
equal to the 0.7~1 times of buried depth of targets, and the apparent detection
depth can give an estimation of the actual detection depth for a given
recording time which have a significant meaning to the field work designing. At
last,We proposed a synthetic model and a filed example to verify the
feasibility and accuracy of using apparent detection depth to estimate the
actual detection depth of SOTEM.
Keyword : electrical
source ; shortoffset ; transient electromagnetic method ; detection
depth
0 Preface
Apparent resistivity and detection depth are the two most important parameters in electrical prospecting, and detection depth is one of the main criteria to measure the detection ability of a method. Different types of electrical devices have different depth concepts and estimation methods. The direct current method is mainly determined according to the geometric arrangement of its receiving and transmitting devices ^{[ 1 ]} ; in the frequency domain electromagnetic method, the skin depth formula is often used to estimate the detection depth of different frequencies ^{[ 2 ]} ; the time domain electromagnetic method (transient electromagnetic method) involves There are many concepts of depth, such as diffusion depth, limit detection depth, effective detection depth and apparent detection depth ^{}
. Of course, in addition to the abovementioned physical mechanism related to the principle of each method, the detection depth is also affected by factors such as signal strength, noise level, instrument sensitivity, and geoelectrical.^{}
The
research on the detection depth of the electromagnetic method can be divided
into two aspects. One is the research on the limit (maximum and minimum)
detection depth of the electromagnetic method. The main purpose is to evaluate
the detection ability of the method and use it to guide the construction
design ; the other is the detection depth measured at different
frequencies or at different times, the main purpose is to explain the measured
data, usually expressed in the form of apparent resistivitydepth section . From
the above two aspects, this paper analyzes and calculates the detection depth
of the electrical source shortoffset transient electromagnetic method (SOTEM),
obtains a qualitative understanding of the SOTEM detection capability, and
provides a reference for field SOTEM data acquisition and construction.
1 Introduction to SOTEM method
Shortoffset
transient electromagnetic method (SOTEM) is a new type of transient electromagnetic
working device proposed on the basis of traditional longoffset transient
electromagnetic method (LOTEM) . It uses a long ground wire with a
length of about 5002 000 m as the emission source, supplies a bipolar
rectangular step current with an intensity of 1040 A, and observes the
transient electromagnetic field within an offset range less than 2 times the
detection depth. ( Figure 1 ). Unlike LOTEM, which adopts
continuous waveform excitation and observes the total field response at a large
offset (generally 3–8 times the detection depth), SOTEM observes the pure
quadratic field response in a small offset range. This working method
improves the signaltonoise ratio of the observed signal on the one hand, and
reduces the influence of the volume effect on the other hand, thereby greatly
reducing the difficulty of data processing and improving the accuracy of the
processing results. In practical work, the time derivative (induced
voltage) of the vertical magnetic field component and the horizontal electric
field component are generally observed.

Fig.1 Schematic
diagram of SOTEM device 
2 Calculation and Analysis of Several Depth Concepts
2.1 Diffusion depth
The
most commonly used depth concept in the transient electromagnetic method is the
diffusion depth, which means the depth at which the maximum value of the
transient eddy current field is located at a given moment ^{[2]]} ,
and the expression is
where: d represents
the diffusion depth, t represents the time, σ represents
the electrical conductivity of the earth, and μ _{0} represents
the magnetic permeability of the air. Equation (1) is usually used to
estimate the detection depth of the transient electromagnetic method.
It
can be seen that the detection depth obtained from the diffusion depth is only
related to time and ground conductivity, but has nothing to do with parameters
such as device type, observation component, and offset distance. This is
inconsistent with the actual situation. First, the electromagnetic fields
excited by different device types have different diffusion and propagation
modes in the underground, and the diffusion direction and speed of the induced
current are quite different. Second, different electromagnetic fields at
different locations The detection ability of various geoelectric models is also
different . Therefore, it is very rough to use the diffusion depth to
estimate the detection depth of the transient electromagnetic method,
especially the SOTEM method observed at different offsets.
2.2 Limit detection depth
On
the basis of the diffusion depth, literature [4] gave the estimation formula of
the limit (maximum) detection depth of the transient electromagnetic method
considering factors such as signal strength, receiver sensitivity, and
construction parameters under different device types. For electrical source
devices, according to the formula
Calculate
the limit detection depth, where: η is the minimum resolvable
voltage of the instrument, ρ is the formation
resistivity, I is the transmission current, and L _{AB} is
the length of the transmission line. Here, no quantitative division is
made between the far zone and the near zone. According to Equation (2) and
Equation (3), the limit detection depth of electric source transient
electromagnetic under different parameters is calculated ( Table 1 ).
Through comparison, it is found that the limit detection depth in the near area
is greater than that in the far area in most cases. .

Table 1 Limit
detection depth of far zone and near zone of electrical source TEM 
2.3 Effective detection depth
The
limit detection depth is evaluated based on the maximum detection depth in
different situations, and a variety of actual working parameters are
considered, which is of great reference significance for the construction
design of field work. However, it is still impossible to accurately judge the
maximum detection depth within the offset range. To this end, the concept
of effective detection depth is defined. Like other geophysical
prospecting methods, the effective detection depth means that the anomalous field
generated by detecting the target layer within this depth range exceeds the
background field level by several times, and the existence of the target layer
can be distinguished from the observation results ^{[ 3 ]} .
Taking
the Htype formation as an example, the effective detection depth of the
electrical source transient electromagnetic method is analyzed. Let the
response value (background field) of a uniform halfspace (resistivity 100 Ω m)
be V _{0} , which contains a thin layer of good
conductivity (resistivity 10 Ω m, thickness 100 m, buried depth constantly
changing) The response value (abnormal field) caused by Htype formation
is V _{a} , and let δ = ��. Constantly
change the burial depth of the wellconducting thin layer, and calculate the
corresponding δ under different offsets . When V _{a} ≥
50 % , it is considered that the existence of a thin
conductive layer can be distinguished under this condition.
Table
2 lists the buried depth of highconductivity thin layers when δ _{max
=50%, that is, the effective detection depth }d . It
can be seen that the maximum effective detection depth is obtained within the
offset range of 700–1000 m, that is, when r/H =0.7–1, the
effective detection depth is the largest.

Table 2 Calculation
results of effective detection depth 
2.4 Apparent detection depth
Based
on the abovementioned several depth concepts, the maximum detection depth and
the corresponding observation offset of the electrical source transient
electromagnetic method can be evaluated. In practical applications, a
concept of depth is also needed to determine the depth corresponding to the formation
resistivity obtained at a certain moment, which is called the apparent
detection depth. The depth needs to consider the actual working parameters
to ensure applicability and accuracy in different situations. Based on the
onedimensional inversion method of equivalent source, the reference [10] gives
the estimation formula of apparent detection depth for electrical source
transient electromagnetic data:
In
the formula: ρ represents the formation resistivity, and
L represents the length of the emission source. This formula can
be used to calculate the actual detection depth corresponding to a given
moment.
Still
take the Htype formation as an example. The model parameters are ρ _{1} =100
Ω m, h _{1} =800 m, ρ _{2} =10
Ω m, h _{2} =200 m, ρ _{3} =100
Ω m. Onedimensional forward modeling is performed on the model to
calculate its vertical magnetic field component, then the fullperiod apparent
resistivity is calculated using the dichotomy method, and finally the
corresponding detection depth is calculated according to formula (4). The
results are shown in Fig. . It can be seen that: firstly, the
apparent resistivities calculated at different offsets in the whole area have
good consistency; secondly, the apparent depth calculated by formula (4) is
roughly the same as the depth position of the real model lowresistivity
layer. The results show that the calculation method of apparent detection
depth given by formula (4) has good accuracy and can be used for estimation of
detection depth and rapid processing and calculation of measured data.

Fig.2 ρ _{s} curves of
the Htype model at different offsets 
3 Application examples
In
order to investigate the waterrichness of the Austrian ash basement in a
coalfield in Shanxi, SOTEM detection was carried out. Table 3 shows
the stratum distribution and lithology and electrical characteristics in the
area summarized according to the geology and drilling data of the work area.

Table 3 Stratum
distribution and electrical properties in the survey area 
According
to Table 3 , it can be deduced that the maximum buried depth of the
Ordovician roof is about 921 m, and the lowest average resistivity of strata
within this depth range ^{[ 1 ]} is about 62 Ω·m. Before
data collection, it is necessary to determine the appropriate working
parameters to ensure that the detection depth can meet the detection
requirements. Assuming that the maximum target depth is 1 300 m (needs to
be greater than the buried depth of the target layer within a certain range),
the length of the emission source is 1 000 m, and the emission current is 10 A,
then according to formula (4), the latest observation time required is about
Therefore, in actual work, the emission current with a fundamental frequency of
2.5 Hz (with a delay of 100 ms at the latest) can meet the detection
requirements.
Onedimensional
inversion processing is performed on the measured data, and the maximum
inversion depth is 1100 m. The results are shown in Fig.
3. According to the map and the geological data of the survey area, it is
inferred that the shallow layers in the survey area are relatively
highresistivity Quaternary and Tertiary strata, the middle lowresistivity
layer is the relatively waterrich Permian strata, and the lower part is
relatively highresistivity Carboniferous strata. strata and Ordovician
limestone basement. It should be noted that the resistivity in the deep
part of the 0100 m measuring point range (the red line frame area in the
figure) is lower than that in other areas, and it is speculated that the
Ordovician limestone in the range may be rich in water. Subsequent
implementation of ZK373 validated this interpretation. Through this
detection test, the feasibility and accuracy of using the concept of apparent
depth to select construction parameters in the preliminary work design are
proved.

Figure 3 Measured
SOTEM onedimensional inversion section 
4 Conclusion
The
most commonly used concept of diffusion depth, its physical meaning represents
the diffusion of the underground eddy current field, has nothing to do with the
device type, construction parameters and other factors, but is only related to
underground electricity and time. Using this depth to estimate the detection
depth has a great influence. error. Considering the sensitivity of the
instrument and the limit detection depth defined by the specific construction
parameters, the estimation of the maximum detection depth of the electrical
source transient electromagnetic method in different field conditions can be
realized.
Through
calculation, it is found that the limit detection depth in the near area is
greater than that in the far area in most cases, which indicates that when
other parameters are the same, the observation in the near area can obtain a
greater detection depth. Then, based on the difference relationship
between the response of the target layer and the uniform halfspace response,
the concept of effective detection depth is defined, and the calculation
results using the Htype formation show that, for the electrical source
transient electromagnetic method, when the receiving offset is approximately
equal to The maximum detection depth can be obtained when the depth of the
target layer is 0.7~1 times.
Using
the abovementioned several depth concepts, only the depth detection capability
of SOTEM can be evaluated, but the real detection depth at a given moment
cannot be judged. The apparent detection depth derived based on the image
source theory overcomes the above shortcomings, and the actual detection depth
at a given moment can be estimated according to the fullperiod apparent
resistivity. The onedimensional forward modeling calculation and the detection
example of a coalfield verify the applicability of the apparent detection
depth. and accuracy.


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