CN110231359B - Hydraulic characteristic parameter estimation method based on ground magnetic resonance relaxation signals - Google Patents
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Abstract
The invention belongs to the field of hydrological characteristic parameter monitoring, and discloses a hydraulic characteristic parameter estimation method based on a ground magnetic resonance relaxation signal,measuring with surface magnetic resonance instrument to obtain multi-index relaxation signal, and obtaining water content and transverse relaxation time of each underground depth by QT inversion method
Spectral distribution, then transverse relaxation time
The spectrum distribution is accumulated to obtain transverse relaxation time
Accumulated spectrum of
According to water content and transverse relaxation time
Determining the interface of the unsaturated zone and the saturated zone according to the change of the spectral distribution with the depth; according to water content and transverse relaxation time of saturation zone
Obtaining saturated hydraulic conductivity; cumulative spectra based on water content and transverse relaxation time in the unsaturated zone
Obtaining relative hydraulic conductivity, unsaturated hydraulic conductivity and effective saturation. The invention overcomes the problems that the traditional resistivity imaging and geological radar non-invasive geophysical methods can only obtain resistivity, dielectric constant and other geophysical information, the correction is difficult and the uncertainty of the calculation result is high.
Description
Technical Field
The invention belongs to the field of hydrological characteristic parameter monitoring, and particularly relates to a hydraulic characteristic parameter estimation method based on a ground magnetic resonance relaxation signal.
Background
The saturated-unsaturated water motion law is researched, and hydraulic characteristic parameters such as a water characteristic curve and unsaturated hydraulic conductivity are determined firstly. At present, hydraulic characteristic parameters such as unsaturated hydraulic conductivity and the like are generally used in laboratories and obtained by using a filter paper method and a pressure plate instrument method, which wastes time and labor and is difficult to obtain results under any conditions. The ground magnetic resonance is used as a groundwater direct detection method, has the advantage of quantitatively detecting groundwater distribution, and the multi-relaxation characteristic of a signal of the ground magnetic resonance is related to pore size distribution, so that a water characteristic curve and unsaturated hydraulic conductivity can be determined. Therefore, the method for estimating the hydraulic characteristic parameters based on the ground magnetic resonance relaxation signals has important significance.
CN107014975A discloses a device and a method for measuring unsaturated hydraulic characteristics with measurable axial and radial deformation, wherein a hydraulic characteristic measuring system comprises a weighing device and a water potential measuring instrument, the axial deformation of a soil mass sample to be measured is calculated by placing the soil mass sample to be measured in a sample container of the measuring instrument, and the readings of a volume measuring device and a displacement sensor are recorded, and the measurement of a soil water characteristic curve and unsaturated permeability coefficient of the soil mass sample to be measured is realized by combining the readings of the soil mass water potential measuring instrument and the weighing device. However, the method has complex measuring steps and low measuring efficiency.
CN104537714A discloses a method for measuring soil moisture characteristic curve and unsaturated hydraulic conductivity. According to the soil column water consumption condition and the reading change of a plurality of tensiometers, the soil water characteristic and the unsaturated hydraulic conductivity are obtained by using relevant data such as soil profile matric potential and the like in the soil evaporation process and by means of a repeated iteration correction technology. However, the method belongs to a traditional method for measuring unsaturated hydraulic conductivity in a laboratory, time is consumed, and the weight of a tensiometer and the weight of a soil column need to be measured 1-2 times per day.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for estimating hydraulic characteristic parameters based on ground magnetic resonance relaxation signals, which aims to nondestructively and rapidly obtain hydrological characteristic parameters such as saturation, hydraulic conductivity and the like based on a ground magnetic resonance method and provide monitoring data for processes such as underground water partial motion and the like.
The present invention is achieved in such a way that,
a method for estimating hydraulic characteristic parameters based on ground magnetic resonance relaxation signals comprises the following steps:
step 1, obtaining a multi-index relaxation signal e (t) by using a ground magnetic resonance instrument, wherein the expression is as follows:
wherein e0Is an initial amplitude, proportional to the water content,
transverse relaxation time, I, for nth pore sizenIs a relaxation time of
T is time;
step 2, obtaining the water content and transverse relaxation time of each underground depth by utilizing a QT inversion method
Spectral distribution, then transverse relaxation time
The spectrum distribution is accumulated to obtain transverse relaxation time
Accumulated spectrum of
Step 3, obtaining the water content and transverse relaxation time according to the step 2
Determining the interface of the unsaturated zone and the saturated zone according to the change of the spectral distribution with the depth;
step 4, according to the water content and transverse relaxation time of the saturated zone
Obtaining a saturated hydraulic conductivity and a cumulative spectrum based on the water content and transverse relaxation time of the unsaturated zone
Obtaining relative hydraulic conductivity, and further obtaining unsaturated hydraulic conductivity and effective saturation.
Further, the saturation band, effective saturation SE1, saturated hydraulic conductivity of
Where upsilon is density, g is gravitational acceleration, τ is curvature defined by arc-to-chord ratio, η is dynamic viscosity, θSIs the saturated water content, D is the self-diffusion constant, p is the surface relaxation, TBIs the bulk water relaxation time.
Further, the air conditioner is provided with a fan,
relative hydraulic conductivity and effective saturation are obtained according to the unsaturated zone, and the relative hydraulic conductivity and the effective saturation comprise:
selecting a VG water characteristic curve model;
based on ground magnetic resonance signals
Cumulative spectrum
Weighted difference establishment of VG and moisture characteristic curve modelAn objective function is fitted to obtain a parameter theta by utilizing a Levenberg-Marquardt optimization algorithmS，θRα, λ and m, where θ is the pore media water content and θ is the pore media water contentRIs the residual moisture content, α is the scaling parameter, h is the pressure head, λ is the pore distribution index, and m is 1-1/λ.
From a parameter thetaS，θRα, and the values of λ and m, calculating the effective saturation of the unsaturated zone S according to equation (5)E，
According to the VG moisture characteristic curve model, the relative hydraulic conductivity is as follows:
wherein KUIs unsaturated hydraulic conductivity, KSAnd calculating to obtain the hydraulic conductivity of the unsaturated zone for the saturated hydraulic conductivity.
Further, VG moisture characteristic curve model:
where θ (h) is pore medium water content, θRIs the residual moisture content, α is the scaling parameter, h is the pressure head, λ is the pore distribution index, and m is 1-1/λ.
Further, the air conditioner is provided with a fan,
the water characteristic curve is equivalent to the cumulative pore size distribution, and the water characteristic curve of the formula (2) and the water characteristic curve obtained in the step 2 are obtained
The accumulated spectrum has the consistent shape and form,
proportional relationship to h:
wherein C is a proportionality coefficient.
Further, a moisture characteristic measurement point is used to calibrate the ground magnetic resonance signal
The proportional relation between the pressure water head h and the pressure water head h is as follows:
using pressure plate means at a fixed value h of pressure head1Time-measuring effective saturation SE1According to the formula (2), the water content theta of the pore medium is calculated1
θ1＝(θS-θR)SE1+θR(4)
The ground magnetic resonance signal obtained in step 2
Cumulative spectrumFinding out the water content theta of the pore medium1Corresponding ground magnetic resonance signal
H is to be1And
substituting the formula (3) to obtain a proportionality coefficient C;
for all in step 2
The value of the pressure head is obtained by multiplying the proportional coefficient C and substituted into the equation (2) to obtain a moisture characteristic curve theta (h).
Compared with the prior art, the invention has the beneficial effects that:
the method can non-invasively and quickly obtain the hydrological characteristic parameters such as saturation, hydraulic conductivity and the like, the traditional non-invasive geophysical methods such as resistivity imaging, geological radar and the like can only obtain the geophysical information such as resistivity, dielectric constant and the like, and the problems that an empirical formula is difficult to correct, the uncertainty of a calculation result is high and the like are faced in the process of converting the resistivity imaging, the geological radar and the like into the hydraulic characteristic parameters available for the model. By adopting the ground magnetic resonance method, the water content and the relaxation time of the underground water can be accurately obtained, the saturation and the hydraulic conductivity can be further obtained, monitoring data are provided for the processes of underground water partial motion and the like, and the method has important significance for realizing reasonable development of the underground water and water resource protection.
Drawings
FIG. 1 is a flow chart of a hydraulic characteristic parameter estimation method;
FIG. 2 shows the ground magnetic resonance signals
A spectrum, and
accumulating the spectrums;
FIG. 3 is a Van Genuchten (VG) moisture profile.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1, the method for estimating the hydraulic characteristic parameters based on the ground magnetic resonance relaxation signals comprises
Step 1, obtaining a multi-index relaxation signal e (t) by using a ground magnetic resonance instrument, wherein the expression is as follows:
wherein e0Is an initial amplitude, proportional to the water content,
transverse relaxation time, I, for nth pore sizenIs a relaxation time of
T is time;
step 2, obtaining the water content and transverse relaxation time of each underground depth by utilizing a QT inversion method
Spectral distribution, then transverse relaxation time
The spectrum distribution is accumulated to obtain transverse relaxation time
Accumulated spectrum of
Step 3, obtaining the water content and transverse relaxation time according to the step 2
Determining the interface of the unsaturated zone and the saturated zone according to the change of the spectral distribution with the depth;
step 4, according to the water content and transverse relaxation time of the saturated zone
Obtaining a saturated hydraulic conductivity and a cumulative spectrum based on the water content and transverse relaxation time of the unsaturated zone
Obtaining relative hydraulic conductivity, and further obtaining unsaturated hydraulic conductivity and effective saturation.
Wherein, in one embodiment, step 2: method for obtaining water content and transverse relaxation time of underground depth by QT inversion method
Spectral distribution, shown by the solid black line in FIG. 2, versus transverse relaxation time
The spectrum distribution is accumulated to obtain transverse relaxation time
Accumulated spectrum of
See the grey dotted line in fig. 2, which is equivalent to the cumulative pore size distribution.
For the saturation band, the effective saturation SE1, saturated hydraulic conductivity of
Where upsilon is density, g is gravitational acceleration, τ is curvature defined by arc-to-chord ratio, η is dynamic viscosity, θSIs the saturated water content, D is the self-diffusion constant, p is the surface relaxation, TBIs the bulk water relaxation time.
For the unsaturated band, it includes:
fitting unknown parameters of the VG moisture characteristic curve model;
calibrating transverse relaxation time T of ground magnetic resonance signal2 *Accumulating the proportional relation between the spectrum and the pressure head;
relative hydraulic conductivity and effective saturation are obtained.
Wherein: a model of Van Genuchten (VG) moisture characteristic curve (see black solid line in FIG. 3) shown in formula (2) was selected:
where θ is the pore media water content, θRIs residual moisture content, α is a zoomThe parameter, h is the pressure head, λ is the pore distribution index, and m is 1-1/λ.
The capillary potential theory shows that the water characteristic curve is equivalent to the cumulative pore size distribution. Therefore, the moisture characteristic curve of the formula (2) and the moisture characteristic curve obtained in the step 2 can be obtained
The accumulated spectra were consistent in morphology. Furthermore, it is possible to provide a liquid crystal display device,
the following proportional relationship exists with h:
wherein C is a proportionality coefficient.
Based on ground magnetic resonance signals
Building a target function by accumulating the weighted difference of the spectrum and the VG water characteristic curve model, and fitting by using a Levenberg-Marquardt optimization algorithm to obtain an unknown parameter thetaS，θRα, values of λ and m in one embodiment, the calculation yields θS＝0.31cm3/cm3，θR＝0.55cm3/cm3，α＝0.13，λ＝3.2，m＝0.69。
Calibrating ground magnetic resonance signals using a moisture characteristic measurement point
The specific implementation method of the proportional relation between the pressure head h and the pressure head is as follows:
using pressure plate means at a fixed value h of pressure head1Time-measuring effective saturation SE1In this embodiment, h is selected1-63 cm. According to the formula (2), the water content theta of the pore medium can be calculated1
θ1＝(θS-θR)SE1+θR(4)
The ground magnetic resonance signal obtained in step 2
Finding out the water content theta of the pore medium in the accumulated spectrum1Corresponding to
H is to be1And
the formula (3) was substituted to obtain the proportionality coefficient C, which was 8.2 in this example. For all in step 2
And multiplying the value by a proportionality coefficient C to obtain a value of the pressure water head, and substituting the value into the formula (2) to obtain a moisture characteristic curve theta (h), wherein the value is shown by a dotted line in figure 3.
Calculating the effective saturation S of the unsaturated zone by using the formula (5) according to the calculated parametersE，
According to the Van Genuchten (VG) moisture characteristic curve model, the relative hydraulic conductivity is as follows:
wherein KUIs unsaturated hydraulic conductivity, KSSaturated hydraulic conductivity. Therefore, the hydraulic conductivity of the unsaturated zone can be calculated.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (5)
1. A method for estimating hydraulic characteristic parameters based on ground magnetic resonance relaxation signals is characterized by comprising the following steps:
step 1, obtaining a multi-index relaxation signal e (t) by using a ground magnetic resonance instrument, wherein the expression is as follows:
wherein e0Is an initial amplitude, proportional to the water content,
transverse relaxation time, I, for nth pore sizenIs a relaxation time of
T is time;
step 2, obtaining the water content and transverse relaxation time of each underground depth by utilizing a QT inversion method
Spectral distribution, then transverse relaxation time
The spectrum distribution is accumulated to obtain transverse relaxation time
Accumulated spectrum of
Step 3, obtaining the water content and transverse relaxation time according to the step 2
Determining the interface of the unsaturated zone and the saturated zone according to the change of the spectral distribution with the depth;
step 4, according to the water content of the saturated zoneAnd transverse relaxation time
Obtaining saturated hydraulic conductivity and accumulated spectrum according to water content of unsaturated zone and transverse relaxation time
Obtaining relative hydraulic conductivity, and further obtaining unsaturated hydraulic conductivity and effective saturation; wherein the accumulated spectrum is based on the water content of the unsaturated zone and the transverse relaxation time
Obtaining relative hydraulic conductivity, further obtaining unsaturated hydraulic conductivity and effective saturation, comprising:
selecting a VG water characteristic curve model;
based on ground magnetic resonance signals
Cumulative spectrum
And establishing a target function by weighting the difference value with a VG water characteristic curve model, and fitting by using a Levenberg-Marquardt optimization algorithm to obtain a parameter thetaS，θRα, λ and m, where θ is the pore media water content and θ is the pore media water contentSIs the saturated water content, thetaRIs the residual moisture content, α is a scaling parameter, h is the pressure head, λ is the pore distribution index, m is 1-1/λ;
from a parameter thetaS，θRα, and the values of λ and m, calculating the effective saturation of the unsaturated zone S according to equation (5)E，
According to the VG moisture characteristic curve model, the relative hydraulic conductivity is as follows:
wherein KUIs unsaturated hydraulic conductivity, KSAnd calculating to obtain the hydraulic conductivity of the unsaturated zone for the saturated hydraulic conductivity.
2. Method according to claim 1, characterized in that said saturation band, effective saturation SE1, saturated hydraulic conductivity of
Where upsilon is density, g is gravitational acceleration, τ is curvature defined by arc-to-chord ratio, η is dynamic viscosity, θSIs the saturated water content, D is the self-diffusion constant, p is the surface relaxation, TBIs the bulk water relaxation time.
3. Method according to claim 1, characterized in that VG moisture characteristic curve model:
where θ (h) is pore medium water content, θRIs the residual moisture content, α is the scaling parameter, h is the pressure head, λ is the pore distribution index, and m is 1-1/λ.
4. The method of claim 3,
the water characteristic curve is equivalent to the cumulative pore size distribution, and the water characteristic curve of the formula (2) and the water characteristic curve obtained in the step 2 are obtained
The accumulated spectrum has the consistent shape and form,
proportional relationship to h:
wherein C is a proportionality coefficient.
5. Method according to claim 4, characterized in that the surface magnetic resonance signal is calibrated with a moisture characteristic measurement point
The proportional relation between the pressure water head h and the pressure water head h is as follows:
using pressure plate means at a fixed value h of pressure head1Time-measuring effective saturation SE1According to the formula (2), the water content theta of the pore medium is calculated1
θ1＝(θS-θR)SE1+θR(4)
The ground magnetic resonance signal obtained in step 2
Cumulative spectrum
Finding out the water content theta of the pore medium1Corresponding ground magnetic resonance signal
H is to be1And
substituting the formula (3) to obtain a proportionality coefficient C;
for all in step 2
Multiplying ratioThe example coefficient C is a value of the pressure head, and is substituted into the equation (2) to obtain a moisture characteristic curve θ (h).
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