Context : A detailed three-dimensional ( 3D ) distribution of interstellar matter in the solar neighborhood is increasingly necessary .
It would allow a more realistic computation of photons and cosmic rays propagation , which is of prime importance for microwave and gamma-ray background emission interpretation , as well as a better understanding of the chain of phenomena that gave rise to the main local structures .

Aims : As part of a 3D mapping program , we aim at assigning a precise distance to the high-latitude HI gas , in particular the northern part ( b \geq 55 ^ { \circ } ) of the shell associated with the conspicuous radio continuum Loop I .
This shell is thought to be the expanding boundary of an interstellar bubble inflated and recently reheated by the strong stellar winds of the nearby Scorpius-Centaurus OB associations .

Methods : We recorded high-resolution spectra of 30 A-type target stars located at various distances in the direction of the northern part of Loop I. Interstellar neutral sodium and singly ionized calcium absorptions ( NaI 5889-5895 and CaII K-H 3934-3968 Å ) are modeled and compared with the HI emission spectra from the LAB Survey .

Results : About two-thirds of our stellar spectra possess narrow interstellar lines , while the remaining spectra show no absorption at all .
Narrow lines are located at the velocity of the main , low-velocity Loop 1 HI shell ( [ -6 , +1 ] km.s ^ { -1 } in the LSR ) .
Using Hipparcos distances to the target stars , we show that the closest boundary of the b \geq +70 ^ { \circ } part of this low-velocity Loop I arch is located at of 98 \pm 6 pc .
The corresponding interval for the lower-latitude part ( 55 \leq b \leq 70 ^ { \circ } ) is 95-157 pc .
However , since the two structures are apparently connected , the lower limit is more likely .
At variance with this shell , the second HI structure , which is characterized by LSR Doppler velocities centered at -30 km.s ^ { -1 } , is NOT detected in any of the optical spectra .
It is located beyond 200 parsecs or totally depleted in NaI and CaII .

Conclusions : We discuss these results in the light of spherical expanding shells and show that they are difficult to reconcile with simple geometries and a nearby shell center close to the Plane .
Instead , this high-latitude gas seems to extend the inclined local chimney wall to high distances from the Plane .