Multi-sensor DInSAR applied to the spatiotemporal evolution analysis of ground surface deformation in Cerro Prieto basin, Baja California, Mexico, for the 1993–2014 period

Abstract

The combined effects of active tectonics and anthropogenic activities, primarily geothermal resources exploitation for electricity production in Cerro Prieto geothermal field, influence the ground surface deformation in Cerro Prieto basin, Baja California, Mexico. In this study, a large set of multi-sensor C-band SAR images have been employed to reconstruct the spatiotemporal evolution of aseismic ground surface deformation that has affected Cerro Prieto basin from 1993 to 2014. Conventional DInSAR together with the interferograms stacking procedure was applied. The results showed that the study area presented considerable surface deformation (mainly subsidence) during the entire time of the investigation. The main changes in rate and pattern of surface deformation have a good correlation in time and space with the changes in production in the Cerro Prieto geothermal field. Comparison of LOS displacement maps from different viewing geometries, and decomposition (where possible) of LOS displacement into vertical and horizontal (east–west) components, revealed considerable horizontal displacement which mostly reflects the ground movement at and beyond the margin of the subsidence basin toward the areas of highest subsidence rates. In addition, the validation of the DInSAR results by comparing them against measurements from leveling surveys was performed, confirming the high reliably of satellite interferometry for the ground surface deformation rate mapping in the study area.

Appendix 1: Decomposition of los deformation

The DInSAR techniques (conventional and advanced approaches) measure ground deformation along the satellite LOS direction (slant range). For 3D displacement vector with components in up ($D_{\text{U}}$), east ($D_{\text{E}}$), and north ($D_{\text{N}}$) directions, the projected LOS deformation ($D_{\text{LOS}} )$ is given by:

$$D_{LOS} = D_{U} \cos \theta - D_{E} \sin \theta \cos \alpha + D_{N} \sin \theta \sin \alpha ,$$

(5)

where $\theta$ is the SAR incidence angle and $\alpha$ is the azimuth of the satellite heading angle (positive clockwise from the north). $D_{\text{LOS}}$ is defined here as positive for displacement toward the satellite. According to equation (A1.1), the sensitivity of a SAR sensor to displacement vector components can be expressed by the partial derivatives as follows:

$$\frac{{\partial D_{\text{LOS}} }}{{\partial D_{\text{U}} }} = \cos \theta ; \frac{{\partial D_{\text{LOS}} }}{{\partial D_{\text{E}} }} = - \sin \theta \cos \alpha ; \frac{{\partial D_{\text{LOS}} }}{{\partial D_{\text{N}} }} = \sin \theta \sin \alpha$$

(6)

The displacement direction and field cannot be recovered by DInSAR, unless at least three independent datasets, or the necessary assumptions based on previous knowledge about the ground deformation components, are available (Wright et al. 2004b).

Considering near-polar orbits and the incidence angle of past and current SAR satellites, DInSAR observations are mostly sensitive to the vertical displacement component while their sensitivity to the north component is minimal.

Purely vertical ground deformation is often assumed for subsidence monitoring using DInSAR techniques (e.g., Luo et al. 2014). Neglecting the horizontal displacement components ($D_{\text{E}}$ and $D_{\text{N}}$), the vertical component ($D_{\text{U}}$) can then be retrieved from $D_{\text{LOS}}$ using the sensor incidence angle ($\theta )$:

$$D_{\text{U}} = D_{\text{LOS}} /\cos \theta$$

(7)

However, ignoring the effect of potential horizontal components can introduce large errors in the final deformation estimates (Samieie-Esfahany et al. 2009). In cases in which DInSAR measurements from two different imaging geometries (i.e., ascending and descending orbits) are available, two of the three components can be retrieved by neglecting the third (usually north–south) component and solving the following linear system of equations:

$$\left\{ {\begin{array}{*{20}c} {D_{{{\text{LOS}}_{A} }} = D_{\text{U}} \cos \theta_{\text{A}} - D_{\text{E}} \sin \theta_{\text{A}} \cos \alpha_{\text{A}} } \\ {D_{{{\text{LOS}}_{D} }} = D_{\text{U}} \cos \theta_{\text{D}} - D_{\text{E}} \sin \theta_{\text{D}} \cos \alpha_{\text{D}} } \\ \end{array} } \right.$$

(8)

where A and D refer to the ascending and descending orbit, respectively.