Normalization engine. More...

#include <stfinvnormalize.h>

Inheritance diagram for stfinv::STFEngineNormalize:

Collaboration diagram for stfinv::STFEngineNormalize:

[legend]

Public Types
typedef Tfftengine::TAseries	TAseries
	type of array for time series values More...

typedef Tfftengine::TAspectrum	TAspectrum
	type of array for Fourier transforms More...

typedef stfinv::STFFourierDomainEngine	Tbase
	typedef to refer to base class More...

typedef fourier::fft::DRFFTWAFFArrayEngine	Tfftengine
	type of underlying Fourier engine More...

Public Member Functions
	STFEngineNormalize (const stfinv::Tvectoroftriples &triples, const stfinv::Waveform &stf, const std::string &parameters)
	Constructor. More...

virtual	~STFEngineNormalize ()
	abstract base requires virtual destructor More...

virtual void	exec ()
	Start engine. More...

virtual void	help (std::ostream &os=std::cout) const
	print online help More...

virtual const char *	name () const
	return name of engine More...

virtual void	usage (std::ostream &os=std::cout) const
	print detailed description More...

Basic interface for users
See also Information for users of libstfinv (programmers)
stfinv::Waveform	run ()
	Start engine and return reference to source correction filter. More...

Shape query functions
unsigned int	nsamples () const
	return number of samples used in time series More...

unsigned int	nreceivers () const
	return number of receiver signals in use More...

unsigned int	npairs () const
	return number of additional signals to be convolved More...

double	dt () const
	return sampling interval More...

Data query functions
Tseries	stf () const
	return source correction filter series More...

Tseries::Tcoc	recording (const unsigned int &i) const
	return recorded data at receiver `i` More...

Tseries::Tcoc	synthetic (const unsigned int &i) const
	return synthetic data at receiver `i` More...

Tseries	convolvedsynthetic (const unsigned int &i) const
	return synthetic data convolved with stf at receiver `i` More...

Tseries::Tcoc	series (const unsigned int &i) const
	return synthetic data of pair `i` More...

Tseries	convolvedseries (const unsigned int &i) const
	return synthetic data convolved with stf for pair `i` More...

Static Public Member Functions
static void	classhelp (std::ostream &os=std::cout)
	print online help More...

static void	classusage (std::ostream &os=std::cout)
	print detailed description More...

Static Public Attributes
static const char *const	description ="Fourier domain normalization"
	short description of this engine More...

static const char *const	ID ="fdnorm"
	ID used to select thsi engine. More...

Protected Member Functions
Access and control functions to be used by derived classes.
These functions are part of the interface implemented in STFFourierDomainEngine.
void	fftinput ()
	copy input signals to workspace and transform input workspace to Fourier domain More...

void	fftoutput ()
	convolve synthetics with Fourier transform of stf and transform convolved synthetics and stf to time domain and pass signals to user memory space More...

TAspectrum	recordingspec () const
	return reference to Fourier transform of recorded data More...

TAspectrum	syntheticspec () const
	return reference to Fourier transform of synthetics More...

TAspectrum	stfspec () const
	return reference to Fourier transform of stf More...

TAspectrum	recordingcoeff (const unsigned int &i) const
	return reference to Fourier coeffients of recorded data for frequency i More...

TAspectrum	syntheticcoeff (const unsigned int &i) const
	return reference to Fourier coefficients of synthetics for frequency i More...

TAspectrum::Tvalue &	stfcoeff (const unsigned int &i) const
	return reference to Fourier coefficients of stf for frequency i More...

double	frequency (const unsigned int &i) const
	return value of frequency i in Hz More...

unsigned int	nfreq () const
	return number of frequencies in use More...

Functions presented to derived classes
std::string	parameter (const std::string &key, const std::string &defvalue="false") const
	return the value of a parameters More...

bool	parameterisset (const std::string &key) const
	check is parameter was set by user More...

void	checkreceiverindex (const unsigned int &i) const
	check for vaid receiver index More...

void	checkseriesindex (const unsigned int &i) const
	check for vaid index off additional time series pair More...

double	weight (const unsigned int &i) const
	return weight for signal at receiver i More...

aff::Series< double >	weights () const
	return weights array More...

Protected Attributes
int	Mdebug
	debug level More...

stfinv::Tvectorofpairs	Mpairs
	Waveform pairs. More...

stfinv::Waveform	Mstf
	source correction filter. More...

stfinv::Tvectoroftriples	Mtriples
	Waveform triples. More...

int	Mverbose
	verbose level More...

Private Member Functions
void	initialize ()
	initialize work space More...

Private Attributes
double	Mwaterlevel
	waterlevel More...

Detailed Description

Normalization engine.

Attention: This engine is not yet implemented. The concept of the approach is drafted in the comments to the class declaration. However this approach is under debate and might not even work properly. As long a stfinv::STFEngineNormalize is not made available through stfinv::STFEngine::initialize it must be regarded as a stub.

Motivation: On the down-side of Fourier domain least squares as is implemented in stfinv::STFEngineFDLeastSquares is the least squares approach. Least squares aims in minimizing the least squares misfit between recorded data and synthetics. In cases where it is difficult to minimize the misfit, e.g. when the wave propagation properties of the synthetics differ from those of the recorded data, the least squares misfit optimum might be a source correction filter equal zero. The current approach (stfinv::STFEngineNormalize) seeks a source correction filter such that the average energy as well as the average phase of data and synthetics equal. This is what you usually want in a early stage of inversion.

Concept of this algorithm

Consider that

$d_{lk}$ is the Fourier coefficient of recorded data at Frequency and receiver at offset and
$s_{lk}$ is the Fourier coefficient of the corresponding synthetics.

Then we seek a source correction filter with Fourier coefficients $q_l$ such that

$\sum\limits_{k}\left|d_{lk}\right|^2 = \sum\limits_{k}\left|s_{lk}\,q_l\right|^2 \quad\forall\, l$

and

$\sum\limits_{k}\Im(\ln(d_{lk})) = \sum\limits_{k}\Im(\ln(s_{lk}\,q_l)) \quad\forall\, l.$

Actually we will apply weights $w_k$ to data from different offsets $r_k$ such that

$\sum\limits_{k}\left|w_k\,d_{lk}\right|^2 = \sum\limits_{k}\left|w_k\,s_{lk}\,q_l\right|^2 \quad\forall\, l$

and

$\sum\limits_{k}w_k\,\Im(\ln(d_{lk})) = \sum\limits_{k}w_k\,\Im(\ln(s_{lk}\,q_l)) \quad\forall\, l.$

Additionally we will apply a waterlevel $\epsilon^2$ , such that Fourier coefficients for which the average weighted energy of the synthetics is smaller than a fraction $\epsilon^2$ of the total average energy of the synthetics, will be damped.

These conditions are satisfied by

$q_l=A_l\,e^{i\Phi_{l}}$

with

$A_l=\sqrt{\frac{\sum\limits_{k}\left|w_k\,d_{lk}\right|^2}{ \sum\limits_{k}\left|w_k\,s_{lk}\right|^{2} + \frac{\epsilon^2}{N_{f}}\,\sum\limits_{k}\sum\limits_{l=0}^{N_{f}-1} \left|w_k\,s_{lk}\right|^2}}$

and

$\Phi_{l}=\frac{\sum\limits_{k}w_{k}\left( \Im\left(\ln(d_{lk})\right)-\Im\left(\ln(s_{lk})\right) \right)}{\sum\limits_k w_{k}}$

Definition at line 134 of file stfinvnormalize.h.

The documentation for this class was generated from the following files:

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description