Next, the ITD–MFFA method was applied to analyze the spring EC time series (2013–2020) for all four spring groups.
Figure 6 shows the multifractal characteristic results. From
Figure 6(a),
h(
q) decreases with the increasing
q; all four spring groups' spring EC time series exhibit multiscale and multifractal characteristics. The
h(2) value reflects the long-term correlation strength. All corresponding
h(2) values of the spring groups are <0.5, indicating that each spring group's EC time series displays a negative long-term correlation, i.e., antipersistence. The
h(2) values decrease in the order of Heihu spring > Tanxi spring > Wangfuchizi spring > Baotu spring; in addition, the antipersistence is the highest for Baotu spring's EC.
Figure 6(b) and Table 3 show the multifractal spectrum of the EC time series and the singular spectrum width Δ
α for each spring group. The variation range is 1.56–1.81, indicating that each spring group's multifractal degree varies. The Wangfuchizi spring's Δ
α value is the largest, indicating that the corresponding EC time series attain the highest multifractality degree, whereas Tanxi, Baotu, and Heihu springs' values considerably fluctuate.
Table 3Long-term correlation exponent h(2) and complexity Δα of the EC time series of each spring group
Spring
. | Long-term correlation exponent h(2)
. | Complexity Δα
. |
---|
Baotu spring | 0.316 | 1.606 |
Heihu spring | 0.331 | 1.559 |
Tanxi spring | 0.374 | 1.722 |
Wangfuchizi | 0.3839 | 1.814 |
Spring
. | Long-term correlation exponent h(2)
. | Complexity Δα
. |
---|
Baotu spring | 0.316 | 1.606 |
Heihu spring | 0.331 | 1.559 |
Tanxi spring | 0.374 | 1.722 |
Wangfuchizi | 0.3839 | 1.814 |
Figure 6
Relationship curve between h(q) and q and the multifractal spectrum for each spring group.
Figure 6
Relationship curve between h(q) and q and the multifractal spectrum for each spring group.
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