Study of cavernous underground conduits in Nam La (Northwest Vietnam) by an integrative approach

Abstract

This paper presents the result of an investigation of underground conduits, which connect the swallow holes and the resurgence of a blind river in the tropical, highly karstified limestone Nam La catchment in the NW of Vietnam. The Nam La River disappears underground in several swallow holes near the outlet of the catchment. In the rainy season this results in flooding upstream of the sinkholes. A hypothesis is that the Nam La River resurges at a large cavern spring 4.5 km east of the catchment outlet. A multi-thematic study of the possible connections between the swallow holes and the resurgence was carried out to investigate the geological structure, tectonics, cave structure analysis and discharge time series. The existence of the underground conduits was also tested and proven by tracer experiments. On the basis of a lineament analysis the location of the underground conduits were predicted. A remote sensing derived lineament-length density map was used to track routes from the swallow holes to the resurgence, having the shortest length but highest lineament density. This resulted in a plan-view prediction of underground conduits that matches with the cave and fault development. The functioning of the conduits was further explained by analysing flooding records of a nearby doline, which turns out to act as a temporary storage reservoir mitigating flooding of the catchment outlet area.

Résumé

Cet article présente les résultats de l’investigation de conduits souterrains, qui mettent en connexion les pertes et les résurgences d’une rivière souterraine dans le bassin versant de Nam La, dans une région tropicale fortement karstique du NW du Vietnam. La rivière Nam La disparaît dans le sous-sol via plusieurs pertes à proximité de l’exutoire du bassin. Durant la saison des pluies, les pertes se mettent en charge et des inondations apparaissent. Une hypothèse serait que la rivière ressort 4.5 km à l’Est de l’exutoire du bassin, dans une grande caverne. Une étude multi-thématique visant les connexions possibles entre les pertes et les résurgences a été réalisée. Elle comprend l’étude de la structure géologique, la tectonique, l’analyse de la structure karstique et des chroniques de débits. L’existence des conduits souterrains est également testée et prouvée par des essais de traçages. Sur base de l’analyse des linéaments, la localisation des conduits souterrains est prédite. Grâce à la télédétection et une cartographie de la densité et de la longueur des linéaments, on peut deviner le cheminement de l’eau entre les pertes et la résurgence (via le chemin le plus court et la densité de fracturation la plus importante). Il en résulte une vue en plan prédisant la localisation des conduits, qui correspond par ailleurs avec le développement des cavités et des failles. Le fonctionnement des conduits est ensuite expliqué sur base de l’analyse des chroniques de débits enregistrés à proximité d’une doline, qui joue le rôle d’un réservoir temporaire, mitigeant les inondations à la zone de l’exutoire du bassin-versant.

Resumen

Este artículo presenta el resultado de una investigación de conductos subterráneos, los cuales conectan dolinas y la resurgencia de un río ciego en la cuenca tropical Nam La, compuesta por calizas altamente karstificadas, en el noroeste de Vietnam. El Río Nam La desaparece en el subsuelo por medio de varias dolinas cerca de la salida de la cuenca. Durante la estación lluviosa esto resulta en inundaciones aguas arriba de las dolinas. Una hipótesis es que el Río Nam La resurge en un manantial de caverna grande a 4.5 km al oriente de la salida de la cuenca. Se llevó a cabo un estudio multi-temático de las conexiones posibles entre las dolinas y la resurgencia para investigar la estructura geológica, tectónica, análisis estructural de cavernas, y series de tiempo de descarga. Se evalúa y se demuestra también la existencia de conductos subterráneos por medio de experimentos con trazadores. En base a análisis de lineamientos se predice la localización de los conductos subterráneos. Se utiliza un mapa de densidad de longitudes de lineamientos construido a partir de sensores remotos para seguir las rutas de las dolinas a la resurgencia, teniendo longitudes más cortas pero densidad de lineamientos más altas. Esto da por resultado una predicción en vista de planta de conductos subterráneos que se ajustan con el desarrollo de cavernas y fallas. El funcionamiento de los conductos se explica posteriormente mediante el análisis de registro de inundaciones de una dolina cercana la cual actúa como un reservorio de almacenamiento temporal que mitiga inundaciones en el área de salida de la cuenca.

Appendices

Appendix

The time series cross analysis used in this study utilizes the cross-correlation function and cross-amplitude function. An overview of these functions is presented here to facilitate the comprehension of the study results. More detailed explanations and complete theoretical backgrounds can be found in Jenkin and Watts (1968), Yevjevich (1972), Oppenhiem and Schafer (1975), Box and Jenkins (1976), and others.

Cross-correlation function (CCF)

Let there be two discretised chronological series: the input, x _i (x ₁ , x ₂ , .., x _n ), is the cause of the output, y _i (y ₁ , y ₂ , ..., y _n ), where n is the total number of data pairs. The autocorrelation function (ACF), r _x (k), quantifies the linear dependency of successive values of the time series x _i and is defined as

$$r_x \left( k \right) = \frac{{C_x \left( k \right)}} {{C_x \left( 0 \right)}}$$

(4)

where k is the time lag (k=0 to m), with m the cutting point, which determines the length of the analysis; C _x (k) is the autocovariance function given by

$$C_x \left( k \right) = \frac{1} {n}\sum\limits_{i = 1}^{n - k} {\left( {x_i - \bar x} \right)} \left( {x_{i + k} - \bar x} \right)$$

(5)

with $\bar x$ the mean of the series.

The correlogram C(k) outlines the memory of the system. If an event has a long-term influence on the time series, the autocorrelation function decreases slowly with increasing time lag.

The cross-correlation function (CCF) represents the impulse response of the system under investigation when the input series is considered to be a white noise, and is described by following expressions

$$r_{ + k} = r_{xy} \left( k \right) = \frac{{C_{xy} \left( k \right)}} {{\sigma _x \sigma _y }}$$

(6)

$$r_{ - k} = r_{yx} \left( k \right) = \frac{{C_{yx} \left( k \right)}} {{\sigma _x \sigma _y }}$$

(7)

where C _xy and C _yx are cross-covariance functions, and σ _x and σ _y standard deviation of the series, given by

$$C_{xy} \left( k \right) = \frac{1} {n}\sum\limits_{t = 1}^{n - k} {\left( {x_t - \bar x} \right)} \left( {y_{t + k} - \bar y} \right)$$

(8)

$$C_{yx} \left( k \right) = \frac{1} {n}\sum\limits_{t = 1}^{n - k} {\left( {y_t - \bar y} \right)} \left( {x_{t + k} - \bar x} \right)$$

(9)

$$\sigma _x = \sqrt {\frac{1} {n}\sum\limits_{t = 1}^n {\left( {x_t - \bar x} \right)} ^2 }$$

(10)

$$\sigma _y = \sqrt {\frac{1} {n}\sum\limits_{t = 1}^n {\left( {y_t - \bar y} \right)} ^2 }$$

(11)

and $\bar y$ is the mean of the series y _i .

Note that the cross-correlation function is not symmetrical, r _xy (k)≠r _yx (k). If r _xy (k)>0 for k>0, the input series x _i influences the output series y _i , while if r _xy (k)>0 for k<0, the output influences the input. The delay time, defined as the time lag between k=0 and the maximum of r _xy (k), gives an estimation of the peak impulse response time of the system.

Cross-amplitude function (CAF)

Spectrum analysis is concerned with the exploration of cyclical patterns. The purpose of the analysis is to decompose a complex time series with cyclical components into a few underlying sinusoidal functions of particular wavelength or frequency, f, the number of cycles per unit time. Thus, by identifying the underlying cyclical components, the phenomenon of interest is characterised. Changing from a time mode to a frequency mode is performed by way of a Fast Fourier Transform (FFT).

The spectral density function, S _x (f), of the time series x _i , corresponding to the discrete-time Fourier transform of the autocorrelation function, is defined as

$$S_x \left( f \right) = \frac{1} {2}\left[ {1 + \sum\limits_{k = 1}^m {D\left( k \right)r_x \left( k \right)\cos \left( {2\pi fk} \right)} } \right]$$

(12)

where D(k) is a filter necessary to overcome the problem of “chaotic” spikes occasionally occurring in the time series. The most frequently used filter in the analysis of the hydrological series is the Turkey filter, which is expressed as

$$D\left( k \right) = \tfrac{1} {2}\left( {1 + \cos \frac{{\pi k}} {m}} \right)$$

(13)

The cross-spectral density function, S _xy (f), gives the frequency mode of the cross-correlation function and is expressed as a complex number

$$S_{xy} \left( f \right) = h_{xy} \left( f \right) - i\lambda _{xy} \left( f \right)$$

(14)

where the real part is the co-spectrum

$$h_{xy} \left( f \right) = 2\left[ {r_{xy} \left( 0 \right) + \sum\limits_1^m {\left( {r_{xy} \left( k \right) + r_{yx} \left( k \right)} \right)D\left( k \right)\text{cos}\left( {2\pi fk} \right)} } \right]$$

(15)

and the imaginary part is the quadrature spectrum

$$\lambda _{xy} \left( f \right) = 2\left[ {r_{xy} \left( 0 \right) + \sum\limits_1^m {\left( {r_{xy} \left( k \right) + r_{yx} \left( k \right)} \right)D\left( k \right)\text{sin}\left( {2\pi fk} \right)} } \right]$$

(16)

The square root of the sum of the squared co-spectrum and quadrature spectrum is called the cross-amplitude function (CAF) and is expressed as

$$\alpha _{xy} \left( f \right) = \sqrt {h_{xy}^2 \left( f \right) + \lambda _{xy}^2 \left( f \right)}$$

(17)

The cross-amplitude can be interpreted as a measure of covariance between the respective frequency components in the two series, and identifies the way in which the input signal has been modified by the system. The CAF can be associated with the duration of the impulse response function and indicates the filtering of the periodic components of the input series Padilla and Pulido-Bosch (1995).