Multistep inversion workflow for 3D long‐offset damped elastic waves in the Fourier domain

We present a new workflow for imaging damped three‐dimensional elastic wavefields in the Fourier domain. The workflow employs a multiscale imaging approach, in which offset lengths are laddered, where frequency content and damping of the data are changed cyclically. Thus, the inversion process is launched using short‐offset and low‐frequency data to recover the long spatial wavelength of the image at a shallow depth. Increasing frequency and offset length leads to the recovery of the fine‐scale features of the model at greater depths. For the fixed offset, we employ (in the imaging process) a few discrete frequencies with a set of Laplace damping parameters. The forward problem is solved with a finite‐difference frequency‐domain method based on a massively parallel iterative solver. The inversion code is based upon the solution of a least squares optimisation problem and is solved using a nonlinear gradient method. It is fully parallelised for distributed memory computational platforms. Our full‐waveform inversion workflow is applied to the 3D Marmousi‐2 and SEG/EAGE Salt models with long‐offset data. The maximum inverted frequencies are 6 Hz for the Marmousi model and 2 Hz for the SEG/EAGE Salt model. The detailed structures are imaged successfully up to the depth approximately equal to one‐third of the maximum offset length at a resolution consistent with the inverted frequencies.     

Ray tracing and geodesic deviation of the SH and SV reference rays in a heterogeneous generally anisotropic medium which is approximately uniaxial

The coupling ray theory is usually applied to anisotropic common reference rays, but it is more accurate if it is applied to reference rays which are closer to the actual wave paths. If we know that a medium is close to uniaxial (transversely isotropic), it may be advantageous to trace reference rays which resemble the SH–wave and SV–wave rays. This paper is devoted to defining and tracing these SH and SV reference rays of elastic S waves in a heterogeneous generally anisotropic medium which is approximately uniaxial (approximately transversely isotropic), and to the corresponding equations of geodesic deviation (dynamic ray tracing). All presented equations are simultaneously applicable to ordinary and extraordinary reference rays of electromagnetic waves in a generally bianisotropic medium which is approximately uniaxially anisotropic. The improvement of the coupling–ray–theory seismograms calculated along the proposed SH and SV reference rays, compared to the coupling–ray–theory seismograms calculated along the anisotropic common reference rays, has already been numerically demonstrated by the authors in four approximately uniaxial velocity models.     

Effects of social and climatic factors on building activity in the Czech lands between 1450 and 1950: a dendrochronological analysis

The development of settlement and building activity is the result of socioeconomic, political and demographic changes in the past. However, accurate information on temporal variation in building activity is rather limited. Dendrochronological databases containing dated historical wooden constructions provide an important resource. We used 6514 tree-felling dates to reconstruct building activity in the Czech lands for the period 1450–1950. Comparing felling dates with historical events demonstrated that building activity was negatively associated with intense wars, particularly during the Thirty Years' War (1618–1648). After the Peace of Westphalia (1648), socioeconomic renewal and demographic growth were reflected in an upsurge of building activity, especially ecclesiastical buildings. While the construction of ecclesiastical and noble buildings culminated around the 1720s, rural buildings peaked in the 1780s and the 1820s. Although no direct effect of climate was demonstrated, adverse climatic conditions leading to harvest failures and subsequent famines (e.g. the ‘Hunger Years’ 1770–1772) significantly contributed to declines in building activity. In contrast, a higher number of felling dates were detected when strong and/or frequent windstorms occurred. This study provides a comprehensive understanding of building activity in Central Europe and advocates the use of dendrochronological databases for the investigation of human activities in history.